Статті в журналах: "Cantilever Euler-Bernoulli beam"

1

Siva Sankara Rao, Yemineni, Kutchibotla Mallikarjuna Rao, and V. V. Subba Rao. "Estimation of damping in riveted short cantilever beams." Journal of Vibration and Control 26, no. 23-24 (March 20, 2020): 2163–73. http://dx.doi.org/10.1177/1077546320915313.

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In layered and riveted structures, vibration damping happens because of a micro slip that occurs because of a relative motion at the common interfaces of the respective jointed layers. Other parameters that influence the damping mechanism in layered and riveted beams are the amplitude of initial excitation, overall length of the beam, rivet diameter, overall beam thickness, and many layers. In this investigation, using the analytical models such as the Euler–Bernoulli beam theory and Timoshenko beam theory and half-power bandwidth method, the free transverse vibration analysis of layered and riveted short cantilever beams is carried out for observing the damping mechanism by estimating the damping ratio, and the obtained results from the Euler–Bernoulli beam theory and Timoshenko beam theory analytical models are validated by the half-power bandwidth method. Although the Euler–Bernoulli beam model overestimates the damping ratio value by a very less fraction, both the models can be used to evaluate damping for short riveted cantilever beams along with the half-power bandwidth method.

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2

Adair, Desmond, and Martin Jaeger. "A power series solution for rotating nonuniform Euler–Bernoulli cantilever beams." Journal of Vibration and Control 24, no. 17 (June 14, 2017): 3855–64. http://dx.doi.org/10.1177/1077546317714183.

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A systematic procedure is developed for studying the dynamic response of a rotating nonuniform Euler–Bernoulli beam with an elastically restrained root. To find the solution, a novel approach is used in that the fourth-order differential equation describing the vibration problem is first written as a first-order matrix differential equation, which is then solved using the power series method. The method can be used to obtain an approximate solution of vibration problems for nonuniform Euler–Bernoulli beams. Specifically, numerical examples are presented here to demonstrate the usefulness of the method in frequency analysis of nonuniform Euler–Bernoulli clamped-free cantilever beams. Results for mode shapes and frequency parameters were found to be in satisfactory agreement with previously published results. The effects of tapering, both equal and unequal, were investigated for both a cantilever wedge and cantilever cone.

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3

Ključanin, Dino, and Abaz Manđuka. "The cantilever beams analysis by the means of the first-order shear deformation and the Euler-Bernoulli theory." Tehnički glasnik 13, no. 1 (March 23, 2019): 63–67. http://dx.doi.org/10.31803/tg-20180802210608.

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The effect of the Timoshenko theory and the Euler-Bernoulli theory are investigated in this paper through numerical and analytical analyses. The investigation was required to obtain the optimized position of the pipes support. The Timoshenko beam theory or the first order shear deformation theory was used regarding thick beams where the shearing effect of the beam is considered. The study of the thin beams was performed with the Euler-Bernoulli theory. The analysis was done for stainless steel AISI-440C beams with the rectangular cross-section. The steel beams were a cantilever and stressed under varying point-centred load.

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4

Savarimuthu, Kirubaveni, Radha Sankararajan, Gulam Nabi Alsath M., and Ani Melfa Roji M. "Design and analysis of cantilever based piezoelectric vibration energy harvester." Circuit World 44, no. 2 (May 8, 2018): 78–86. http://dx.doi.org/10.1108/cw-11-2017-0067.

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Purpose This paper aims to present the design of a cantilever beam with various kinds of geometries for application in energy harvesting devices with a view to enhance the harvested power. The cantilever beams in rectangular, triangular and trapezoidal geometries are simulated, designed and evaluated experimentally. A power conditioning circuit is designed and fabricated for rectification and regulation. Design/methodology/approach The analytical model based on Euler–Bernoulli beam theory is analyzed for various cantilever geometries. The aluminum beam with Lead Zirconate Titanate (PZT) 5H strip is used for performing frequency, displacement, strain distribution, stress and potential analysis. A comparative analysis is done based on the estimated performance of the cantilevers with different topologies of 4,500 mm3 volume. Findings The analysis shows the trapezoidal cantilever yielding a maximum voltage of 66.13 V at 30 Hz. It exhibits maximum power density of 171.29 W/mm3 at optimal resistive load of 330 kΩ. The generated power of 770.8 µW is used to power up a C-mote wireless sensor network. Originality/value This study provides a complete structural analysis and implementation of the cantilever for energy harvesting application, integration of power conditioning circuit with the energy harvester and evaluation of the designed cantilevers under various performance metrics.

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5

Daneshmehr, Ali Reza, Majid Akbarzadeh Khorshidi, and Delara Soltani. "Dynamic Analysis of a Micro-Cantilever Subjected to Harmonic Base Excitation via RVIM." Applied Mechanics and Materials 332 (July 2013): 545–50. http://dx.doi.org/10.4028/www.scientific.net/amm.332.545.

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In this paper, dynamic analysis of a cantilever beam with micro-scale dimensions is presented. The micro-cantilever is subjected to harmonic base excitation and constant force at micro-cantilever tip. By Euler-Bernoulli beam theory assumptions, the mathematical formulation of vibrating micro-cantilever beam is derived using extended Hamilton principle. The governing partial-diffrential equation is solved by reconstruction of variational iteration method (RVIM), with possession of its boundary conditions. The RVIM is an approximate method of solving that answers easy and quick and has high accuracy.

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6

Jalali, Mohammad Hadi, and Geoff Rideout. "Analytical and experimental investigation of cable–beam system dynamics." Journal of Vibration and Control 25, no. 19-20 (August 2019): 2678–91. http://dx.doi.org/10.1177/1077546319867171.

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Interactions between cables and structures affect the design and nondestructive testing of electricity transmission lines, guyed towers, and bridges. An analytical model for an electricity pole beam–cable system is presented, which can be extended to other applications. A cantilever beam is connected to two stranded cables. The cables are modeled as tensioned Euler–Bernoulli beams, considering the sag due to self-weight. The pole is also modeled as a cantilever Euler–Bernoulli beam and the equations of motion are derived using Hamilton’s principle. The model was validated with a reduced-scale system in the laboratory and a setup was designed to accurately measure the bending stiffness of the stranded cable under tension. It is concluded that the bending stiffness and sag of the cable have a significant effect on the dynamics of beam–cable structures. By adding the cable to the pole structure, some hybrid modes emerge in the eigenvalue solution of the system. Modes with antisymmetric cable motion are sag-independent and the modes with symmetric cable motion are dependent on the cable sag. The effect of sag on the natural frequencies is more significant when the bending stiffness of the cables is higher.

