Vibration analysis of a functionally graded beam under a moving mass by using different beam theories

2010 ◽  
Vol 92 (4) ◽  
pp. 904-917 ◽  
Author(s):  
Mesut Şimşek
Keyword(s):  
Vibration Analysis ◽  
Functionally Graded ◽  
Moving Mass ◽  
Functionally Graded Beam ◽  
Beam Theories

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

2020 ◽  
Vol 23 (16) ◽  
pp. 3415-3428
Author(s):  
Yusuf Cunedioglu ◽  
Shkelzen Shabani
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Single Edge ◽  
Functionally Graded Beam ◽  
Cross Sectional

Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail.

Nonlinear free and forced vibration analysis of embedded functionally graded sandwich micro beam with moving mass

2016 ◽  
Vol 20 (4) ◽  
pp. 462-492 ◽  
Author(s):  
M Arefi ◽  
M Pourjamshidian ◽  
A Ghorbanpour Arani
Keyword(s):  
Differential Equation ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Scale Effects ◽  
Nonlinear Partial Differential Equation ◽  
Gradient Elasticity ◽  
Functionally Graded ◽  
Small Scale ◽  
Moving Mass ◽  
Forced Vibration Analysis

In this study, nonlinear free and forced vibration analysis of an embedded functionally graded sandwich micro-beam with a moving mass is investigated. The velocity of moving mass is assumed constant. The structure is resting on nonlinear Pasternak foundation. The governing equation of motion is obtained using Hamilton's principle based on the Euler–Bernouli model with considering nonlinear terms in strain–displacement relation. Strain gradient elasticity theory is used to model the small scale effects. The micro-beam contains a homogenous core and two integrated functionally graded face-sheets. Mechanical properties except Poisson ratio are assumed to be variable based on the power-law distribution along the thickness direction. Galerkin's decomposition technique is implemented to convert nonlinear partial differential equation to a nonlinear ordinary differential equation. Multiple times scale method is applied to derive closed form approximate solution for free and forced vibration and nonlinear natural frequencies of the micro-beams. Accuracy of the obtained results using current issue may be justified by comparing with those obtained by existing results of the literature. The effect of some important parameters such as length scale parameter, power gradient index, nonlinear elastic foundation, aspect ratio, position, and velocity of moving mass and boundary conditions is studied on the various responses of the micro-beam such as nonlinear natural frequency, frequency response, and force–response curves.

Analytical responses of functionally graded beam under moving mass using Caputo and Caputo–Fabrizio fractional derivative models

2020 ◽  
Vol 26 (19-20) ◽  
pp. 1859-1867 ◽  
Author(s):  
Ibrahim M Abu-Alshaikh ◽  
Amro A Almbaidin
Keyword(s):  
Fractional Derivative ◽  
Functionally Graded ◽  
Beam Deflection ◽  
Moving Mass ◽  
Functionally Graded Beam ◽  
The Laplace Transform ◽  
Voigt Model ◽  
The Difference ◽  
Euler Bernoulli Beam

In this article, a functionally graded simply supported Euler–Bernoulli beam subjected to moving mass is considered in which the beam-damping is described using fractional Kelvin–Voigt model. A comparison between Caputo and Caputo–Fabrizio fractional derivatives for obtaining the analytical dynamic response of the beam is carried out. The equation of motion is solved by the decomposition method with the cooperation of the Laplace transform. Two verification studies were performed to check the validity of the solutions. The results show that the grading order, the velocity of the moving mass and the fractional derivative order have significant effects on the beam deflection, whereas the difference between the results of the two fractional derivative models is expressed by the determination of the correlation coefficient.

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