Journal articles: 'Shell vibration'

1

Zhao, Ming Hui. "Vibration Analysis of a Shell Structure by Finite Element Method." Advanced Materials Research 591-593 (November 2012): 1929–33. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.1929.

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Plate-shell structures, especially cylindrical shells and spherical shells, are widely used in engineering fields, such as aircraft and tanks, missiles, submarines, ships, hydraulic pumps, infusion pipelines and gas pipelines, and so on. These structures are usually in a fluid medium, which are related to the structure fluid-solid coupling and acoustic radiation field. As many experiments show that enclosed air in a thin walled structure, just like the violin, affects some modes of vibration significantly, air coupling between vibrating sides of the structure cannot be neglected. In order to explore the sound pressure distribution of vibrational frequencies, this paper, considering the material anisotropy, analyzes a typical complex shell structure of the violin by finite element method, including acoustic-structure coupling analysis and post-processing, especially sound pressure vibration frequency extraction. Finally, we get the conclusion that the distribution of sound pressure vibration frequency is similar to the normal distribution.

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SUN, YANG, and CHENG-LI WU. "MULTI-MAJOR-SHELL SHELL MODEL FOR HEAVY NUCLEI–AN EXTENDED PROJECTED SHELL MODEL." International Journal of Modern Physics E 17, supp01 (December 2008): 159–76. http://dx.doi.org/10.1142/s0218301308011835.

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The projected shell model (PSM) in its original version is an efficient shell model truncation scheme for well deformed nuclei. However, the model is applicable only to rotational motion, but not collective vibrations. In this paper, we discuss a scheme that extends the PSM applicability to low-lying rotational and vibrational states possibly in all kinds of heavy nuclei (from deformed via transitional to spherical), thus rendering it to be a more general multi-major-shell shell model for heavy nuclei. Three known types of vibration (β, γ, and scissors-mode) are discussed.

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Hambric, Stephen. "Practical Tutorial on cylindrical structure vibro-acoustics Part 1 - Vibrations." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 7 (February 1, 2023): 140–49. http://dx.doi.org/10.3397/in_2022_0026.

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The mathematics which describe the vibroacoustic behavior of cylindrical structures are imposing to say the least. Part 1 of this practical tutorial demystifies cylindrical shell vibration theory by using measured data from actual shells and pipes to explain key concepts. For any shell, you can estimate frequency ranges where shells behave like simple beams and flat plates, greatly simplifying calculations of modes of vibration and mobilities. The key is first calculating the ring frequency - the frequency where membrane waves can propagate fully around the shell circumference. Simple infinite structure theory may then be used to compute mean mobilities for beam, shell, and flat plate behavior. Modes of vibration for a cylinder depend on both longitudinal and circumferential harmonics, or a helical wavenumber. Cremer's simple approximate resonance frequency formula is used to show examples for a large diameter short shell and a small diameter long shell (a pipe). Finally, the measured modal densities of an elbowed pipe are compared to estimates from an empirical expression for modal density of a shell. In all cases in this tutorial, measurements and simple estimates agree well, showing that cylindrical shell vibrations may be estimated without difficult math or complex computer models.

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Amabili, M. "Flexural Vibration of Cylindrical Shells Partially Coupled With External and Internal Fluids." Journal of Vibration and Acoustics 119, no. 3 (July 1, 1997): 476–84. http://dx.doi.org/10.1115/1.2889748.

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In this paper, the free flexural vibrations of a partially fluid-loaded simply supported circular cylindrical shell are studied; the fluid is assumed to be inviscid and to present a free-surface parallel to the shell axis. The presence of external and internal fluids are both studied and the problem for incompressible and compressible fluid are both discussed by using the added virtual mass approach. Circumferential dependence of displacement is extended in a Fourier series. The maximum potential energy of the cylinder is evaluated using a sum of reference kinetic energies of the shell vibrating in vacuum; this fact allows the proposed method to be independent from the theory of shells used. Then, the Rayleigh quotient for fluid-shell coupled vibration is formulated and minimized to obtain the Galerkin equation whose solution gives the natural frequencies and mode shapes. Numerical computations are performed to obtain the modal characteristics as functions of the level of water in contact with the shell in the range of good accuracy of the theory, that is around the half-wet shell level. Results for both a shell partially surrounded and filled with water are obtained and compared.

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Pang, Fuzhen, Chuang Wu, Hongbao Song, and Haichao Li. "The free vibration characteristics of isotropic coupled conical-cylindrical shells based on the precise integration transfer matrix method." Curved and Layered Structures 4, no. 1 (November 27, 2017): 272–87. http://dx.doi.org/10.1515/cls-2017-0018.

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Abstract Based on the transfer matrix theory and precise integration method, the precise integration transfer matrix method (PITMM) is implemented to investigate the free vibration characteristics of isotropic coupled conicalcylindrical shells. The influence on the boundary conditions, the shell thickness and the semi-vertex conical angle on the vibration characteristics are discussed. Based on the Flügge thin shell theory and the transfer matrix method, the field transfer matrix of cylindrical and conical shells is obtained. Taking continuity conditions at the junction of the coupled conical-cylindrical shell into consideration, the field transfer matrix of the coupled shell is constructed. According to the boundary conditions at the ends of the coupled shell, the natural frequencies of the coupled shell are solved by the precise integration method. An approach for studying the free vibration characteristics of isotropic coupled conical-cylindrical shells is obtained. Comparison of the natural frequencies obtained using the present method with those from literature confirms the validity of the proposed approach. The effects of the boundary conditions, the shell thickness and the semivertex conical angle on vibration characteristics are presented.

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Grigorenko, A., M. Borysenko, and O. Boychuk. "Numerical analysis of free vibrations of open cylindrical shells with elliptical cross section." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 2 (2019): 52–59. http://dx.doi.org/10.17721/1812-5409.2019/2.5.

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The natural frequencies and the corresponding vibration modes of open cylindrical shells with an elliptical cross-section and variable thickness are analyzed. Various opening angle of the shell along both the minor and major axes are allowed and various boundary conditions are considered. The numerical solutions are obtained using the finite element package FEMAP with the NASTRAN solver. A number of lowfrequency vibrations are investigated in terms of their dependence on the opening angle along major and minor axes of the shell. The vibration forms for the first ten frequencies with different boundary conditions at the same opening angles are shown.

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Yu, Anbin, Yinglong Zhao, and Qeqing Jin. "Theoretical and experimental study on coupling characteristics of double-sided immersion cylindrical shells with arbitrary boundary." AIP Advances 12, no. 7 (July 1, 2022): 075320. http://dx.doi.org/10.1063/5.0090608.