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7

Mishra, Manish Kumar, P. M. Mishra, and Vikas Dubey. "Deflection Modelling of MEMS Cantilever Beam Through Collocation Method Taking B-Splinesas Approximating Functions." International Journal of Social Ecology and Sustainable Development 13, no. 3 (May 2022): 1–15. http://dx.doi.org/10.4018/ijsesd.290007.

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The Mathematical Modeling and Analysis of cantilever beam adhesion problem, under the action of electrostatic attraction force iscarried out. The model uses Euler-Bernoulli beam theory for one end fixed and other end free type beams for small deflection. A MATLAB code has prepared to predict and plot the deflection profile of MEMS cantilever beam during the action of stiction force on application of applied voltage as snap down occurs. The model predicts the cantilever behavior on occurrence of snap downvoltage. To envisage the deflection profile, A collocation method employing B-Spline as approximating functions & Gaussian quadrature point as collocation points has been utilized for solving the governing equation by keeping the four end boundary conditions of cantilever beam in mind. The numerical results reveal the deflection profile of the MEMS cantilever Beam, which are validated with the previous data & deflection profile available by numerous published research papers

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8

Zhang, Kai, De Shi Wang, and Qi Zheng Zhou. "Study on the Electromechanical Coupling Performance of Bimorph Piezoelectric Cantilever." Applied Mechanics and Materials 302 (February 2013): 447–51. http://dx.doi.org/10.4028/www.scientific.net/amm.302.447.

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In order to accurately predict the electromechanical coupling performance of bimorph piezoelectric cantilever structure. Based on Euler-Bernoulli beam assumption, the expression of output voltage response of the bimorph piezoelectric cantilever is written, the output voltage curve of unit acceleration excitation are obtained, the law of the output voltage influenced by the structure parameters of the cantilever beam length, width and thickness of the metal beam and the piezoelectric layer are analyzed, the results will play an important theoretical and engineering significance in the development of high efficient piezoelectric energy harvesting device.

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9

Nikolić, Aleksandar, and Slaviša Šalinić. "A rigid multibody method for free vibration analysis of beams with variable axial parameters." Journal of Vibration and Control 23, no. 1 (August 8, 2016): 131–46. http://dx.doi.org/10.1177/1077546315575818.

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This paper presents a new approach to the problem of determining the frequencies and mode shapes of Euler–Bernoulli tapered cantilever beams with a tip mass and a spring at the free end. The approach is based on the replacement of the flexible beam by a rigid multibody system. Beams with constant thickness and exponentially and linearly tapered width, as well as double-tapered cantilever beams are considered. The influence of the tip mass, stiffness of the spring, and taper on the frequencies of the free transverse vibrations of tapered cantilever beams are examined. Numerical examples with results confirming the convergence and accuracy of the approach are given.

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10

Shterev, Kiril, and Emil Manoach. "Geometrically Non-Linear Vibration of a Cantilever Interacting with Rarefied Gas Flow." Cybernetics and Information Technologies 20, no. 6 (December 1, 2020): 126–39. http://dx.doi.org/10.2478/cait-2020-0067.

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Abstract The work is devoted to study 2D pressure driven rarefied gas flow in a microchannel having an elastic obstacle. The elastic obstacle is clamped at the bottom channel wall and its length is half of the channel height. The gas flow is simulated by Direct Simulation Monte Carlo (DSMC) method applying the advanced Simplified Bernoulli Trial (SBT) collision scheme. The elastic obstacle is modelled as geometrically nonlinear Euler Bernoulli beam. A reduced 3 modes reduction model of the beam is created. The influence of the gas flow on the beam vibration is studied, considering the linear and nonlinear beam theories.

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11

Cavacece, M., and L. Vita. "Optimal Cantilever Dynamic Vibration Absorbers by Timoshenko Beam Theory." Shock and Vibration 11, no. 3-4 (2004): 199–207. http://dx.doi.org/10.1155/2004/710924.

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A double-ended cantilever beam as a distributed parameter dynamic vibration absorber has been applied to a single-degree-of-freedom system subjected to harmonic forces.In this investigation, the beam has been analyzed under the well known model of Timoshenko and the computation of best parameters is based on the Chebyshev’s optimality criterion.This is somewhat novel in the field since:The design of cantilever beams as dynamic vibration absorbers is usually made under the hypotheses of the Euler-Bernoulli theory;It is the first time that the Chebyshev’s criterion is applied to the design of a double-ended cantilever beam used as a dynamic vibration absorber.For a ready use of the results herein presented, design charts allow a quick choice of optimal parameters such as tuning ratio and mass ratio.

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12

Chondros, T. G., and A. D. Dimarogonas. "Vibration of a Cracked Cantilever Beam." Journal of Vibration and Acoustics 120, no. 3 (July 1, 1998): 742–46. http://dx.doi.org/10.1115/1.2893892.

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A continuous cracked bar vibration model is developed for the lateral vibration of a cracked Euler-Bernoulli cantilevered beam with an edge crack. The Hu-Washizu-Barr variational formulation was used to develop the differential equation and the boundary conditions for the cracked beam as an one-dimensional continuum. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods. The results of three independent evaluations of the lowest natural frequency of lateral vibrations of an aluminum cantilever beam with a single-edge crack are presented: the continuous cracked beam vibration model, the lumped crack model vibration analysis, and experimental results. Experimental results fall very close to the values predicted by the continuous crack formulation. Moreover, the continuous cracked beam theory agrees better with the experimental results than the lumped crack flexibility theory.

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13

Gesing, Andre, Daniel Platz, and Ulrich Schmid. "Viscous fluid–structure interaction of micro-resonators in the beam–plate transition." Journal of Applied Physics 131, no. 13 (April 7, 2022): 134502. http://dx.doi.org/10.1063/5.0085514.

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We numerically investigate the fluid–structure interaction of thin elastic cantilever micro-structures in viscous fluids. The Kirchhoff plate equation describes the dynamics of the structure, and a boundary integral formulation represents the fluid flow. We show how the displacement spectrum of the structures changes as the geometry is altered from a narrow beam to a wide plate in a liquid. For narrow beams, the displacement spectrum exhibits only a few resonance frequencies, which correspond to the vibrational modes described by the Euler–Bernoulli equation (Euler–Bernoulli modes). The spectrum of wide plates exhibits several additional resonance frequencies associated with the plate’s torsional and higher-order vibrational modes. Wide plates in Euler–Bernoulli modes exhibit higher damping coefficients, but due to an increased added-mass effect, also higher Q-factors than slender beams. An investigation into the fluid flow reveals that for the Euler–Bernoulli modes of wider plates, the fluid flow and energy dissipation near the plate’s edges increase, resulting in increased damping coefficients. Concomitantly, a region of minimal viscous dissipation near the plate’s center appears for wider plates, resulting in an increased added-mass effect. Higher-order modes of wider plates exhibit lower Q-factor than the Euler–Bernoulli modes due to a decreased fluid flow at the plate’s edges caused by the appearance of circulation zones on both sides of the plate. This decreased flow at the edge reduces the damping and the added-mass effect, yielding lower Q-factors. We anticipate that the results presented here will play a vital role in conceiving novel MEMS resonators for operation in viscous fluids.

