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Journal articles on the topic 'Higher-order beam theory'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Bhimaraddi, A., and K. Chandrashekhara. "Observations on Higher‐Order Beam Theory." Journal of Aerospace Engineering 6, no. 4 (October 1993): 408–13. http://dx.doi.org/10.1061/(asce)0893-1321(1993)6:4(408).

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2

Senjanović, Ivo, and Ying Fan. "A higher-order flexural beam theory." Computers & Structures 32, no. 5 (January 1989): 973–86. http://dx.doi.org/10.1016/0045-7949(89)90400-8.

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3

Widera, G. E. O., and W. C. Zheng. "New Higher Order Engineering Beam Theory." Journal of Pressure Vessel Technology 115, no. 3 (August 1, 1993): 325–27. http://dx.doi.org/10.1115/1.2929535.

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A refined engineering theory for beams is presented. It contains higher order effects not present in such refined theories as the one by Timoshenko. A comparison with the latter theory is carried out.

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4

Nolde, E., A. V. Pichugin, and J. Kaplunov. "An asymptotic higher-order theory for rectangular beams." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2214 (June 2018): 20180001. http://dx.doi.org/10.1098/rspa.2018.0001.

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A direct asymptotic integration of the full three-dimensional problem of elasticity is employed to derive a consistent governing equation for a beam with the rectangular cross section. The governing equation is consistent in the sense that it has the same long-wave low-frequency behaviour as the exact solution of the original three-dimensional problem. Performance of the new beam equation is illustrated by comparing its predictions against the results of direct finite-element computations. Limiting behaviours for beams with large (and small) aspect ratios, which can be established using classical plate theories, are recovered from the new governing equation to illustrate its consistency and also to illustrate the importance of using plate theories with the correctly refined boundary conditions. The implications for the correct choice of the shear correction factor in Timoshenko's beam theory are also discussed.

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5

Levinson, Mark. "On Bickford's consistent higher order beam theory." Mechanics Research Communications 12, no. 1 (January 1985): 1–9. http://dx.doi.org/10.1016/0093-6413(85)90027-8.

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6

Lim, Jae Kyoo, and Seok Yoon Han. "Development of Orthotropic Beam Element Using a Consistent Higher Order Deformation Theory." Key Engineering Materials 261-263 (April 2004): 519–24. http://dx.doi.org/10.4028/www.scientific.net/kem.261-263.519.

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In order to analyze beam structures more accurately and effectively, a two-node orthotropic beam element is proposed. This beam element is formulated using a consistent higher order deformation theory of orthotropic beams of which the transverse normal deformation can be effectively estimated. The stiffness matrix and the vector of equivalent nodal forces of the beam element are derived explicitly by the Galerkin method. In order to examine the reliability and the characteristics of the beam element, the analytical and the finite element solutions of a simple cantilevered beam are compared with each other. As a result, the following conclusions are obtained; (1) the accuracy of the suggested orthotropic beam element is very excellent and so the transverse normal deformation and shear stress of an orthotropic beam can be effectively estimated. (2) It can be used for accurately analyzing the general beam structures regardless of the Euler's or the Timoshenko's beam.

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7

Narkhede, Kundan M., and Appaso M. Gadade. "Response of Composite Laminate Beam Using Higher Order Beam Theory." Journal of Physics: Conference Series 1240 (July 2019): 012005. http://dx.doi.org/10.1088/1742-6596/1240/1/012005.

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8

McCarthy, Thomas R., and Aditi Chattopadhyay. "A refined higher-order composite box beam theory." Composites Part B: Engineering 28, no. 5-6 (January 1997): 523–34. http://dx.doi.org/10.1016/s1359-8368(96)00053-4.

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9

Sapountzakis, Evangelos, and Amalia Argyridi. "Influence of in-Plane Deformation in Higher Order Beam Theories." Strojnícky casopis – Journal of Mechanical Engineering 68, no. 3 (November 1, 2018): 77–94. http://dx.doi.org/10.2478/scjme-2018-0028.

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AbstractComparing Euler-Bernoulli or Tismoshenko beam theory to higher order beam theories, an essential difference can be depicted: the additional degrees of freedom accounting for out-of plane (warping) and in-plane (distortional) phenomena leading to the appearance of respective higher order geometric constants. In this paper, after briefly overviewing literature of the major beam theories taking account warping and distortional deformation, the influence of distortion in the response of beams evaluated by higher order beam theories is examined via a numerical example of buckling drawn from the literature.