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Based on the wave propagation method and improved Fourier series, the coupled vibration model of double-sided immersion (DI) cylindrical shell under arbitrary boundary conditions is established, and its coupled vibration characteristics are solved. The coupling vibration characteristic experiment of a cylindrical shell under the DI condition is carried out for the first time. The calculated natural frequency and vibration acceleration are compared with the model experimental results, which not only verifies the reliability of the theoretical method but also proves the effectiveness of the experimental results. Finally, the coupled vibration characteristics of DI cylindrical shells with arbitrary boundary conditions are analyzed. The results show that the natural frequency and acceleration of underwater immersed cylindrical shells are consistent with those of liquid filling cylindrical shells. The natural frequency and peak acceleration of the single-sided submerged cylindrical shell are greater than that of the DI cylindrical shell. The spring stiffness at both ends of the DI cylindrical shell can be divided into three sections: free boundary, elastic boundary, and rigid boundary.

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Yang, Zhong, and Jing Cao. "Vibration Reduction Analysis of Reticulated Shell." Advanced Materials Research 243-249 (May 2011): 1062–66. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.1062.

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Reticulated shell is one type of the common spatial structure form. This paper proposes a vibration reduction method by supplementing viscous dampers in the reticulated shell. It analyzes the seismic performance on the optimum partial double-layer reticulated shell with dampers by ANSYS soft, gains the stress in the members and the nodal displacements, and compares the dynamic responses between the normal and vibration reduction structure. By means of different parameters, the rules of vibration reduction effect in the reticulated shell with viscous dampers are acquired. It is shown through the calculation that the method developed in this paper is efficient for the dynamic analysis of the reticulated shells.

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Ghasemi, Ahmad Reza, and Masood Mohandes. "Free vibration analysis of rotating fiber–metal laminate circular cylindrical shells." Journal of Sandwich Structures & Materials 21, no. 3 (May 22, 2017): 1009–31. http://dx.doi.org/10.1177/1099636217706912.

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In this article, free vibration of rotating fiber–metal laminate thin circular cylindrical shells has been analyzed. Strain–displacement relations have been obtained based on Love’s first approximation shell theory. The variations of frequencies of the fiber–metal laminate cylindrical shell with rotational speeds for different axial and circumferential wave numbers, L/R ratios, metal thicknesses and volume fractions of metal have been presented. Also, free vibrations of the rotating fiber–metal laminate shell have been studied for carbon/epoxy, glass/epoxy and aramid/epoxy composite materials combining thin aluminum layers. The results showed that with increasing rotating speed, the gap between backward and forward waves frequencies increased.

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Brischetto, Salvatore. "Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels." Shock and Vibration 2014 (2014): 1–29. http://dx.doi.org/10.1155/2014/479738.

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The paper proposes a three-dimensional elastic analysis of the free vibration problem of one-layered spherical, cylindrical, and flat panels. The exact solution is developed for the differential equations of equilibrium written in orthogonal curvilinear coordinates for the free vibrations of simply supported structures. These equations consider an exact geometry for shells without simplifications. The main novelty is the possibility of a general formulation for different geometries. The equations written in general orthogonal curvilinear coordinates allow the analysis of spherical shell panels and they automatically degenerate into cylindrical shell panel, cylindrical closed shell, and plate cases. Results are proposed for isotropic and orthotropic structures. An exhaustive overview is given of the vibration modes for a number of thickness ratios, imposed wave numbers, geometries, embedded materials, and angles of orthotropy. These results can also be used as reference solutions to validate two-dimensional models for plates and shells in both analytical and numerical form (e.g., closed solutions, finite element method, differential quadrature method, and global collocation method).

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Anwar, Rabia, Madiha Ghamkhar, Muhammad Imran Khan, Rabia Safdar, Muhammad Zafar Iqbal, Wasim Jamshed, Esra Karatas Akgül, and M. Prakash. "Frequency Analysis for Functionally Graded Material Cylindrical Shells: A Significant Case Study." Mathematical Problems in Engineering 2021 (November 5, 2021): 1–10. http://dx.doi.org/10.1155/2021/4843321.

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Cylindrical shells play an important role for the construction of functionally graded materials (FGMs). Functionally graded materials are valuable in order to develop durable materials. They are made of two or more materials such as nickel, stainless steel, zirconia, and alumina. They are extremely beneficial for the manufacturing of structural elements. Functionally graded materials are broadly used in several fields such as chemistry, biomedicine, optics, and electronics. In the present research, vibrations of natural frequencies are investigated for different layered cylindrical shells, those constructed from FGMs. The behavior of shell vibration is based on different parameters of geometrical material. The problem of the shell is expressed from the constitutive relations of strain and stress with displacement, as well as it is adopted from Love’s shell theory. Vibrations of natural frequencies (NFs) are calculated for simply supported-simply supported (SS-SS) and clamped-free (C-F) edge conditions. The Rayleigh–Ritz technique is employed to obtain the shell frequency equation. The shell equation is solved by MATLAB software.

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12

XIANG, Y., C. W. LIM, and S. KITIPORNCHAI. "AXISYMMETRIC VIBRATION OF CYLINDRICAL SHELLS WITH INTERMEDIATE RING SUPPORTS." International Journal of Structural Stability and Dynamics 03, no. 01 (March 2003): 35–53. http://dx.doi.org/10.1142/s021945540300080x.

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This paper treats the axisymmetric vibration of thin circular cylindrical shells with intermediate ring supports based on the Goldenveizer–Novozhilov thin shell theory. An analytical method is proposed, and new exact solutions are presented to study the axisymmetric vibration characteristics of the ring supported cylindrical shells. In the proposed method, the state-space technique is employed to derive a homogenous differential equation system for a shell segment, and a domain decomposition approach is developed to cater for the continuity requirements between shell segments. Exact frequency parameters are presented for circular cylindrical shells that have multiple intermediate ring supports and various combinations of end support conditions. These exact vibration frequencies may serve as important benchmarks against which researchers can validate their numerical methods for such circular cylindrical shell problems.

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13

Sun, J. Q., M. A. Norris, D. J. Rossetti, and J. H. Highfill. "Distributed Piezoelectric Actuators for Shell Interior Noise Control." Journal of Vibration and Acoustics 118, no. 4 (October 1, 1996): 676–81. http://dx.doi.org/10.1115/1.2888351.