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14

Hajheidari, Peyman, Ion Stiharu, and Rama Bhat. "Analysis of bimorph piezoelectric beam energy harvesters using superconvergent element." Journal of Intelligent Material Systems and Structures 30, no. 15 (July 17, 2019): 2299–313. http://dx.doi.org/10.1177/1045389x19862360.

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Cantilever-based piezoelectric energy harvesters have been utilized as structures to extract mechanical energy from the ambient mechanical vibrations and transfer it into the electrical output. In this article, the performance of bimorph piezoelectric beam energy harvesters is investigated. The cantilever beam is modeled by using both Timoshenko and Euler–Bernoulli beam theories. The equations are discretized using the conventional finite element method and superconvergent element. Besides the high rate of convergence, easy switching between the above beam theories is enabled by such type of element. The current model is presented for a Timoshenko beam model, but it could as well be used for a Euler–Bernoulli beam model. In addition, voltage, current, and power frequency response functions for different ranges of load resistance varying from the short-circuit to open-circuit conditions are determined to reach the maximum values. Effects of the slenderness ratio and the required beam model based on the geometric properties of the piezoelectric energy harvesters are discussed in the final part of this study. The results show that only for smaller values of the slenderness ratio (below 5), it is necessary to model the beam using the Timoshenko assumptions; otherwise both beam theories provide approximately the same responses.

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15

Gu, Xudong, Bingxin Zhao, Ruolin Gao, Yongfeng Yang, and Yuhao Liu. "Dynamical response of a cantilever beam under moving mass with fractional damping." Journal of Physics: Conference Series 2478, no. 9 (June 1, 2023): 092030. http://dx.doi.org/10.1088/1742-6596/2478/9/092030.

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Abstract In the present paper, the dynamical response of a cantilever beam with fractional damping excited by the moving mass load is studied. First, the vibration equation of the cantilever beam is established by adopting Euler-Bernoulli beam theory. Then, the established equation is discretized by using Galerkin discretization. The discrete equation is difficult to solve due to the fractional damping. Based on the generalized harmonic function technology, the fractional damping force is approximated by a damping force and a conservative force. Then, an efficient algorithm is used to calculated the truncated equation to derive the dynamical response. The displacement at the end of the cantilever beam is calculated, and the influence of fractional damping coefficients is analysed.

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16

Song, Jiang Yong. "An Elliptic Integral Solution to the Multiple Inflections Large Deflection Beams in Compliant Mechanisms." Advanced Materials Research 971-973 (June 2014): 349–52. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.349.

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In this paper, a solution based on the elliptic integrals is proposed for solving multiples inflection points large deflection. Application of the Bernoulli Euler equations of compliant mechanisms with large deflection equation of beam is obtained ,there is no inflection point and inflection points in two cases respectively. The elliptic integral solution which is the most accurate method at present for analyzing large deflections of cantilever beams in compliant mechanisms.

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17

Koh, Sung K., and Guangjun Liu. "Optimal plane beams modelling elastic linear objects." Robotica 28, no. 1 (May 15, 2009): 135–48. http://dx.doi.org/10.1017/s0263574709005669.

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SUMMARYThis paper discusses analytical and deterministic models for a plane curve with minimum deformation that may be utilized in planning the motion of elastic linear objects and investigating the inverse kinematics of a hyper-redundant robot. It usually requires intensive computation to determine the configuration of elastic linear objects. In addition, conventional optimization-based numerical techniques that identify the shape of elastic linear objects in equilibrium involve non-deterministic aspects. Several analytical models that produce the configuration of elastic linear objects in an efficient and deterministic manner are presented in this paper. To develop the analytical expressions for elastic linear objects, we consider a cantilever beam where the deflections are determined according to the Euler–Bernoulli beam theory. The deflections of the cantilever beam are determined for prescribed constraints imposed on the deflections at the free end to replicate various elastic linear objects. Deflections of a cantilever beam with roller supports are explored to replicate elastic linear objects in contact with rigid objects. We verify the analytical models by comparing them with exact beam deflections. The analytical model is precisely accurate for beams with small deflections as it is developed on the basis of the Euler–Bernoulli beam theory. Although it is applied to beams undergoing large deflections, it is still reasonably accurate and at least as precise as the conventional pseudo-rigid-body model. The computational demand involved in using the analytical models is negligible. Therefore, efficient motion planning for elastic linear objects can be realized when the proposed analytical models are combined with conventional motion planning algorithms. We also demonstrate that the analytical model solves the inverse kinematics problem in an efficient and robust manner through numerical simulations.

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18

Abbaszadeh Bidokhti, Ali, Amir Reza Shahani, and Mohammad Reza Amini Fasakhodi. "Displacement-controlled crack growth in double cantilever beam specimen: A comparative study of different models." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 15 (April 7, 2016): 2835–47. http://dx.doi.org/10.1177/0954406216642474.

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This paper presents, discusses, and compares different techniques to model fracture initiation and static crack growth in double cantilever beam specimen under displacement-controlled loading. Energy release rate, critical displacement for the onset of crack growth, and critical load were determined by analytical solution, standard, and extended finite element method. The crack growth was also examined, and the advantages of each method were described as well. In addition, the compliance technique was used in the analytical method. In this regard, the crack growth relations were formulated based on four models including simple Euler–Bernoulli model, Euler–Bernoulli on the elastic foundation, simple Timoshenko beam, and the beam on the elastic foundation considering shear effects. Closed-form relations were extracted for the fracture parameters. Afterward, the Abaqus software was utilized to simulate the crack growth by the standard finite element method. Since the extended finite element has the ability to model the discontinuities inside the elements, the problem was also simulated by this method. Cohesive fracture of double cantilever beam specimen was performed using a closed-form solution and using a finite element model. Results of different modeling techniques were determined and compared.

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19

Maleki-Bigdeli, Mohammad-Ali, Majid Baniassadi, Kui Wang, and Mostafa Baghani. "Developing a beam formulation for semi-crystalline two-way shape memory polymers." Journal of Intelligent Material Systems and Structures 31, no. 12 (May 30, 2020): 1465–76. http://dx.doi.org/10.1177/1045389x20924837.