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10

Argyridi, Amalia K., and Evangelos J. Sapountzakis. "Higher order beam theory for linear local buckling analysis." Engineering Structures 177 (December 2018): 770–84. http://dx.doi.org/10.1016/j.engstruct.2018.08.069.

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11

Corre, Grégoire, Arthur Lebée, Karam Sab, Mohammed Khalil Ferradi, and Xavier Cespedes. "Higher-order beam model with eigenstrains: theory and illustrations." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 98, no. 7 (March 5, 2018): 1040–65. http://dx.doi.org/10.1002/zamm.201700180.

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12

Usuki, Tsuneo, and Aritake Maki. "Behavior of beams under transverse impact according to higher-order beam theory." International Journal of Solids and Structures 40, no. 13-14 (June 2003): 3737–85. http://dx.doi.org/10.1016/s0020-7683(03)00142-2.

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13

KATORI, Hiroaki, and Masaki MAEDA. "Beam Element Based on a Higher-Order Shear Deformation Theory." Transactions of the Japan Society of Mechanical Engineers Series A 69, no. 685 (2003): 1374–79. http://dx.doi.org/10.1299/kikaia.69.1374.

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14

Marur, S. R., and T. Kant. "A Higher Order Finite Element Model for the Vibration Analysis of Laminated Beams." Journal of Vibration and Acoustics 120, no. 3 (July 1, 1998): 822–24. http://dx.doi.org/10.1115/1.2893903.

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A higher order displacement model based on a cubic axial strain, cubic transverse shear strain and quadratic transverse normal strain across the thickness of the beam, to model exactly the warping of the cross section is proposed which maintains zero stress at the top and bottom of the beam with out the aid of any shear correction factor. Numerical experiments carried out clearly bring out the efficacy of this model over the first order theory for laminated beams.

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15

Shabanlou, Gh, S. A. A. Hosseini, and M. Zamanian. "Free Vibration Analysis of Spinning Beams Using Higher-Order Shear Deformation Beam Theory." Iranian Journal of Science and Technology, Transactions of Mechanical Engineering 42, no. 4 (July 21, 2017): 363–82. http://dx.doi.org/10.1007/s40997-017-0104-2.

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16

Shi, G., and K. Y. Lam. "FINITE ELEMENT VIBRATION ANALYSIS OF COMPOSITE BEAMS BASED ON HIGHER-ORDER BEAM THEORY." Journal of Sound and Vibration 219, no. 4 (January 1999): 707–21. http://dx.doi.org/10.1006/jsvi.1998.1903.

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17

Pölöskei, Tamás, and András Szekrényes. "Dynamic Stability of a Structurally Damped Delaminated Beam Using Higher Order Theory." Mathematical Problems in Engineering 2018 (June 6, 2018): 1–15. http://dx.doi.org/10.1155/2018/2674813.

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The static and dynamic stability of the composite beam with a single delamination are investigated using the Timoshenko beam theory. The mechanical model is discretized using the finite element method and the equation of motion is obtained using Hamilton’s principle. The coefficients of the mass and stiffness matrix for the damping matrix are determined using experimental modal analysis. The effect of harmonic excitation on the dynamic stability of a single delaminated composite beam is investigated using Bolotin’s harmonic balance method. The stability boundaries of the damped and undamped system are compared for different static load values and delamination lengths on the excitation frequency-excitation force amplitude parameter field.

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18

VALLALA, V. P., G. S. PAYETTE, and J. N. REDDY. "A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY." International Journal of Applied Mechanics 04, no. 01 (March 2012): 1250010. http://dx.doi.org/10.1142/s1758825112001397.

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In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic beams is presented. The principle of virtual work is utilized in conjunction with the third-order beam theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order beam theory admits C0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the beam may undergo von Kármán nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.

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19

Thom, Tran Thi, and Nguyen Dinh Kien. "FREE VIBRATION OF TWO-DIRECTIONAL FGM BEAMS USING A HIGHER-ORDER TIMOSHENKO BEAM ELEMENT." Vietnam Journal of Science and Technology 56, no. 3 (June 11, 2018): 380. http://dx.doi.org/10.15625/2525-2518/56/3/10754.