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Structural controls have been recently used to reduce acoustic radiation from vibrating structures. It is well known that in some cases, a control system can reduce the noise and, at the same time, increase the structural vibration. This is one of the concerns with the structural control approach to solve the noise problem. Developing a control system that can reduce the noise and structural vibration at the same time is an important task. This paper proposes one of possible approaches for accomplishing this task. The emphasis of the present approach is not on control strategies, but rather on the design of distributed piezoelectric actuators for the structural control system. In the paper, we study the interior noise radiation and the structural vibrations of uniform cylindrical shells, which are taken as a simplified model of a fuselage section. Two distributed piezoelectric actuators are developed based upon the understanding of the structural-acoustic coupling properties of the system. These actuators can reduce the shell structural vibration and the interior noise at the same time in a wide range of frequencies by using only the acoustic error sensors. Hence, an optimal noise reduction is achieved. Computer simulations and the experiments have shown that the actuators can lead to global noise and vibration reduction. Excellent agreement between the analytical predictions and the experiments strongly supports the theoretical development.

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14

Thangaratnam, Kari, and Evangeline Kumar. "Investigation on Application of Semiloof Shell Element for Isotropic, Composite and Functionally Graded Material." Applied Mechanics and Materials 877 (February 2018): 372–77. http://dx.doi.org/10.4028/www.scientific.net/amm.877.372.

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In this research article, semiloof shell element was used to study the behaviour of plate and shells under mechanical and thermal load for stress, free vibration, initially stressed vibration, mechanical buckling, and non-linear vibration. In the above cases, the material properties: Isotropic, Composite and Functionally Graded Material (FGM) were considered. Wherein, the material property for the FGM shells was assumed to vary through the thickness of the shell by varying the volume fraction of the constituent, whereas, for composites, classical laminated theory was used. Utilizing the semiloof shell element, and the above material properties, the package COMSAP was developed. From the obtained results, we have observed that with coarse meshes, semiloof shell elements present better results, and it is especially effective in the case of thin plates and shells.

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15

Kang, Jae-Hoon. "3D Vibration Analysis of Combined Shells of Revolution." International Journal of Structural Stability and Dynamics 19, no. 02 (February 2019): 1950005. http://dx.doi.org/10.1142/s0219455419500056.

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A three-dimensional (3D) method of analysis is presented for determining the natural frequencies and the mode shapes of combined hemispherical–cylindrical shells of revolution with and without a top opening by the Ritz method. Instead of mathematically two-dimensional (2D) conventional thin shell theories or higher-order thick shell theories, the present method is based upon the 3D dynamic equations of elasticity. Mathematically, minimal or orthonormal Legendre polynomials are used as admissible functions in place of ordinary simple algebraic polynomials which are usually applied in the Ritz method. The analysis is based upon the circular cylindrical coordinates instead of the shell coordinates which are normal and tangent to the shell mid-surface. Strain and kinetic energies of the combined shell of revolution with and without a top opening are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. Numerical results are presented for the combined shells of revolution with or without a top opening, which are completely free and fixed at the bottom of the combined shells. The frequencies from the present 3D Ritz method are compared with those from 2D thin shell theories by previous researchers. The present analysis is applicable to very thick shells as well as very thin shells.

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Sarkheil, Saeed, Mahmud S. Foumani, and Hossein M. Navazi. "Free vibration of bi-material cylindrical shells." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 15 (August 9, 2016): 2637–49. http://dx.doi.org/10.1177/0954406215602037.

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Based on the Sanders thin shell theory, this paper presents an exact solution for the vibration of circular cylindrical shell made of two different materials. The shell is sub-divided into two segments and the state-space technique is employed to derive the homogenous differential equations. Then continuity conditions are applied where the material of the cylindrical shell changes. Shells with various combinations of end boundary conditions are analyzed by the proposed method. Finally, solving different examples, the effect of geometric parameters as well as BCs on the vibration of the bi-material shell is studied.

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Qatu, Mohamad S. "Vibration of Homogeneous and Composite Thick Barrel Shells." Journal of Vibration and Control 10, no. 3 (March 2004): 319–41. http://dx.doi.org/10.1177/1077546304031845.

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This paper presents a vibration analysis for homogeneous and laminated composite deep, thick barrel shells using recently derived equations of elastic deformation. Assuming a first-order linear displacement field, the equations include accurate force and moment resultants, in which the stresses over the thickness of the shell are integrated exactly on a trapezoidal-like cross-section of a shell element. Exact solutions were obtained for thick barrel, open and closed, shells having shear diaphragm boundary conditions and cross-ply lamination sequence. The results were compared with previously obtained results where various other thick shell theories were used. The effects of various parameters including radii of curvature on shell frequencies are studied.

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Takayanagi, M. "Parametric Resonance of Liquid Storage Axisymmetric Shell Under Horizontal Excitation." Journal of Pressure Vessel Technology 113, no. 4 (November 1, 1991): 511–16. http://dx.doi.org/10.1115/1.2928788.

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A procedure for analyzing parametric resonance of liquid storage axisymmetric shells is proposed that is an extension of the procedure presented at PVP-89 for parametric resonance of empty axisymmetric shells with lumped weights. Free vibration modes of axisymmetric shells containing liquid are calculated considering the effect of initial stress due to static liquid pressure by using a conical shell finite element. The calculated free vibration modes are used to expand the free vibration modes of the axisymmetric shell with lumped weights and internal liquid. A type of Mathieu equation is derived considering the effects of the translational motion of the attached weight in the radial direction or the effects of the beam-type motion of the shell without lumped weight. The harmonic balance method is used to obtain the parametric resonance regions. Principal resonance of a circular cylindrical shell with an attached weight and combination resonance of a liquid storage circular cylindrical shell without attached weights are analyzed. Analytical results show good agreement with experimental results.

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Shingu, Kiyoshi, and Kiyotoshi Hiratsuka. "Dynamic Response of Base Isolated Rotational Shell with Edge Beam and Fuzzy Vibration Control of the Shell." International Journal of Space Structures 12, no. 3-4 (September 1997): 173–79. http://dx.doi.org/10.1177/026635119701200306.

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Seismic isolation and fuzzy vibration control systems, which consist of a shell with an edge beam which has springs and variable dampers between the edge beam and the ground, are suggested by one of the authors. In this paper, natural vibration modes and natural frequencies of base isolated rotational shells with edge beams are shown. When the shell shakes due to vertical seismic forces, the seismic isolated system is implemented. As a result, stresses in the shell are significantly reduced. Furthermore, vibration control of the shell is carried out. Then the damping ratios are adjusted by the fuzzy theory, and stresses in the shell are further reduced.

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Bich, Dao Huy, and Vu Do Long. "Non-linear vibration of eccentrically stiffened laminated composite shells." Vietnam Journal of Mechanics 30, no. 2 (July 1, 2008): 67–70. http://dx.doi.org/10.15625/0866-7136/30/2/5619.