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In this research, the bending of a two-way shape memory polymer beam is examined implementing a one-dimensional phenomenological macroscopic constitutive model into Euler–Bernoulli and von-Karman beam theories. Since bending loading is a fundamental problem in engineering applications, a combination of bending problem and two-way shape memory effect capable of switching between two temporary shapes can be used in different applications, for example, thermally activated sensors and actuators. Shape memory polymers as a branch of soft materials can undergo large deformation. Hence, Euler–Bernoulli beam theory does not apply to the bending of a shape memory polymer beam where moderate rotations may occur. To overcome this limitation, von-Karman beam theory accounting for the mid-plane stretching as well as moderate rotations can be employed. To investigate the difference between the two beam theories, the deflection and rotating angles of a shape memory polymer cantilever beam are analyzed under small and moderate deflections and rotations. A semi-analytical approach is used to inspect Euler–Bernoulli beam theory, while finite-element method is employed to study von-Karman beam theory. In the following, a smart structure is analyzed using a prepared user-defined subroutine, VUMAT, in finite-element package, ABAQUS/EXPLICIT. Utilizing generated user-defined subroutine, smart structures composed of shape memory polymer material can be analyzed under complex loading circumstances through the two-way shape memory effect.

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20

Amiot, F. "An Euler–Bernoulli second strain gradient beam theory for cantilever sensors." Philosophical Magazine Letters 93, no. 4 (April 2013): 204–12. http://dx.doi.org/10.1080/09500839.2012.759294.

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21

Theinchai, Ratchata, Siriwan Chankan, and Weera Yukunthorn. "Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam." International Journal of Mathematics and Mathematical Sciences 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/5052194.

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We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.

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22

Digilov, Rafael M., and Haim Abramovich. "The impact of root flexibility on the fundamental frequency of a restrained cantilever beam." International Journal of Mechanical Engineering Education 45, no. 2 (January 22, 2017): 184–93. http://dx.doi.org/10.1177/0306419016689502.

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This study presents the theoretical and experimental studies of the impact of root flexibility on the fundamental frequency of the free bending vibration of a uniform Euler–Bernoulli cantilever beam elastically restrained at the root. The dispersion relation between the natural frequency and modal number has been derived and solved numerically and approximately using the series method of the expansion in terms of the modal number. It is shown that the approximate solution is reduced to the empirical Dunkerley rule, which is sound not universally true. A commercial force sensor is used for the experimental detection of the effect of root flexibility on the fundamental frequency of bending vibrations of a cantilevered beam. The strip-shape specimen attached to the force sensor forms a cantilever beam restrained at the root against rotation and translation and it fundamental frequency is identified. The results of measurements for a series of industrial materials are compared with exact calculations and those predicted by Dunkerley’s formula and an excellent agreement is observed.

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23

Mohanty, R. C., and B. K. Nanda. "Investigation into the Dynamics of Layered and Jointed Cantilevered Beams." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 10 (April 22, 2010): 2129–39. http://dx.doi.org/10.1243/09544062jmes1939.

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Damping occurring at the joints due to interfacial relative motion is the major source of inherent damping in fabricated structures. In the present investigation, the dynamic analysis of layered cantilever beams jointed with rivets was carried out using the finite element approach for the Euler—Bernoulli beam model. The solution is based on one-dimensional beam elements, with each element consisting of two nodes having two degrees of freedom (i.e. transverse displacement and rotation) at each node. The cubic shape functions are considered for the transverse vibration of the beam in terms of nodal variables. The stiffness and mass matrices are evaluated from the bending strain energy and kinetic energy of the beam, respectively, which are further used to determine the natural frequency and mode shapes by modal analysis. The damping capacity of the cantilever specimens was computed using the energy approach. Experiments were conducted for validating the numerical results. The results establish that the damping capacity of built-up structures having lower beam thickness ratio and higher cantilever length can be improved substantially using larger diameter rivets at lower amplitude of excitation.

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Hajheidari, Peyman, Ion Stiharu, and Rama Bhat. "Performance of tapered cantilever piezoelectric energy harvester based on Euler–Bernoulli and Timoshenko Beam theories." Journal of Intelligent Material Systems and Structures 31, no. 4 (December 11, 2019): 487–502. http://dx.doi.org/10.1177/1045389x19891526.

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The cantilever beam configuration plays an important role in the power extracted from the vibration-based piezoelectric energy harvesters. Although it has already been proven that triangular and trapezoidal shapes optimize and improve the electrical output of the piezoelectric energy harvesters, the impact of other shapes has not been considered. It is necessary to figure out which shape can provide the maximum amount of power and efficiency, as well. In this article, a complete study regarding the influence of non-uniform theories using both Timoshenko and Euler–Bernoulli beams for both unimorph and bimorph states is carried out. The width and height of the cantilever beams are changed based on the degree of the polynomial function. To solve the equations, finite element method with the application of two different elements including 4-degree-of-freedom model and 8-degree-of-freedom model is adopted. Based on the analysis, it can be concluded that by increasing the degree of non-uniformity and slenderness ratio, the amount of harvested electrical output rises. Moreover, the difference between two beam theories is significant for thick beams with small slenderness ratios. In addition, the effects of non-uniformity including the tapering ratio described by polynomial functions on the efficiency of piezoelectric energy harvesters are studied.

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25

Hamioud, Saida. "Free Vibration of a Cantilever Euler-Bernoulli Beam Carrying a Point Mass by Using SEM." Tehnički glasnik 16, no. 4 (September 26, 2022): 519–22. http://dx.doi.org/10.31803/tg-20210807191129.

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The objective of this research is to study the free vibration of a cantilever Euler-Bernoulli beam carrying a point mass with moment of inertia at the free end using the spectral element method (SEM). Typically, the shape (or interpolation) functions used in the Spectral element method are derived from exact solutions of the governing differential equations of motion in the frequency domain. The beam was discretized by a single spectral element which was connected by a point mass at the free end. The dynamic stiffness matrix of the beam is formulated in frequency domain by considering compatibility conditions at the additional mass position. Then, the first three natural frequencies of the cantilever beam are determined. After the validation of the spectral element method, the influence of the non-dimensional mass parameter and the non-dimensional mass moment of inertia on the first three natural frequencies and shape mode are examined.

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Escedi, István, and Attila Baksa. "Deformation of a cantilever curved beam with variable cross section." Journal of Computational and Applied Mechanics 16, no. 1 (2021): 23–36. http://dx.doi.org/10.32973/jcam.2021.002.

