Dynamic Analysis of a Fiber-Reinforced Composite Beam under a Moving Load by the Ritz Method

Akbaş, Şeref Doğuşcan; Ersoy, Hakan; Akgöz, Bekir; Cívalek, Ömer

doi:10.3390/math9091048

Cited by 87 publications

(20 citation statements)

References 53 publications

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“…Akgöz and Civalek [24] investigated the static bending and buckling behavior of the size dependent micro-beams based on shear deformation and modified strain gradient theory. Akbas et al [25] discussed the dynamic responses of fiberreinforced composite Timoshenko beam obtained using the Ritz method. The systems analyzed in the above works can be re-modeled using FG rotors/beams, and the DSM formulations can be developed based on the approach used in this study to investigate the advantages and disadvantages of replacing the materials used in these systems with FGMs.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Stiffness Matrix Approach to Free Vibration Analysis of Functionally Graded Rotor Bearing System Subjected to Thermal Gradients

2022

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The dynamic stiffness matrix (DSM) method, an analytical method that provides exact solutions, has been used for the first time for the free vibration analysis of a functionally graded (FG) rotor bearing system subjected to temperature gradients and to investigate its application to FG rotors. The material gradation occurs based on the power law between the inner metal core and the outer ceramic rich layer of the FG rotor. The temperature gradation follows the Fourier law of heat conduction which leads to non-linear temperature distribution (NLTD) in the radial direction of the FG rotor. The development of the DSM formulations for Timoshenko FG rotor elements using the governing equations derived from translational and rotational equilibrium conditions is the novelty of the present work. The DSM of the FG rotor elements, rigid disk and linear isotropic bearings are assembled to obtain the global dynamic stiffness matrix of the FG rotor bearing system. The natural whirl frequencies are computed from the global DSM using the Wittrick–William algorithm as a root searching technique. The natural and whirl frequencies are validated with the results available in the literature and the exactness of the DSM method has been exemplified.

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Section: Introductionmentioning

confidence: 99%

Dynamic Stiffness Matrix Approach to Free Vibration Analysis of Functionally Graded Rotor Bearing System Subjected to Thermal Gradients

2022

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“…And the analysis results provide a theoretical basis for optimizing the weaving process parameters and a method for investigating beam vibration problems for different shapes 24,25 and materials. 26,27 Theoretical model construction…”

Section: Introductionmentioning

confidence: 99%

Analysis of 3D composite preform contour locking parameters based on vibration characteristics

Sun

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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To ensure the smooth insertion of the side rod/fiber bundle during the three-dimensional woven preform contour locking process, the influence of the diameter, speed, and other parameters on the free end vibration displacement response of the side rod and the fiber-carrying needle is analyzed. By calculating the kinetic energy and potential energy of the two separately, the dynamic equations of the side rod and the fiber-carrying needle are established based on Hamilton's principle and discretized. The state equations are solved using the Runge–Kutta method, and the free end vibration displacement responses of the side rod and the fiber-carrying needle for different parameters are obtained. The results show that the equilibrium position and the maximum amplitude of the free end of the side rod and the fiber-carrying needle decrease with the increase of the section diameter and the decrease of the axial speed. And the circular tube wall thickness has less impact on the free end vibration displacement of the fiber-carrying needle. The overall analysis shows that the fiber-carrying needle vibration response is smaller than that of the side rod under the same parameters.

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“…7 Moreover, many studies have been performed on the mechanical characteristics of composite structures reinforced by carbon nanotubes. [8][9][10][11][12][13][14] On the other hand, nanowire/rod structures of some chemical molecules are employed in field effect transistor, solar cell, and gas sensor systems. [15][16][17] It can be stated that small-scaled structures perform a task in living physiology as well as such applications.…”

Section: Introductionmentioning

confidence: 99%

A new eigenvalue problem solver for thermo‐mechanical vibration of Timoshenko nanobeams by an innovative nonlocal finite element method

Numanoğlu

Ersoy

Akgöz

et al. 2021

Math Methods in App Sciences

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121

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In this study, size‐dependent thermo‐mechanical vibration analysis of nanobeams is examined. Size‐dependent dynamic equations are obtained by implementing Hamilton's principle based on Timoshenko beam theory and then combined with stress equation of nonlocal elasticity theory. The separation of variables total method and finite element formulation is utilized to solve the eigenvalue problem. Local and nonlocal stiffness and mass matrices are firstly derived by using a weighted residual method for the finite element analysis. The accuracy of the finite element solution is demonstrated by comparisons with the earlier studies. Then, nondimensional frequencies of nanobeams with different boundary conditions based on a nonlocal finite element method are presented for vibration analysis that cannot be analytically solved under different parameters. It is aimed to emphasize the importance of the nonlocal finite element method in the size‐dependent vibration behavior of nanobeams which form different components of nano‐electro‐mechanical systems.

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Dynamic Analysis of a Fiber-Reinforced Composite Beam under a Moving Load by the Ritz Method

Cited by 87 publications

References 53 publications

Dynamic Stiffness Matrix Approach to Free Vibration Analysis of Functionally Graded Rotor Bearing System Subjected to Thermal Gradients

Dynamic Stiffness Matrix Approach to Free Vibration Analysis of Functionally Graded Rotor Bearing System Subjected to Thermal Gradients

Analysis of 3D composite preform contour locking parameters based on vibration characteristics

A new eigenvalue problem solver for thermo‐mechanical vibration of Timoshenko nanobeams by an innovative nonlocal finite element method

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