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The present paper deals with a non-linear vibration of eccentrically stiffened laminated composite doubly curved shallow shells. The calculations of internal forces and displacements of the shell are based upon the thin shell theory considering the geometrical non-linearity and the Lekhnitsky's smeared stiffeners technique. From the deformation compatibility equation and the motion equation a system of partial differential equations for stress function and deflection of shell is obtained. The Bubnov-Galerkin's method and iterative procedure in conjunction with Newmark constant acceleration scheme are used for dynamical analysis of shells to give the frequency-amplitude relation of free nonlinear vibration and non-linear transient responses. Numerical results show the influence of boundary conditions and Gauss curvature on the non-linear vibration of shells.

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Li, H., and Z. B. Chen. "Torsional Sensors for Conical Shell in Torsional Vibrations." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 11 (March 19, 2010): 2382–89. http://dx.doi.org/10.1243/09544062jmes1940.

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This paper presents shear piezoelectric sensors for conical shell sensing. The piezoelectric patch is polarized in the longitudinal direction of conical shell structure. The electrodes are fixed at the sides parallel to the directions of polarization. Sensors in this arrangement are only sensitive to the in-plane shear strains. Both sensing equations and modal signals are derived based on the thin-shell assumption and piezoelectric effect. Numerical results are presented for free torsional vibrations of frustum shell of revolution with clamped-free boundary, and the effects of sensor length on the output are evaluated. The amplitudes of the output signal of the sensors are lower than that of modal ones, but they are all share the same trends. The amplitudes depend on the deformation of the shell and the length of the sensor. The results indicate the optimal locations of the piezoelectric sensor for sensing the torsional vibration of clamped-free shell. The output signals of the sensor can be used as the control input for later active vibration control. The sensing equations are applicable to sense shear strains and torsion of other type shells by replacing the strain equation.

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Sadygov, I. "FREE AND FORCED VIBRATIONS OF SHELLS OF VARIOUS SHAPES, TAKING INTO ACCOUNT THE VARIABILITY OF THE NON-LINEAR ELASTIC MATERIAL." Construction Materials and Products 3, no. 1 (July 8, 2020): 70–75. http://dx.doi.org/10.34031/2618-7183-2020-3-1-70-75.

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the article considers issues of shell vibrations, which are widely used in various industries and construction. Shells serve as elements of building structures with large spans. The chapter “Introduction” discussed issues related to the use of shells in all areas of industry, in aviation, rocket and space technology, railway transport, in the oil and gas industry and provides examples of shells for use in ceilings of circuses, stations, hangars; in industry: shells of rotation used as tanks, containers, columns, reactors, etc. In the section “Materials and research methods” free and forced vibrations of shells of variable thickness made out of nonlinear elastic material reviewed. In shell calculations the Kirchhoff – Law hypothesis was used. It was found that, during vibrations, the shells experience relative deformation of elongation and shear of the surface with coordinates (x, y), as well as bending and torsion strains. It is established that vibrations in the shells lead to a rotation of the main directions of elasticity and regarding to the adopted coordinate axis to angle θ, and the elastic constants of the material depend on the elastic constant Biy – the main directions of the nonlinear elastic shells. When solving the system of equations of motion of the shell relative to the displacements arising in it during vibration, based on theory R and various methods. The values of the dimensionless frequency parameter for a spherical shell taking into account changes in its curvature, variability and thickness of elastic properties are obtained.

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Zhang, Chao, De Jiang Shang, and Qi Li. "Effect of Drive Location on Vibro-Acoustic Characteristics of Submerged Double Cylindrical Shells with Damping Layers." Applied Mechanics and Materials 387 (August 2013): 59–63. http://dx.doi.org/10.4028/www.scientific.net/amm.387.59.

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Based on the modal superposition method, the analytical model of vibration and sound radiation from submerged double cylindrical shells with damping layers was presented. The shells were described by the classical thin shell theory. The damping layers were described by three-dimensional viscoelastic theory. The annular plates, connecting the double shells, were analyzed with in-plane motion theory. For different drive locations of radial point force on the inner shell, the sound radiated power and the radial quadratic velocity of the model were calculated and analyzed. The results show that making the drive location near the annular plate helps to reduce the sound radiated power and radial quadratic velocity of model, and making the drive location far from the middle of model also helps to reduce the sound radiated power. The drive applied on the location of annular plate causes high similarity of vibrations from inner shell and outer shell.

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Liu, Xiao Wan, and Bin Liang. "Effect of Ring Support Position and Geometrical Dimension on the Free Vibration of Ring-Stiffened Cylindrical Shells." Applied Mechanics and Materials 580-583 (July 2014): 2879–82. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.2879.

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Effect of ring support position and geometrical dimension on the free vibration of ring-stiffened cylindrical shells is studied in this paper. The study is carried out by using Sanders shell theory. Based on the Rayleigh-Ritz method, the shell eigenvalue governing equation is derived. The present analysis is validated by comparing results with those in the literature. The vibration characteristics are obtained investigating two different boundary conditions with simply supported-simply supported and clamped-free as the examples. Key Words: Ring-stiffened cylindrical shell; Free vibration; Rayleigh-Ritz method.

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Melaibari, Ammar, Ahmed Amine Daikh, Muhammad Basha, Ahmed Wagih, Ramzi Othman, Khalid H. Almitani, Mostafa A. Hamed, Alaa Abdelrahman, and Mohamed A. Eltaher. "A Dynamic Analysis of Randomly Oriented Functionally Graded Carbon Nanotubes/Fiber-Reinforced Composite Laminated Shells with Different Geometries." Mathematics 10, no. 3 (January 27, 2022): 408. http://dx.doi.org/10.3390/math10030408.

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The present study demonstrates the free vibration behavior of composite laminated shells reinforced by both randomly oriented single-walled carbon nanotubes (SWCNTs) and functionally graded fibers. The shell structures with different principal radii of curvature are considered, such as cylindrical, spherical, elliptical–paraboloid shell, hyperbolic–paraboloid shell, and plate. The volume fraction of the fibers has a linear variation along the shell thickness from layer to layer, while the volume fraction of CNTs is constant in all shell layers and uniformly distributed. The fiber-reinforced elements are distributed with three functions which are V-distribution, O-distribution, and X-distribution in addition to the uniform distribution. A numerical analysis was carried out systematically to validate the proposed solution. A new analytical solution is presented based on the Galerkin approach for shells and is exploited to illustrate the influence of some factors on the free vibration behavior of CNTs/fibe-reinforced composite (CNTs/F-RC) laminated shells, including the distributions and volume fractions, various boundary conditions, and geometrical properties of the reinforcement materials. The proposed solution is shown to be an effective theoretical tool to analyze the free vibration response of shells.

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Tzou, H. S., and J. P. Zhong. "Spatially Filtered Vibration Control of Cylindrical Shells." Shock and Vibration 3, no. 4 (1996): 269–78. http://dx.doi.org/10.1155/1996/456397.