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This paper deals with the determination of the displacements and stresses in a curved cantilever beam. The considered curved beam has circular centerline and the thickness of its cross section depends on the circumferential coordinate. The kinematics of Euler-Bernoulli beam theory are used. The curved elastic beam is fixed at one end and on the other end is subjected to concentrated moment and force; three different loading cases are considered. The paper gives analytical solutions for radial and circumferential displacements and cross-sectional rotation and circumferential stresses. The presented examples can be used as benchmark for the other types of solutions as given in this paper.

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27

Chen, Yuhang, Maomao Zhang, Yaxuan Su, and Zhidong Zhou. "Coupling Analysis of Flexoelectric Effect on Functionally Graded Piezoelectric Cantilever Nanobeams." Micromachines 12, no. 6 (May 21, 2021): 595. http://dx.doi.org/10.3390/mi12060595.

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The flexoelectric effect has a significant influence on the electro-mechanical coupling of micro-nano devices. This paper studies the mechanical and electrical properties of functionally graded flexo-piezoelectric beams under different electrical boundary conditions. The generalized variational principle and Euler–Bernoulli beam theory are employed to deduce the governing equations and corresponding electro-mechanical boundary conditions of the beam model. The deflection and induced electric potential are given as analytical expressions for the functionally graded cantilever beam. The numerical results show that the flexoelectric effect, piezoelectric effect, and gradient distribution have considerable influences on the electro-mechanical performance of the functionally graded beams. Moreover, the nonuniform piezoelectricity and polarization direction will play a leading role in the induced electric potential at a large scale. The flexoelectric effect will dominate the induced electric potential as the beam thickness decreases. This work provides helpful guidance to resolve the application of flexoelectric and piezoelectric effects in functionally graded materials, especially on micro-nano devices.

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28

Xue, Yan Xia, and Zhen Chao Su. "Dynamical Analysis of a Cantilever Column with a Tip Mass Subjected to Subtangential Follower Force." Applied Mechanics and Materials 427-429 (September 2013): 346–49. http://dx.doi.org/10.4028/www.scientific.net/amm.427-429.346.

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Based on the theory of Bernoulli-Euler beam and d Alembert principle, the differential equation of a cantilever column with a tip mass subjected to a subtangential follower force is built, the solution of the differential equation under the specific boundary conditions is found, frequency equation is formed for computing the system frequencies, several cases of this system is investigated.

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29

Abdulsahib, Imad A., and Qasim A. Atiyah. "Vibration Analysis of a Symmetric Double-Beam with an Elastic Middle Layer at Arbitrary Boundary Conditions." Mathematical Modelling of Engineering Problems 9, no. 4 (August 31, 2022): 1136–42. http://dx.doi.org/10.18280/mmep.090433.

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Vibration of double beams with an elastic connected layer has been studied in this paper by assuming that the beam is a Bernoulli-Euler beam. The natural frequencies equations of the symmetric double beam have been computed at arbitrary boundary conditions. The behavior of those frequencies has been investigated with a change in the stiffness of connected layer, modulus of elasticity of beam, length of beam, mass density of beam, and thickness of beam. The high effect of the elastic connected layer on the higher natural frequencies of a cantilever double beam is less than that in the clamped and free double beams. The increase in the thickness of upper and lower beams made a high increase in the values of lower natural frequencies in all types of beams. The change in the modulus of elasticity values of double beam becomes high on the lower natural frequencies but without enlarging the influence on the higher frequencies, especially in the cantilever double beam. The similar effect of change in the mass density of the beam resulted in the same influence on the higher and lower natural frequencies in all types of beams. The length of the beam enlarges the influence on the higher natural frequencies of clamped and free.

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30

Abraham, Rosmi, Faheem Khan, Syed A. Bukhari, Qingxia Liu, Thomas Thundat, Hyun-Joong Chung, and Chun Il Kim. "Effect of Surface and Interfacial Tension on the Resonance Frequency of Microfluidic Channel Cantilever." Sensors 20, no. 22 (November 12, 2020): 6459. http://dx.doi.org/10.3390/s20226459.

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The bending resonance of micro-sized resonators has been utilized to study adsorption of analyte molecules in complex fluids of picogram quantity. Traditionally, the analysis to characterize the resonance frequency has focused solely on the mass change, whereas the effect of interfacial tension of the fluid has been largely neglected. By observing forced vibrations of a microfluidic cantilever filled with a series of alkanes using a laser Doppler vibrometer (LDV), we studied the effect of surface and interfacial tension on the resonance frequency. Here, we incorporated the Young–Laplace equation into the Euler–Bernoulli beam theory to consider extra stress that surface and interface tension exerts on the vibration of the cantilever. Based on the hypothesis that the near-surface region of a continuum is subject to the extra stress, thin surface and interface layers are introduced to our model. The thin layer is subject to an axial force exerted by the extra stress, which in turn affects the transverse vibration of the cantilever. We tested the analytical model by varying the interfacial tension between the silicon nitride microchannel cantilever and the filled alkanes, whose interfacial tension varies with chain length. Compared with the conventional Euler–Bernoulli model, our enhanced model provides a better agreement to the experimental results, shedding light on precision measurements using micro-sized cantilever resonators.

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31

Zorić, Andrija, Marina Trajković-Milenković, Dragan Zlatkov, and Todor Vacev. "Semi-Analytical Solution for Elastoplastic Deflection of Non-Prismatic Cantilever Beams with Circular Cross-Section." Applied Sciences 12, no. 11 (May 27, 2022): 5439. http://dx.doi.org/10.3390/app12115439.

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A solution for the elastoplastic deflection of cantilever beams with linearly variable circular cross-section loaded by shear force at the free end, which is suitable for practical use, has not yet been developed. A semi-analytical solution for such a problem is proposed in this paper. The solution involves beams made of homogenous and isotropic materials with bilinear elastoplastic strain hardening behavior. The Bernoulli–Euler formula is used for determining the elastic deflection. However, for the plastic domain of material behavior, the differential equation of beam bending does not have a solution in closed form. Therefore, an incremental procedure for determining the curvature of the plastified region of the beam is suggested. Deflection of the cantilever beam is calculated via integration of the approximated function of the beam curvature. The proposed semi-analytical solution is validated using experimental results of the seismic energy dissipation device components which have been selected as a sample of a real engineering system. Also, validation is done via finite element analysis of six different cantilever beam models with varying geometric and material characteristics. A satisfying agreement between the proposed semi-analytical results and the subsequent experimental and numerical results is herein achieved, confirming its reliability.