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Free vibration of two-directional functionally graded material (2-D FGM) beams is studied by the finite element method (FEM). The material properties are assumed to be graded in both the thickness and longitudinal directions by a power-law distribution. Equations of motion based on Timoshenko beam theory are derived from Hamilton's principle. A higher-order beam element using hierarchical functions to interpolate the displacements and rotation is formulated and employed in the analysis. In order to improve the efficiency of the element, the shear strain is constrained to constant. Validation of the derived element is confirmed by comparing the natural frequencies obtained in the present paper with the data available in the literature. Numerical investigations show that the proposed beam element is efficient, and it is capable to give accurate frequencies by a small number of elements. The effects of the material composition and aspect ratio on the vibration characteristics of the beams are examined in detail and highlighted.

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20

Ibrahim, S. M., Y. A. Al-Salloum, and H. Abbas. "Dynamic Analysis of Tapered Plates Based on Higher Order Beam Theory." Advanced Materials Research 919-921 (April 2014): 79–82. http://dx.doi.org/10.4028/www.scientific.net/amr.919-921.79.

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Modal solutions of plates with uniformly varying cross section using unified beam theory are presented. The results are given in the form of Euler-Bernoulli, Timoshenko and quasi 3D solutions. Numerical results for cantilever and CFCF supported rectangular planform plates are presented. Different types of modes, i.e. axial, bending and torsional modes are observed. The frequency values are in good agreement with 3D finite element results as well as published literature. Due to uniform taper in plate cross section, bending vibration modes become asymmetric along the longitudinal axis of the structure. Further, it can also be noticed that the vibration behavior of thick tapered plates is characterized by the appearance of significant number of axial and torsional modes at lower frequency values.

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21

McCarthy, Thomas R., and Aditi Chattopadhyay. "Investigation of composite ☐ beam dynamics using a higher-order theory." Composite Structures 41, no. 3-4 (March 1998): 273–84. http://dx.doi.org/10.1016/s0263-8223(98)00041-5.

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22

Geng, P. S., T. C. Duan, and L. X. Li. "An uncoupled higher-order beam theory and its finite element implementation." International Journal of Mechanical Sciences 134 (December 2017): 525–31. http://dx.doi.org/10.1016/j.ijmecsci.2017.10.041.

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23

Kroker, Andreas M., and Wilfried Becker. "Closed-form analysis of a higher-order composite box beam theory." PAMM 9, no. 1 (December 2009): 213–14. http://dx.doi.org/10.1002/pamm.200910080.

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24

Roozbahani, M. M., N. Heydarzadeh Arani, M. Moghimi Zand, and M. Mousavi Mashhadi. "Analytical solutions to nonlinear oscillations of micro/nano beams using higher-order beam theory." Scientia Iranica 23, no. 5 (October 1, 2016): 2179–93. http://dx.doi.org/10.24200/sci.2016.3947.

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25

Chakrabarti, A., A. H. Sheikh, M. Griffith, and D. J. Oehlers. "Analysis of composite beams with partial shear interactions using a higher order beam theory." Engineering Structures 36 (March 2012): 283–91. http://dx.doi.org/10.1016/j.engstruct.2011.12.019.

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26

Kumar, D. V. T. G. Pavan, and B. K. Raghu Prasad. "Higher-Order Beam Theories for Mode II Fracture of Unidirectional Composites." Journal of Applied Mechanics 70, no. 6 (November 1, 2003): 840–52. http://dx.doi.org/10.1115/1.1607357.

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Mathematical models, for the stress analyses of unidirectional end notch flexure and end notch cantilever specimens using classical beam theory, first, second, and third-order shear deformation beam theories, have been developed to determine the interlaminar fracture toughness of unidirectional composites in mode II. In the present study, appropriate matching conditions, in terms of generalized displacements and stress resultants, have been derived and applied at the crack tip by enforcing the displacement continuity at the crack tip in conjunction with the variational equation. Strain energy release rate has been calculated using compliance approach. The compliance and strain energy release rate obtained from present formulations have been compared with the existing experimental, analytical, and finite element results and found that results from third-order shear deformation beam theory are in close agreement with the existing experimental and finite element results.

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27

Giunta, G., and S. Belouettar. "Higher-Order Hierarchical Models for the Free Vibration Analysis of Thin-Walled Beams." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/940347.

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This paper addresses a free vibration analysis of thin-walled isotropic beams via higher-order refined theories. The unknown kinematic variables are approximated along the beam cross section as aN-order polynomial expansion, whereNis a free parameter of the formulation. The governing equations are derived via the dynamic version of the Principle of Virtual Displacements and are written in a unified form in terms of a “fundamental nucleus.” This latter does not depend upon order of expansion of the theory over the cross section. Analyses are carried out through a closed form, Navier-type solution. Simply supported, slender, and short beams are investigated. Besides “classical” modes (such as bending and torsion), several higher modes are investigated. Results are assessed toward three-dimensional finite element solutions. The numerical investigation shows that the proposed Unified Formulation yields accurate results as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam.