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Distributed actuators offer spatially distributed actuations and they are usually effective to multiple modes of a continuum. Spatially filtered distributed vibration controls of a laminated cylindrical shell and a piezoelectric shell are investigated, and their control effectivenesses are evaluated in this study. In general, there are two control actions, the in-plane membrane control forces and the counteracting control moments, induced by the distributed actuator in the laminated shell. There is only an in-plane circumferential control force in the piezoelectric shell. Analyses suggest that in either case the control actions are effective in odd natural modes and ineffective in even modes. Spatially filtered control effectiveness and active damping of both shells are studied.

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BRISCHETTO, SALVATORE. "AN EXACT 3D SOLUTION FOR FREE VIBRATIONS OF MULTILAYERED CROSS-PLY COMPOSITE AND SANDWICH PLATES AND SHELLS." International Journal of Applied Mechanics 06, no. 06 (December 2014): 1450076. http://dx.doi.org/10.1142/s1758825114500768.

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A 3D free vibration analysis of multilayered structures is proposed. An exact solution is developed for the differential equations of equilibrium written in general orthogonal curvilinear coordinates. The equations consider a geometry for shells without simplifications and allow the analysis of spherical shell panels, cylindrical shell panels, cylindrical closed shells and plates. The method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structures. Results are given for multilayered composite and sandwich plates and shells. A free vibration analysis is proposed for a number of vibration modes, thickness ratios, imposed wave numbers, geometries and multilayer configurations embedding isotropic and orthotropic composite materials. These results can also be used as reference solutions for plate and shell 2D models developed for the analysis of multilayered structures.

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Monslin, Sugirtha Singh J., and Thangaratnam R. Kari. "Vibration of Initially Stressed Functionally Graded Material Plates and Shells." Applied Mechanics and Materials 684 (October 2014): 158–64. http://dx.doi.org/10.4028/www.scientific.net/amm.684.158.

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Finite element formulation using semiloof shell element for initially stressed vibration of Functionally Graded Material (FGM) plates and shells are presented. The influence of volume fraction index on the vibration frequencies of thin functionally graded plates and shells and variation of temperature on frequency are studied. New results are presented for initially stressed vibration of FGM plates and shells.

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Roberts, Louise, and Mark E. Laidre. "Get off my back: vibrational assessment of homeowner strength." Biology Letters 15, no. 4 (April 2019): 20180819. http://dx.doi.org/10.1098/rsbl.2018.0819.

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Animals may use a variety of sensory modalities to assess ownership and resource-holding potential (RHP). However, few studies have experimentally tested whether animals can assess these key variables through a purely vibrational modality, exclusively involving substrate-borne vibrations. Here we studied social terrestrial hermit crabs ( Coenobita compressus ), where competitors assess homeowners by climbing on top of a solid external structure—an architecturally remodelled shell home, inside of which the owner then produces vibrations. In the field, we used a miniature vibratory device, hidden within an empty shell, to experimentally simulate a ‘phantom owner’, with variable amplitudes of vibration representing different levels of homeowner strength. We found that assessors could use these vibrations to deduce the owner's RHP: for strong vibrations (indicative of a high RHP owner) assessors were least likely to escalate the conflict; for weak vibrations (indicative of a low RHP owner) assessors showed intermediate escalation; and in the absence of vibration (indicative of an extremely weak or absent owner) assessors were most likely to escalate. These results reveal that animals can assess homeowner strength based solely on substrate vibrations, thereby making important decisions about whether to escalate social conflicts over property.

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V. Naumenko, Yury, Vasyl I. Gnitko, and Elena A. Strelnikova. "Liquid Induced Vibrations of Truncated Elastic Conical Shells with Elastic and Rigid Bottoms." International Journal of Engineering & Technology 7, no. 2.23 (April 20, 2018): 335. http://dx.doi.org/10.14419/ijet.v7i2.23.15327.

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A method of estimating natural modes and frequencies of vibrations for elastic shells of revolution conveying a liquid is proposed. The vibration modes of the liquid-filled elastic shells are presented as linear combinations of their own vibration modes without liquid. The explicit expression for fluid pressure is defined using Bernoulli’s integral and potential theory suppositions. Non-penetration, kinematic, and dynamic boundary conditions are applied at the shell walls and on a free liquid surface, respectively. The solution of the hydro-elasticity problem is found out using an effective technique based on coupled finite and boundary element methods. Computational vibration analysis of elastic truncated conical shells with different fixation conditions is accomplished. Sloshing and elastic walls frequencies and modes of liquid-filled truncated conical tanks are estimated. Both rigid and elastic bottoms of shells are considered. Some examples of numerical estimations are provided to testify the efficiency of the developed method

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Liu, Jingxi, Wentao He, and De Xie. "Study on Vibrational Power Flow Propagation Characteristics in a Laminated Composite Cylindrical Shell Filled with Fluid." Shock and Vibration 2018 (June 25, 2018): 1–19. http://dx.doi.org/10.1155/2018/4026140.

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The characteristics of vibrational power flow in an infinite laminated composite cylindrical shell filled with fluid excited by a circumferential line cosine harmonic force are investigated using wave propagation approach. The harmonic motions of the shell and the fluid filled in the shell are described by Love shell theory and acoustic wave equation, respectively. Under the driving force, the vibrational power flow input into the coupled system and the transmission of the power flow carried by different internal forces (moments) of the shell in the axial direction are established. Numerical computations are implemented to investigate the vibrational power flow input and its propagation. It is found that characteristics of the vibrational power flow vary with different circumferential mode orders and frequencies, and the presence of fluid in the shell significantly affects the vibration of the shell structure. Additionally, parametric investigations are carried out to study the effects of the fiber orientation, modulus ratio E11/E22, and thickness-to-radius parameter h/R on input power into the coupled system and propagation power along the shell axial direction. This work will provide some guidance for the vibration control of the laminated composite cylindrical shell.

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YAN, Y., W. Q. WANG, and L. X. ZHANG. "NONLINEAR VIBRATION CHARACTERISTICS OF FLUID-FILLED DOUBLE-WALLED CARBON NANOTUBES." Modern Physics Letters B 23, no. 22 (August 30, 2009): 2625–36. http://dx.doi.org/10.1142/s0217984909020746.