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32

Shao, Mingyu, Chicheng Ma, Shuaizhao Hu, Chuansong Sun, and Dong Jing. "Effects of Time-Varying Fluid on Dynamical Characteristics of Cantilever Beams: Numerical Simulations and Experimental Measurements." Mathematical Problems in Engineering 2020 (December 21, 2020): 1–18. http://dx.doi.org/10.1155/2020/6679443.

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In order to obtain the effects of time-varying fluid on dynamical characteristics of cantilever beams, this paper gives a comprehensive study of cantilever beams vibrating in a fluid with variable depth. The mathematical model of the cantilever beams in time-varying fluid is derived by combining Euler–Bernoulli beam theory and velocity potential theory, and the influence of the time-varying fluid is discussed. Then, a two-way fluid-structure interaction (FSI) numerical simulation procedure is proposed to calculate the transient responses of the beam. The validity and accuracy are verified according to the comparison among theoretical analysis, numerical simulations, and experimental measurements. Results show that, besides the added mass effect, a damping-like term is also induced due to the motion of the fluid, which is proportional to the moving velocity of the fluid. Both the added mass and the added damping increase with the increment of the width of the beam. The surrounding fluid near the free end affects the beam more significantly. As a negative damping is caused while the fluid decreases, resulting in a much slower decay of the time responses. Therefore, the added damping should not be neglected in the analysis of the FSI problems with time-varying fluid.

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33

S Patil, Sushil, and Pradeep J Awasare. "Vibration Isolation of Lumped Masses Supported on Beam by Imposing Nodes Using Multiple Vibration Absorbers." Mechanical Engineering Research 6, no. 1 (May 11, 2016): 88. http://dx.doi.org/10.5539/mer.v6n1p88.

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<p class="1Body">In this paper, variable stiffness damped absorbers are used to isolate the substructures of Euler-Bernoulli beam, modelled as lumped masses, from vibrations. The novel algorithm is developed that can be used to determine the required absorber masses and resonance frequencies to impose nodes at selected locations on beam with the constraint of vibration amplitude of absorber mass. Numerical simulations are performed to show the effectiveness of the proposed algorithm. Experimental test is conducted on a cantilever beam with two absorbers to verify the numerical results.</p>

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34

Xiong, Yi Bo, Chun Ming Wang, and Lu Peng. "Numerical Simulation on Combined Deformation of Tip-Loaded Cantilever Beam with Particle Flow Code." Advanced Materials Research 378-379 (October 2011): 31–34. http://dx.doi.org/10.4028/www.scientific.net/amr.378-379.31.

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In order to calculate the combined deformations of an Euler-Bernoulli cantilever beam subjected to bending moment, twisting moment, transverse load and axial load, particle flow code in 3 dimensions (PFC3D) is used with parallel bonds model. The computed deformations, including transverse deflections, rotations about axis, maximum normal and shear stresses, were compared with the analytical beam-theory solution in terms of axial tension, axial compression and none axial load, respectively. Between computed results and analytical beam-theory solution, the error bands are greater than 99.7% at the beam tip, while the error of the transverse deflection of the whole beam is less than 0.6%. So, the PFC3D is able to precisely simulate the combined deformation of cantilever beam, and this work has special reference to engineering calculations and designs when PFC is applied to model the mechanical behaviors of continuum materials.

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35

Larsen, Kyle, Stefan Lehnardt, Bryce Anderson, Joseph Rowley, Richard Vanfleet, and Robert Davis. "Determining local modulus and strength of heterogeneous films by force–deflection mapping of microcantilevers." Review of Scientific Instruments 94, no. 3 (March 1, 2023): 033904. http://dx.doi.org/10.1063/5.0092934.

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Estimating the elastic modulus and strength of heterogeneous films requires local measurement techniques. For local mechanical film testing, microcantilevers were cut into suspended many-layer graphene using a focused ion beam. An optical transmittance technique was used to map thickness near the cantilevers, and multipoint force–deflection mapping with an atomic force microscope was used to record the compliance of the cantilevers. These data were used to estimate the elastic modulus of the film by fitting the compliance at multiple locations along the cantilever to a fixed-free Euler–Bernoulli beam model. This method resulted in a lower uncertainty than is possible from analyzing only a single force–deflection. The breaking strength of the film was also found by deflecting cantilevers until fracture. The average modulus and strength of the many-layer graphene films are 300 and 12 GPa, respectively. The multipoint force–deflection method is well suited to analyze films that are heterogeneous in thickness or wrinkled.

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36

Streator, J. L., and D. B. Bogy. "Accounting for Transducer Dynamics in the Measurement of Friction." Journal of Tribology 114, no. 1 (January 1, 1992): 86–94. http://dx.doi.org/10.1115/1.2920873.

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In many studies of sliding interfaces, the measurement of friction is complicated by quasi-harmonic vibrations of the transducer system. An analytical technique is introduced which accounts for the dynamic characteristics of a force transducer under periodic excitation, and is used to compute the forcing function in the sliding interface. The force transducer is modeled as an elastic cantilever-beam with an attached rigid mass. The forcing function is obtained by solving the time-dependent, fourth-order partial differential equation of Euler-Bernoulli beam theory. The solution is facilitated by the application of Fourier series expansions in time and eigenfunction expansions in space. Results of the method are compared to previous analyses of friction-induced vibration in which the elasticity of the transducer is modeled as a simple spring and the rigid body as a lumped mass, leading to a single degree-of-freedom (DOF) governing equation. It is found that a single DOF calculation based on instantaneous measurement of displacement agrees surprisingly well with the results of the Euler-Bernoulli analysis. A single DOF model based on instantaneous measurement of strain and a static displacement-strain calibration factor agrees well with the Euler-Bernoulli analysis for a low frequency range but deviates at higher frequencies.

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37

Cafeo, John A., Martin W. Trethewey, and H. Joseph Sommer. "Beam Element Structural Dynamics Modification Using Experimental Modal Rotational Data." Journal of Vibration and Acoustics 117, no. 3A (July 1, 1995): 265–71. http://dx.doi.org/10.1115/1.2874446.

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Structural dynamic modification (SDM) of a fixed-free (cantilever) beam to convert it into a fixed-fixed beam with experimental modal data is presented. The SDM focuses on incorporating experimental rotational degrees-of-freedom (DOF) measured with a novel laser measurement technique. A cantilever beam is tested to develop the experimental modal database including rotational degrees of freedom. A modal database from a finite-element model also is developed for comparison. A structural dynamic modification, with both databases, is performed using a Bernoulli-Euler beam to ground the free end of the cantilever beam. The hardware is then modified and a second experimental modal analysis of the resulting fixed-fixed beam performed. A finite-element model of the fixed-fixed beam also was created. Comparison of results from these four tests are used to assess the effectiveness of SDM using experimental modal rotational data. The evaluation shows that provided high quality experimental rotational modal data can be acquired, SDM work with beam elements can be effective in yielding accurate results.