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28

Wang, Yuanbin, Hu Ding, and Li-Qun Chen. "Modeling and analysis of an axially acceleration beam based on a higher order beam theory." Meccanica 53, no. 10 (March 17, 2018): 2525–42. http://dx.doi.org/10.1007/s11012-018-0840-4.

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29

Shin, Dongil, Soomin Choi, Gang-Won Jang, and Yoon Young Kim. "Higher-order beam theory for static and vibration analysis of composite thin-walled box beam." Composite Structures 206 (December 2018): 140–54. http://dx.doi.org/10.1016/j.compstruct.2018.08.016.

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30

Kim, Do-Min, Suh In Kim, Soomin Choi, Gang-Won Jang, and Yoon Young Kim. "Topology optimization of thin-walled box beam structures based on the higher-order beam theory." International Journal for Numerical Methods in Engineering 106, no. 7 (December 8, 2015): 576–90. http://dx.doi.org/10.1002/nme.5143.

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31

Ebrahimi, F., and M. R. Barati. "Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams." Journal of Mechanics 33, no. 1 (May 24, 2016): 23–33. http://dx.doi.org/10.1017/jmech.2016.46.

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AbstractThe present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

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32

Marur, Sudhakar R., and Tarun Kant. "On the angle ply higher order beam vibrations." Computational Mechanics 40, no. 1 (July 18, 2006): 25–33. http://dx.doi.org/10.1007/s00466-006-0079-0.

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33

Chakrabarti, A., A. H. Sheikh, M. Griffith, and D. J. Oehlers. "Dynamic Response of Composite Beams with Partial Shear Interaction Using a Higher-Order Beam Theory." Journal of Structural Engineering 139, no. 1 (January 2013): 47–56. http://dx.doi.org/10.1061/(asce)st.1943-541x.0000603.

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34

Chakrabarti, A., A. H. Sheikh, M. Griffith, and D. J. Oehlers. "Analysis of composite beams with longitudinal and transverse partial interactions using higher order beam theory." International Journal of Mechanical Sciences 59, no. 1 (June 2012): 115–25. http://dx.doi.org/10.1016/j.ijmecsci.2012.03.012.

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35

Ebrahimi, Farzad, and Ali Jafari. "A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities." Journal of Engineering 2016 (2016): 1–20. http://dx.doi.org/10.1155/2016/9561504.

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In the present paper, thermomechanical vibration characteristics of functionally graded (FG) Reddy beams made of porous material subjected to various thermal loadings are investigated by utilizing a Navier solution method for the first time. Four types of thermal loadings, namely, uniform, linear, nonlinear, and sinusoidal temperature rises, through the thickness direction are considered. Thermomechanical material properties of FG beam are assumed to be temperature-dependent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of motion are derived based on higher order shear deformation beam theory. Hamilton’s principle is applied to obtain the governing differential equations of motion which are solved by employing an analytical technique called the Navier type solution method. Influences of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, thermal effects, and slenderness ratios on natural frequencies of the temperature-dependent FG beams with porosities are investigated and discussed in detail. It is concluded that these effects play significant role in the thermodynamic behavior of porous FG beams.

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36

Phuc, Pham Minh, and Vu Nguyen Thanh. "On the Vibration Analysis of Rotating Piezoelectric Functionally Graded Beams Resting on Elastic Foundation with a Higher-Order Theory." International Journal of Aerospace Engineering 2022 (January 28, 2022): 1–16. http://dx.doi.org/10.1155/2022/9998691.

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This work numerically simulates the natural vibration response of rotating piezoelectric functionally graded (FG) beams resting on two-parameter elastic mediums. This is a common kind of design seen in reality, such as marine engine gas turbine blades, rotating railway bridges, and helicopter rotors, where these components may be thought of as beam models rotating around a fixed axis. For the first time, this study uses the finite element method (FEM) in conjunction with Reddy’s theory of high-order shear deformation to model the vibration response of a beam rotating around one fixed axis. The present theory eliminates the necessity for shear correction factors while precisely describing the structure’s mechanical response. The piezoelectric layers are firmly connected to the top and bottom surfaces of the beam, while the core layer is composed of the FG material, whose material and physical characteristics are expected to gradually change along the thickness direction of the beam in accordance with a power law function as the thickness of the beam is increased. This study is conducted to determine the influences of the structure’s geometric and material characteristics on the beam’s free vibration behavior, including the rotational speed, distance between the fixed axis and beam endpoint, thickness of piezoelectric layers, and elastic foundation parameters, among other things. Due to the obvious calculation results, the free vibration response of this structure can be easily seen by readers, which serves as a foundation for its design and use in engineering practice.