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Nonlinear vibration behaviors of double-walled carbon nanotubes (DWCNTs) with fluid inside the inner tube are investigated based on Donnell's cylindrical shell model and the more refined van der Waals (vdW) interaction formula. The Galerkin method and harmonic balance method are used to study the issue. The results obtained show that the radial vibrational modes of simply supported DWCNTs have twice the dynamical mode transitions as the frequency increases. The transitions correspond to twice the noncoaxial vibrations which play a critical role in electronic and transport properties of CNTs. Moreover, comparisons of the dynamical behaviors of fluid-filled DWCNTs with different wave numbers, radii and aspect ratios demonstrate that the amplitude–frequency curve topological forms are identical. Meanwhile, it is also concluded that the existence of fluid is significant for the value of amplitude ratio corresponding to noncoaxial vibration whereas it does not change the nonlinear vibrating topological pattern of amplitude–frequency curves.

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Bich, Dao Huy, and Le Kha Hoa. "Non-linear vibration of functionally graded shallow spherical shells." Vietnam Journal of Mechanics 32, no. 4 (December 22, 2010): 199–210. http://dx.doi.org/10.15625/0866-7136/32/4/289.

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The present paper deals with the non-linear vibration of functionally graded shallow spherical shells. The properties of shell material are graded in the thickness direction according to the power law distribution in terms of volume fractions of the material constituents. In the derived governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. From the deformation compatibility equation and the motion equation a system of partial differential equations for stress function and deflection of shell is obtained. The Galerkin method and Runge-Kutta method are used for dynamical analysis of shells to give expressions of natural frequencies and non-linear dynamic responses. Numerical results show the essential influence of characteristics of functionally graded materials and dimension ratios on the dynamical behaviors of shells.

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Khatri, K. N. "Vibration Control of Conical Shells Using Viscoelastic Materials." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 206, no. 3 (May 1992): 167–78. http://dx.doi.org/10.1243/pime_proc_1992_206_113_02.

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The vibration and damping analysis of multi-layered conical shells incorporating layers of viscoelastic materials in addition to elastic ones, the former causing dissipation of vibratory energy, is the subject matter of this paper. The analysis given herein uses Hamilton's variational principle for deriving equations of motion of a general multi-layered conical shell. In view of the correspondence principle of linear viscoelasticity which is valid for harmonic vibrations, the solution is obtained by replacing the moduli of viscoelastic layers by complex moduli. An approximate solution for axisymmetric vibrations of multi-layered conical shells with two end conditions—simply supported edges and clamped edges—is obtained by utilizing the Galerkin procedure. The damping effectiveness in terms of the system loss factor for all families of modes of vibrations for three-, five- and seven-layered shells is evaluated and its variation with geometrical parameters is investigated.

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Sysoev, E. O., A. Yu Dobryshkin, E. O. Volik, and O. E. Pushkareva. "Influence of the Multilayer Nature of Reinforcement of Open Thin-Walled Cylindrical Carbon Shells on Their Natural Vibrations." IOP Conference Series: Earth and Environmental Science 988, no. 5 (February 1, 2022): 052067. http://dx.doi.org/10.1088/1755-1315/988/5/052067.

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Abstract In the near future, mega-long-span structures will be required for creating stable microclimate over large areas, regardless of the natural conditions, for comfortable living of people. Thin-walled shell structures made of carbon materials with high strength properties are best suited for this purpose. The problem with thin-walled shells resides in vibrations caused by the action of external forces, which can lead to structural failure. The paper presents and experimental study of influence of the multilayer nature of reinforcement of open thin-walled cylindrical carbon shells on their natural vibrations. Experimental data have been compared to the theoretical calculations of open thin-walled cylindrical shell vibrations taking into account the frequency spectrum splitting. It has been found that with the increase in the number of carbon fabric reinforcement layers, vibration frequency deviation in open thin-walled cylindrical carbon shells increases at the initial stage as compared to the analytic model.

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Dyachenko, I. A., and A. A. Mironov. "ANALYTICAL AND NUMERICAL STUDIES OF FREE VIBRATIONS OF CYLINDRICAL SHELL WITH ACOUSTIC MEDIUM." Problems of strenght and plasticity 83, no. 1 (2021): 35–48. http://dx.doi.org/10.32326/1814-9146-2021-83-1-35-48.

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The research materials are related to the problem of ensuring vibration resistance of pipelines exposed to dynamic loads, for which increased vibration is the main cause of damage. The solution to this problem involves studying the parameters of free vibrations of the structure. The paper solves the problem of determining the natural frequencies and forms of vibrations of a section of a circular cylindrical shell filled with an medium considered in the acoustic approximation. The results of studies of the parameters of free vibrations were obtained both by the analytical method of shell theory based on the Kirchhoff-Love hypotheses, and using the finite element complex of engineering analysis ANSYS. It is shown that the influence of the medium density on the parameters of free vibrations of the shell depends on the ratio of the shell thickness to its radius it turns out to be significant only for the shape of vibrations associated with bending deformation, and insignificant for forms associated with deformations of the middle layer. A comparative analysis of the results of calculations obtained for models of compressible and incompressible medium shows that when solving the problem of determining the parameters of free vibrations of the shell, the compressibility of the medium can be neglected. At the same time, to solve practical problems that require taking into account the full spectrum of natural frequencies of the shell–medium system, a compressible medium model should be used, in which the results on the effect of shell stiffness on the frequency spectrum of the medium volume are obtained. When solving practical problems of pipeline systems vibration, the use of the finite element method in a coupled formulation is an effective tool that allows us to consider all physical processes taking into account their mutual influence on each other.

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Sun, Longfei, Weijia Li, Yaozhong Wu, and Qiuhua Lan. "Active vibration control of a conical shell using piezoelectric ceramics." Journal of Low Frequency Noise, Vibration and Active Control 36, no. 4 (December 2017): 366–75. http://dx.doi.org/10.1177/1461348417744304.

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Conical shell structures are commonly used in many engineering systems, and vibration suppression is very important to realize the desired function. In this study, piezoelectric ceramics were used as actuators/sensors with a multimodal fuzzy sliding mode controller to suppress vibrations of conical shell structure for the first time. The structure’s natural frequencies and mode shapes were obtained through modal analysis using finite element method and verified by modal tests. The agreement between analysis and test results verified the finite element method was appropriate. A multimodal fuzzy sliding mode controller was subsequently designed based on the analysis to provide active vibration control. The resulting controller was tested experimentally for the conical shell structure. The experimental results indicated that the proposed controller can effectively use to suppress vibration for the conical shell structure.

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Dai, Lu, Tie Jun Yang, Yao Sun, and Ji Xin Liu. "Influence of Boundary Conditions on the Active Control of Vibration and Sound Radiation for a Circular Cylindrical Shell." Applied Mechanics and Materials 66-68 (July 2011): 1270–77. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.1270.