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38

Garg, Anshul, and Santosha K. Dwivedy. "Theoretical and experimental investigation of parametrically excited piezoelectric energy harvester." MATEC Web of Conferences 211 (2018): 02009. http://dx.doi.org/10.1051/matecconf/201821102009.

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In the present work, a cantilever beam based piezoelectric energy harvester is investigated both theoretically and experimentally. The harvester is consists of a harmonically base excited vertical cantilever beam with a piezoelectric patch at the fixed end and a mass attached at an arbitrary position. The Euler-Bernoulli beam theory is applied considering the cantilever beam to be slender. The temporal nonlinear electromechanical governing equation of motion is obtained by using generalized Galerkin’s method considering two-mode approximation. Here for principal parametric resonance condition the steady state response of the voltage is obtained by using the method of multiple scales. The results are validated by developing an experimental setup of the harvester. For the harvester having a dimension of 295 mm×24 mm×7.6 mm, a maximum voltage of 40 V is obtained for a base motion of 9 mm with a frequency of 10.07 Hz when 15 gm mass is attached at a distance of 140 mm from the fixed end.

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39

Mobki, Hamed, Kaveh Rashvand, Saeid Afrang, Morteza H. Sadeghi, and Ghader Rezazadeh. "DESIGN, SIMULATION AND BIFURCATION ANALYSIS OF A NOVEL MICROMACHINED TUNABLE CAPACITOR WITH EXTENDED TUNABILITY." Transactions of the Canadian Society for Mechanical Engineering 38, no. 1 (March 2014): 15–29. http://dx.doi.org/10.1139/tcsme-2014-0002.

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In this paper, a novel RF MEMS variable capacitor has been presented. The applied techniques for increasing the tunability of the capacitor are the increasing of the maximum capacitance and decreasing of the minimum capacitance. The proposed structure is a simple cantilever Euler–Bernoulli micro-beam suspended between two conductive plates, in which the lower plate is considered as stationary reference electrode. In this structure, two pedestals are located in both tips of the cantilever beam. In the capacitive micro-structures, increasing the applied voltage decreases the equivalent stiffness of the structure and leads the system to an unstable condition (pull-in phenomenon). By deflecting the beam toward the upper (lower) plate the minimum (maximum) capacitance decreases (increases) and tunability increases consequently. The located pedestals increase and decrease the maximum and minimum capacitance respectively. The results show that the proposed structure increases the tunability of cantilever beam significantly. Furthermore, bifurcation behavior of movable electrode has been investigated.

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40

Voiculescu, I. R., M. E. Zaghloul, R. A. McGill, and J. F. Vignola. "Modelling and measurements of a composite microcantilever beam for chemical sensing applications." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220, no. 10 (October 1, 2006): 1601–8. http://dx.doi.org/10.1243/09544062jmes150.

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A resonant microcantilever beam gas sensor was designed and fabricated in Carnegie Mellon University using complementary metal oxide semiconductor (CMU-CMOS) technology. The cantilever beam modified with a suitable sorbent coating was demonstrated as a chemical transducer for monitoring hazardous vapours and gases at trace concentrations. The design of the cantilever beam included interdigitated fingers to allow electrostatic actuation of the device and a piezoresistive Wheatstone bridge design to read out the deflection signal. The cantilever beam resonant frequency was modelled using the Euler-Bernoulli beam theory and ANSYS. The beam resonant frequency was measured with an optical laser Doppler vibrometer. Good agreement was obtained among the measured, simulated, and modelled resonant frequencies. A custom sorbent polymer layer was coated on the surface of the cantilever beam to allow its operation as a gas-sensing device. The frequency response as a function of exposure to the nerve agent simulant dimethylmethylphosphonate (DMMP) at different concentrations was measured, which allowed a demonstrated detection at a concentration of 20 ppb or 0.1 mg/m3. The air-polymer partition coefficient K, for DMMP was estimated and compared favourably with the known values for related polymers.

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41

Li, Cheng, Wei Guo Huang, and Lin Quan Yao. "Micro Cantilever Beam Theory for Transverse Dynamics Using a Continuum Mechanics Model." Advanced Materials Research 415-417 (December 2011): 760–63. http://dx.doi.org/10.4028/www.scientific.net/amr.415-417.760.

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The vibrational characteristics of cantilever beams with initial axial tension were studied using a nonlocal continuum Euler-Bernoulli beam model. Small size effects are essential to nanotechnology and it can not be ignored in micro or nano scale. Nonlocal elasticity theory has been proved to work well in nanomechanics and it is considered into the governing equation which can be transformed into a fourth-order ordinary differential equation together with a dispersion relation. Boundary conditions are applied so as to determine the analytical solutions of vibrational mode shape and transverse deformation through a numerical method. Relations between natural frequency and the small scale parameter are obtained, including the fundamental and the second order frequencies. It is found that both the small scale parameter and dimensionless initial axial tension play remarkable roles in dynamic behaviors of micro cantilever beams and their effects are analyzed and discussed in detail.

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42

Sadeghi, Ali. "Increasing the Image Contrast of Atomic Force Microscope by Using Improved Rectangular Micro Cantilever." Applied Mechanics and Materials 110-116 (October 2011): 4888–92. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.4888.

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The resonant frequency of flexural vibrations for an atomic force microscope (AFM) cantilever has been investigated using the Euler-Bernoulli beam theory. The results show that for flexural vibration the frequency is sensitive to the contact position, the first frequency is sensitive only to the lower contact stiffness, but high order modes are sensitive in a larger range of contact stiffness. By increasing the height H, for a limited range of contact stiffness the sensitivity to the contact stiffness increases. This sensitivity controls the image contrast, or image quality. Furthermore, by increasing the angle between the cantilever and sample surface, the frequency decreases.

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43

Земсков, Андрей Владимирович, and Георгий Михайлович Файкин. "Euler-Bernoulli cantilever beam bending considering the inner diffusion flows finite propagation speed." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 4(46) (December 30, 2020): 107–14. http://dx.doi.org/10.37972/chgpu.2020.46.4.007.

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Исследуются нестационарные колебания балки Эйлера-Бернулли с учетом массопереноса. Используется модель упругой диффузии для многокомпонентных сред. Для получения решения задачи используются вариационный принцип Даламбера и метод эквивалентный граничных условий. Unsteady vibrations of the Euler-Bernoulli beam are studied taking into account mass transfer. The model of elastic diffusion for multicomponent media is used. To obtain a solution to the problem, the d’Alembert variational principle and the equivalent boundary conditions method are used.