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37

Ganapathi, M., and O. Polit. "Dynamic characteristics of curved nanobeams using nonlocal higher-order curved beam theory." Physica E: Low-dimensional Systems and Nanostructures 91 (July 2017): 190–202. http://dx.doi.org/10.1016/j.physe.2017.04.012.

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38

Negishi, Yoshikazu, and Ken-ichi Hirashima. "General Higher-Order Beam Theory Including Effects of Transverse and Lateral Components." Transactions of the Japan Society of Mechanical Engineers Series A 60, no. 576 (1994): 1821–28. http://dx.doi.org/10.1299/kikaia.60.1821.

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39

Nguyen, Nghia Huu, and Dong-Yeon Lee. "Bending analysis of a single leaf flexure using higher-order beam theory." Structural Engineering and Mechanics 53, no. 4 (February 25, 2015): 781–90. http://dx.doi.org/10.12989/sem.2015.53.4.781.

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40

Sun, Zhendong, Lianzhi Yang, and Yang Gao. "The displacement boundary conditions for Reddy higher-order shear cantilever beam theory." Acta Mechanica 226, no. 5 (October 29, 2014): 1359–67. http://dx.doi.org/10.1007/s00707-014-1253-7.

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41

Kant, T., and A. Gupta. "A finite element model for a higher-order shear-deformable beam theory." Journal of Sound and Vibration 125, no. 2 (September 1988): 193–202. http://dx.doi.org/10.1016/0022-460x(88)90278-7.

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42

Sujuan, Jiao, Li Jun, Hua Hongxing, and Shen Rongying. "A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory." Shock and Vibration 15, no. 2 (2008): 179–92. http://dx.doi.org/10.1155/2008/953639.

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The spectral element matrix is derived for a straight and uniform beam element having an arbitrary cross-section. The general higher-order beam theory is used, which accurately accounts for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the cross-sectional plane. Two coupled equations of motion are derived by use of Hamilton's principle along with the full three-dimensional constitutive relations. The theoretical expressions of the spectral element matrix are formulated from the exact solutions of the coupled governing equations. The developed spectral element matrix is directly applied to calculate the exact natural frequencies and mode shapes of the illustrative examples. Numerical results of the thick isotropic beams with rectangular and elliptical cross-sections are presented for a wide variety of cross-section aspect ratios.

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43

Bekhadda, Ahmed, Ismail Bensaid, Abdelmadjid Cheikh, and Bachir Kerboua. "Static buckling and vibration analysis of continuously graded ceramic-metal beams using a refined higher order shear deformation theory." Multidiscipline Modeling in Materials and Structures 15, no. 6 (November 4, 2019): 1152–69. http://dx.doi.org/10.1108/mmms-03-2019-0057.

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Purpose The purpose of this paper is to study the static buckling and free vibration of continuously graded ceramic-metal beams by employing a refined higher-order shear deformation, which is also the primary goal of this paper. Design/methodology/approach The proposed model is able to catch both the microstructural and shear deformation impacts without employing any shear correction factors, due to the realistic distribution of transverse shear stresses. The material properties are supposed to vary across the thickness direction in a graded form and are estimated by a power-law model. The equations of motion and related boundary conditions are extracted using Hamilton’s principle and then resolved by analytical solutions for calculating the critical buckling loads and natural frequencies. Findings The obtained results are checked and compared with those of other theories that exist in the literature. At last, a parametric study is provided to exhibit the influence of different parameters such as the power-law index, beam geometrical parameters, modulus ratio and axial load on the dynamic and buckling characteristics of FG beams. Originality/value Searching in the literature and to the best of the authors’ knowledge, there are limited works that consider the coupled effect between the vibration and the axial load of FG beams based on new four-variable refined beam theory. In comparison with a beam model, the number of unknown variables resulting is only four in the general cases, as against five in the case of other shear deformation theories. The actual model represents a real distribution of transverse shear effects besides a parabolic arrangement of the transverse shear strains over the thickness of the beam, so it is needless to use of any shear correction factors.