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Vibration and acoustic radiation of circular cylindrical shells are hot topics in the structural engineering field. However for a long period, this sort of problems is only limit to classical homogeneous boundary conditions. In this paper, the vibration of a circular cylindrical shell with elastic boundary supports is studied using modified Fourier series method, and the far-field pressure for a baffled shell is calculated by Helmholtz integral equation. Active control of vibration and acoustic radiation are carried out by minimizing structural kinetic energy and radiated acoustic power respectively. The influence of boundary conditions on the active control is investigated throughout several numerical examples. It is shown that the active control of vibration and acoustic for an elastically restrained shell can exhibit unexpected and complicated behaviors.

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Oh, J., M. Ruzzene, and A. Baz. "Passive Control of the Vibration and Sound Radiation from Submerged Shells." Journal of Vibration and Control 8, no. 4 (April 2002): 425–45. http://dx.doi.org/10.1177/107754602023689.

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Vibration and noise radiation from fluid-loaded cylindrical shells are controlled using multiple stiffeners and Passive Constrained Layer Damping treatment. Dynamic and fluid finite element models are developed to study the fundamental phenomena governing the interaction between the stiffened shell, with and without damping, and the fluid domain surrounding it. The models are used to predict the response of the shell and to evaluate the effect of the stiffening rings and damping treatment on both the structural vibration and noise radiation in the fluid domain. The prediction of the models are validated experimentally and against the predictions of a commercial FE software package (ANSYS). It is shown that stiffening of the shell reduces the amplitude of the vibration and noise radiation, particularly for high order lobar modes. The attenuation of the shell response and sound radiation can be significantly increased through the application of Passive Constrained Layer Damping treatment on the inner surface of the stiffening rings. The numerical and experimental validations demonstrate the accuracy of the developed models and emphasize its potential extension to the application of smart materials for active control of vibration and noise radiation from fluid-loaded shells.

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Ko, Soo-Min, and Jae-Hoon Kang. "Vibration of Hemispherical-Cylindrical-Hemispherical Shells and Complete Hollow Spherical Shells with Variable Thickness." International Journal of Structural Stability and Dynamics 19, no. 03 (March 2019): 1950018. http://dx.doi.org/10.1142/s0219455419500184.

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The natural frequencies and mode shapes of enclosed shell typed structures with variable thickness (hemispherical-cylindrical-hemispherical shells and complete hollow spherical shells) are determined by the Ritz method using a three-dimensional (3D) analysis. However, in the conventional shell analysis, mathematically two-dimensional (2D) thin shell theories or higher order thick shell theories are often employed, which adopt limiting assumptions about the displacement variation through the shell thickness. While most researchers have adopted the 3D shell coordinates that are normal and tangential to the shell mid-surface, the present analysis is based upon the circular cylindrical coordinates. By the Ritz method, the Legendre polynomials, which are mathematically orthonormal and minimal, are used as the admissible functions, instead of the ordinary algebraic polynomials. The strain and kinetic energies of the combined shell structures are formulated, and upper bound solutions of the frequencies are obtained by minimizing the solution for frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. The frequencies from the present 3D method are compared with those from other 3D approach and 2D thin and thick shell theories existing in the literature. The present 3D analysis is applicable to both very thick shells and very thin shells.

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Narita, Yoshihiro. "Accurate Results for Free Vibration of Doubly Curved Shallow Shells of Rectangular Planform (Part.2 Thickness effect)." EPI International Journal of Engineering 4, no. 2 (August 30, 2021): 204–11. http://dx.doi.org/10.25042/10.25042/epi-ije.082021.13.

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This paper presents a follow-up study of a previous work that deals with the free vibration of moderately thin isotropic shallow shells under general edge conditions. The same semi-analytical method is used in this study for identical shape and degree of curvature in doubly curved geometry, and accurate natural frequencies are tabulated for a wide range of the shell edge conditions. Emphasis is made, however, to present the frequency parameters for the shallow shells with very thin thickness (representative length/shell thickness=100). In numerical experiments, convergence test is made against series terms in the case of very thin shallow shells. Twenty-one sets of frequency parameters are tabulated for three shell shapes (spherical, cylindrical and hyperbolic paraboloidal shells) and two curvature ratios. These two papers (Part.1 and 2) will constitute the accurate standard in the area of shallow shell vibration of rectangular planform and serve for future comparison and practical design purpose.

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Vinh, Le Quang, and Nguyen Manh Cuong. "Dynamic analysis of FG stepped truncated conical shells surrounded by Pasternak elastic foundations." Vietnam Journal of Mechanics 42, no. 2 (June 29, 2020): 133–52. http://dx.doi.org/10.15625/0866-7136/14749.

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This research presents a continuous element model for solving vibration problems of FG stepped truncated conical shells having various material properties and surrounded by Pasternak foundations. Based on the First Order Shear Deformation Theory (FSDT) and the equations of the FGM conical shells, the dynamic stiffness matrix is obtained for each segment of the shell having constant thickness. The interesting assembly procedure of continuous element method (CEM) is employed for joining those segments in order to analyze the dynamic behavior of the FG stepped truncated conical shells an assembly procedure of continuous element method (CEM) is employed for joining those segments. Free vibrations of different configurations of FG stepped truncated conical shells on elastic foundations are examined. Effects of structural parameters, stepped thickness and elastic foundations on the free vibration of FG stepped truncated conical shells are also presented.

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Xuebin, Li, and Chen Yaju. "Free Vibration Analysis of Orthotropic Circular Cylindrical Shell Under External Hydrostatic Pressure." Journal of Ship Research 46, no. 03 (September 1, 2002): 201–7. http://dx.doi.org/10.5957/jsr.2002.46.3.201.

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An analysis is presented for the free vibration of an orthotropic circular cylindrical shell subjected to hydrostatic pressure. Based on Flügge shell theory, the equations of free vibrations of an orthotropic circular cylindrical shell under hydrostatic pressure are obtained. For shear diaphragms at both ends, the resulting characteristic equations about pressure and frequency are given. These two parameters are calculated exactly. The effect of the shell's parameters (L/R, h/R) and material properties on the free vibration characteristics are studied in detail. Differences between Love-Timoshenko, Donnell equations and that of the Flügge theory are examined as well.

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Yusefzad, Mahdi, and Firouz Bakhtiari Nejad. "A Study on the Free Vibration of the Prestressed Joined Cylindricalspherical Shell Structures." Applied Mechanics and Materials 390 (August 2013): 207–14. http://dx.doi.org/10.4028/www.scientific.net/amm.390.207.

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The free vibration characteristics of the prestressed joined spherical–cylindrical shell with free-free boundary conditions are investigated. The Flügge shell theory and Rayleigh-Ritz energy method are applied in order to analyze the free vibration characteristics of the joined shell. In the modal test, the LMS software is used to calculate mode shapes and natural frequencies of the joined shell structure. The natural frequencies and mode shapes are calculated numerically and they are compared with those of the FEM and modal test to confirm the reliability of the analytical solution. The effects of the shallowness and length of the cylindrical shell to the free vibrational behavior of joined shell structure and the effect of internal pressure on the modal charactristics are investigated.

