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Nonlinear vibration of Timoshenko FG porous sandwich beams subjected to a harmonic axial load

Earthquake Engineering and Engineering Vibration 2024年第3期23卷 649-662页

作者： Milad Lezgi Moein Zanjanchi Nikoo majid ghadiri Department of Civil Engineering Sharif University of TechnologyTehran ***Iran Civil Engineering Department K.N.Toosi University of TechnologyTehran ***Iran Faculty of Engineering Department of MechanicsImam Khomeini International UniversityQazvin ***Iran

In this study,the instability and bifurcation diagrams of a functionally graded(FG)porous sandwich beam on an elastic,viscous foundation which is influenced by an axial load,are investigated with an analytical *** do so,the Timoshenko beam theory is utilized to take the shear deformations into account,and the nonlinear Von-Karman approach is adopted to acquire the equations of ***,to turn the partial differential equations(PDEs)into ordinary differential equations(ODEs)in the case of equations of motion,the method of Galerkin is employed,followed by the multiple time scale method to solve the resulting *** impact of parameters affecting the response of the beam,including the porosity distribution,porosity coefficient,temperature increments,slenderness,thickness,and damping ratios,are explicitly *** is found that the parameters mentioned above affect the bifurcation points and instability of the sandwich porous beams,some of which,including the effect of temperature and porosity distribution,are less noticeable.

关键词： sandwich beam Timoshenko beam parametric excitation bifurcation diagrams dynamic instability

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Nonlinear Vibration Analysis of Functionally GradedNanobeam Using Homotopy Perturbation Method

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Advances in Applied Mathematics and Mechanics 2017年第1期9卷 144-156页

作者： majid ghadiri Mohsen Safi Faculty of Engineering Department of MechanicsImam Khomeini International UniversityQazvinIran

In this paper, He’s homotopy perturbation method is utilized to obtainthe analytical solution for the nonlinear natural frequency of functionally gradednanobeam. The functionally graded nanobeam is modeled using the Eringen’s nonlocalelasticity theory based on Euler-Bernoulli beam theory with von Karman nonlinearityrelation. The boundary conditions of problem are considered with both sidessimply supported and simply supported-clamped. The Galerkin’s method is utilizedto decrease the nonlinear partial differential equation to a nonlinear second-order ordinarydifferential equation. Based on numerical results, homotopy perturbationmethodconvergence is illustrated. According to obtained results, it is seen that the second termof the homotopy perturbation method gives extremely precise solution.

关键词： Homotopy perturbation method Lindstedt-Poincare method analytical solution nonlocal nonlinear free vibration functionally graded nanobeam

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