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44

Nguyen, Ngoc-Linh, Gang-Won Jang, Soomin Choi, Jaeyong Kim, and Yoon Young Kim. "Analysis of thin-walled beam-shell structures for concept modeling based on higher-order beam theory." Computers & Structures 195 (January 2018): 16–33. http://dx.doi.org/10.1016/j.compstruc.2017.09.009.

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45

Shabanlou, Gh, S. A. A. Hosseini, and M. Zamanian. "Vibration analysis of FG spinning beam using higher-order shear deformation beam theory in thermal environment." Applied Mathematical Modelling 56 (April 2018): 325–41. http://dx.doi.org/10.1016/j.apm.2017.11.021.

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46

Cui, Hao, Sotiris Koussios, Yulong Li, and Adriaan Beukers. "Measurement of adhesive shear properties by short beam shear test based on higher order beam theory." International Journal of Adhesion and Adhesives 40 (January 2013): 19–30. http://dx.doi.org/10.1016/j.ijadhadh.2012.08.009.

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47

Shimpi, Rameshchandra P., Rajesh A. Shetty, and Anirban Guha. "A simple single variable shear deformation theory for a rectangular beam." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 24 (September 29, 2016): 4576–91. http://dx.doi.org/10.1177/0954406216670682.

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This paper proposes a simple single variable shear deformation theory for an isotropic beam of rectangular cross-section. The theory involves only one fourth-order governing differential equation. For beam bending problems, the governing equation and the expressions for the bending moment and shear force of the theory are strikingly similar to those of Euler–Bernoulli beam theory. For vibration and buckling problems, the Euler–Bernoulli beam theory governing equation comes out as a special case when terms pertaining to the effects of shear deformation are ignored from the governing equation of present theory. The chosen displacement functions of the theory give rise to a realistic parabolic distribution of transverse shear stress across the beam cross-section. The theory does not require a shear correction factor. Efficacy of the proposed theory is demonstrated through illustrative examples for bending, free vibrations and buckling of isotropic beams of rectangular cross-section. The numerical results obtained are compared with those of exact theory (two-dimensional theory of elasticity) and other first-order and higher-order shear deformation beam theory results. The results obtained are found to be accurate.

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Gordaninejad, F., and A. Ghazavi. "Effect of Shear Deformation on Bending of Laminated Composite Beams." Journal of Pressure Vessel Technology 111, no. 2 (May 1, 1989): 159–64. http://dx.doi.org/10.1115/1.3265652.

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A higher-order shear deformation beam theory is utilized to analyze the bending of thick laminated composite beams. This theory accounts for parabolic distribution of shear strain through the thickness of the beam. The predicted displacements show improvement over the Bresse-Timoshenko beam theory. Mixed finite element results are obtained for those cases where closed-form solutions are not available. The finite element and exact solutions are in close agreement. Numerical results are presented for single, two and three-layer beams under uniform and sinusoidal distributed transverse loadings.

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Pulido, Manuel, and Claudio Rodas. "A Higher-Order Ray Approximation Applied to Orographic Gravity Waves: Gaussian Beam Approximation." Journal of the Atmospheric Sciences 68, no. 1 (January 1, 2011): 46–60. http://dx.doi.org/10.1175/2010jas3468.1.

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Abstract Ray techniques are a promising tool for developing orographic gravity wave drag schemes. However, the modeling of the propagation of orographic waves using standard ray theory in realistic background wind conditions usually encounters several regions, called caustics, where the first-order ray approximation breaks down. In this work the authors develop a higher-order approximation than standard ray theory, named the Gaussian beam approximation, for orographic gravity waves in a background wind that depends on height. The analytical results show that this formulation is free of the singularities that arise in ray theory. Orographic gravity waves that propagate in a background wind that turns with height—the same conditions as in the work of Shutts—are examined under the Gaussian beam approximation. The evolution of the amplitude is well defined in this approximation even at caustics and at the forcing level. When comparing results from the Gaussian beam approximation with high-resolution numerical simulations that compute the exact solution, there is good agreement of the amplitude and phase fields. Realistic orography is represented by means of a superposition of multiple Gaussians in wavenumber space that fit the spectrum of the orography. The technique appears to give a good representation of the disturbances generated by flow over realistic orography.

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He, Guanghui, Dejiang Wang, and Xiao Yang. "Analytical Solutions for Free Vibration and Buckling of Composite Beams Using a Higher Order Beam Theory." Acta Mechanica Solida Sinica 29, no. 3 (June 2016): 300–315. http://dx.doi.org/10.1016/s0894-9166(16)30163-x.

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