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Xia, Qi Qiang, Zhi Jian Chen, Jie Gong, and Li Jun Zhang. "Research on Metal-Rubber Composite Damping Steel Plate Application in Acoustic Bridge for Double Cylindrical Shell." Advanced Materials Research 490-495 (March 2012): 3505–10. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.3505.

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In order to reduce the low-frequency line spectrum of double cylindrical shell, the research was done to apply composite damping steel plate in acoustic bridge between two shells. By suppressing vibration energy transmission along acoustic bridge, two types of composite damping rib-plate were designed with the resistance increasing technology based on the principle of damping vibration attenuation. Then the vibro-acoustic characteristics of double cylindrical shell were analyzed through numerical calculations, considering original and improved acoustic bridge. The results shows that: composite damping steel plate applying in acoustic bridge can reduce sound radiation of double cylindrical shell effectively, properly increasing damping between composite plates is beneficial for vibration and noise reduction. These research results could be a reference for submarine acoustic stealth design.

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Dong, Ting, Xinhua Chen, and Jun Zhang. "Study on Dynamic Snap-Through and Nonlinear Vibrations of an Energy Harvester Based on an Asymmetric Bistable Composite Laminated Shell." Symmetry 13, no. 12 (December 13, 2021): 2405. http://dx.doi.org/10.3390/sym13122405.

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Bistable energy harvesters have been extensively studied. However, theoretical research on the dynamics of bistable energy harvesters based on asymmetric bistable composite laminated plate and shell structures has not been conducted. In this paper, a theoretical model on the dynamics of an energy harvester based on an asymmetric bistable composite laminated shell is established. The dynamic snap-through, the nonlinear vibrations and the voltage output with two potential wells of the bistable energy harvester are studied. The influence of the amplitude and the frequency for the base excitation on the bistable energy harvester is studied. When the frequency for the base excitation with a suitable amplitude in the frequency sweeping is located in a specific range or the amplitude for the base excitation with a suitable frequency in the amplitude sweeping is located in a specific range, the large-amplitude dynamic snap-through, nonlinear vibrations and voltage output with two potential wells can be found to occur. The amplitude and the frequency for the base excitation interact on each other for the specific amplitude or frequency range which migrates due to the softening nonlinearity. The vibration in the process of the dynamic snap-through behaves as the chaotic vibration. The nonlinear vibrations of the bistable system behave as the periodic vibration, the quasi-periodic vibration and the chaotic vibration. This study provides a theoretical reference for the design of energy harvesters based on asymmetric bistable composite laminated plate and shell structures.

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Parmar, Vikram, Najeeb ur Rahman, Naushad Alam, Varun Sharma, and Aftab Alam. "Finite Element Modelling for Bending and Vibration Analysis of Composite and Sandwich Spherical Shells." IOP Conference Series: Materials Science and Engineering 1225, no. 1 (February 1, 2022): 012037. http://dx.doi.org/10.1088/1757-899x/1225/1/012037.

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Abstract Finite element modelling is used to illustrate the bending and vibration response of composite and sandwich spherical shells. ABAQUS is used to model the shell as a three-dimensional deformable solid part. Composites are modelled using mixed modelling technique. The quadrilateral continuum shell element, which has eight nodes, is used for finite element meshing. For a three-layered composite spherical shell with simply supported boundary conditions, the accuracy of the employed element is first evaluated. After that, three potential end conditions are evaluated for further analysis: cantilever (CFFF), two opposing sides clamped (CFCF), and all sides clamped (CCCC). Bending response is produced by applying two types of pressure loads to the exterior surfaces of composite and sandwich spherical shells: uniformly distributed load (UDL) and sinusoidal load (SINO). For various span to thickness ratios, free vibration response and forced vibration response (Time History) are provided under step pressure (UDL and SINO) loading. The element type being used is found to be quite precise and sturdy.

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Shi, Hui, Teijun Yang, Shiliang Jiang, W. L. Li, and Zhigang Liu. "Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints." Shock and Vibration 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/435903.

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Effects of curvature upon the vibration characteristics of doubly curved shallow shells are assessed in this paper. Boundary conditions of the shell are generally specified in terms of distributed elastic restraints along the edges. The classical homogeneous boundary supports can be easily simulated by setting the stiffnesses of restraining springs to either zero or infinite. Vibration problems of the shell are solved by a modified Fourier series method that each of the displacements is invariably expressed as a simple trigonometric series which converges uniformly and acceleratedly over the solution domain. All the unknown expansion coefficients are treated equally as a set of independent generalized coordinates and solved using the Rayleigh-Ritz technique. The current method provides a unified solution to the vibration problems of curved shallow shells involving different geometric properties and boundary conditions with no need of modifying the formulations and solution procedures. Extensive tabular and graphical results are presented to show the curvature effects on the natural frequencies of the shell with various boundary conditions.

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Mohandes, Masood, Ahmad Reza Ghasemi, Mohsen Irani-Rahagi, Keivan Torabi, and Fathollah Taheri-Behrooz. "Development of beam modal function for free vibration analysis of FML circular cylindrical shells." Journal of Vibration and Control 24, no. 14 (March 21, 2017): 3026–35. http://dx.doi.org/10.1177/1077546317698619.

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The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable.

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Roots, Larissa. "Non-Axisymmetric Vibrations of Stepped Cylindrical Shells Containing Cracks." Advanced Materials Research 934 (May 2014): 136–42. http://dx.doi.org/10.4028/www.scientific.net/amr.934.136.

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Based on the Donnell’s approximations of the thin shell theory, this paper presents solutions for the problem of free non-axisymmetric vibration of stepped circular cylindrical shells with cracks. The shell under consideration is sub-divided into multiple segments separated by the locations of thickness variations. It is assumed that at thejth step there exists a circumferential surface crack with uniform depthcj. The influence of circular cracks with constant depth on the vibration of the shell is prescribed with the aid of a matrix of local flexibility. The latter is related to the coefficient of the stress intensity known in the linear fracture mechanics. Numerical results are obtained for cylindrical shells of stepped thickness containing cracks at re-entrant corners of steps. Shells with various combinations of boundary conditions can be analyzed by the proposed method. Furthermore, the influences of the shell thicknesses, locations of step-wise variations of the thickness and other parameters on the natural frequencies are examined. The results can be used for the approximate evaluation of dynamic parameters of cylindrical shells with cracks and flaws.

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Journal articles on the topic 'Shell vibration'

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