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44

Keshmiri, Alireza, Nan Wu, and Quan Wang. "Free Vibration Analysis of a Nonlinearly Tapered Cone Beam by Adomian Decomposition Method." International Journal of Structural Stability and Dynamics 18, no. 07 (July 2018): 1850101. http://dx.doi.org/10.1142/s0219455418501018.

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In this paper, the free vibration of a nonlinearly tapered cone beam is analyzed based on the Euler–Bernoulli hypothesis. The characteristic/eigenvalue equation and mode shape functions of the nonlinearly tapered cone beam are derived by the Adomian decomposition method for the first time. Using a modified mathematical procedure, the natural frequencies and mode shape functions of a general nonuniform beam are analytically derived. Several numerical examples for the vibration of uniform and linearly tapered cantilever beams are presented and compared with previous results to validate the accuracy and fast convergence of the present approach. The natural frequencies and mode shapes of vibration of exponentially and trigonometrically tapered cone beams with different taper ratios are presented. The present approach enables engineers to analytically analyze tapered beams of nonuniform configurations used as various structural components in a mathematically efficient way.

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45

Hetnarski, Richard B., Ray A. West, and Joseph S. Torok. "Damping of Vibrations of Layered Elastic-Viscoelastic Beams." Applied Mechanics Reviews 46, no. 11S (November 1, 1993): S305—S311. http://dx.doi.org/10.1115/1.3122651.

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A five-layer cantilever beam consisting of an elastic core, two symmetric viscoelastic layers, and two elastic constraining layers is considered. The viscoelastic effects are incorporated in the Euler-Bernoulli beam theory. If the contraction and extension of the constraining layers is neglecterd a fourth order differential equation of motion is received. Inclusion of contraction and extension of the constraining layers results in a more accurate sixth order differential equation. Appropriate boundary conditions are derived. Laplace transforms are used extensively. Both the analytical solution and the numerical results are presented.

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46

Li, Xiang Fang, and Bao Lin Wang. "Bending and Fracture Properties of Small Scale Elastic Beams – A Nonlocal Analysis." Applied Mechanics and Materials 152-154 (January 2012): 1417–26. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.1417.

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Using the nonlocal elasticity theory, this paper presents a static analysis of a microbeam according to the Timoshenko beam model. A fourth-order governing differential equation is derived and a general solution is suggested. For a cantilever beam at nanoscale subjected to uniform distributed loading, explicit expressions for deflection, rotation and strain energy are obtained. The nonlocal effect decreases the deflection and maximum stress distribution. With a double cantilever beam model, the strain energy release rate of a cracked beam is evaluated, and the results obtained show that the strain energy release rate is decreased (hence an increased apparent fracture toughness is measured) when the beam thickness is several times the material characteristic length. However, in the absence of a uniformly distributed loading, the nonlocal beam theory fails to account for the size-dependent properties for static analysis. Particularly, the nonlocal Euler-Bernoulli beam can be analytically obtained from the nonlocal Timoshenko beam if the apparent shear modulus is sufficiently large.

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47

Fedotov, A. V. "Active vibration suppression of Bernoulli–Euler beam: experiment and numerical simulation." Cybernetics and Physics, Volume 8, 2019, Number 4 (December 30, 2019): 228–34. http://dx.doi.org/10.35470/2226-4116-2019-8-4-228-234.

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In order to design the most effective systems of vibration control of a distributed elastic object, it is necessary to have a model of this object, which would allow one to obtain the control results numerically without experiment. This gives an opportunity to compare the results of different control systems with each other and choose the most efficient ones. The paper is concerned with numerical simulation of the results of experimental study on suppression of forced vibrations of a cantilever metal beam with piezoelectric sensors and actuators by finite element method. The new designed control systems are based upon the results of numerical simulation and turn out to be more effective than those tested in the experiment. The numerical results previously received for modal control systems were significantly improved by using the optimization procedure, which allows one to select the optimal parameters of the filters used in the feedback loops of the designed control systems.

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48

Viet, N. V., W. Zaki, and Quan Wang. "Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis." Applied Mathematics and Mechanics 41, no. 12 (November 18, 2020): 1787–804. http://dx.doi.org/10.1007/s10483-020-2664-8.

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AbstractAdvancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex functionally graded material (FGM) sectioned beams. Portions of these beams may be made from different materials with possibly different gradients of material properties. The present work proposes models to investigate the free vibration of FGM sectioned beams based on one-dimensional (1D) finite element analysis. For this purpose, a sample beam is divided into discrete elements, and the total energy stored in each element during vibration is computed by considering either Timoshenko or Euler-Bernoulli beam theories. Then, Hamilton’s principle is used to derive the equations of motion for the beam. The effects of material properties and dimensions of FGM sections on the beam’s natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model (TM). The presented model is validated by comparison with three-dimensional (3D) finite element simulations of the first three mode shapes of the beam.

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49

Lu, Xu Bin, Zhong Rong Lv, and Ji Ke Liu. "Vibration Response Analysis of a Stepped Beam with Crack Using Composite Element Method." Advanced Materials Research 199-200 (February 2011): 835–38. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.835.

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The composite element method is utilized to discretise a stepped Euler-Bernoulli beam with a crack. The local stiffness reduction due to the crack is introduced by using a simplified crack model. The finite element equation for the forced vibration analysis is obtained using the composite element method (CEM). The forced vibration response of the cracked stepped beam is numerically calculated using Newmark integration method. Numerical results indicate that the position and depth of a crack affects the low and high natural frequencies and modes of a cantilever beam, respectively. And the position of the crack has significant effects on the dynamic responses of the beam.

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50

Li, Jiantao, Hua Deng, and Wenjun Jiang. "Dynamic response and vibration suppression of a cantilevered pipe conveying fluid under periodic excitation." Journal of Vibration and Control 25, no. 11 (March 25, 2019): 1695–705. http://dx.doi.org/10.1177/1077546319837789.

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A feedforward vibration suppression method is proposed for cantilever pipes conveying fluid. The fluid–structure interaction dynamic equation of the cantilever pipeline system is first established, based on the Euler–Bernoulli beam model. Next, the pulsation function of pipeline pressure is established using the Fourier series, which will serve as the input of the cantilever pipeline system. Then, analysis of transient response is carried out, and the relationship between input signal parameters and the end vibration is studied. Finally, a feedforward control strategy based on optimization of input signal parameters is proposed for minimizing the end vibration. Both theoretical derivation and experimental results in industrial equipment show that the proposed method (i.e., optimization of pressure function parameters) is effective and can suppress the structural vibration of a cantilever pipe conveying fluid.

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