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Based on the modified couple stress theory and the Timoshenko beam theory, the free vibration and buckling mechanics model for 2D functionally graded microbeams with variable cross sections was established by means of the variational principle. The model contains the intrinsic material length scale parameters of the metal and ceramic components, which can predict the size effects of microbeams. The Ritz method was used to obtain the numerical solution of the vibration frequencies and critical buckling loads of the microbeams under arbitrary boundary conditions. Numerical examples reveal that, when the thickness of the microbeam decreases, the dimensionless 1st-order frequency and the dimensionless critical buckling load will increase, and the scale effect will grow larger. The effect of the taper ratio on the dimensionless 1st-order frequency of the microbeam is closely related to the boundary conditions. At the same time, the effects of the taper ratios of the thickness and the width are also significantly different. The dimensionless 1st-order frequencies of microbeams increase with the material length scale parameter ratios of ceramic and metal, and the degrees of increase are different under different boundary conditions. The thick-direction and axial material gradient indexes also have significant influences on the free vibration and buckling behavior of the microbeam. [ABSTRACT FROM AUTHOR]

To acquire exact solutions of double-functionally graded Timoshenko beam system on Winkler-Pasternk elastic foundation, which are benchmarks of double-beam systems in the field of engineering, motion differential equations of double-beam system are derived using Hamilton’s principle. In this paper, the exact dynamic stiffness matrix of double-functionally graded Timoshenko beam system on Winkler-Pasternak under axial loading are established and the damping of the connecting layer is also taken into consideration. The exact natural frequency and buckling load are obtained using Wittrick-William algorithm. To comprehensively analyze dynamic characteristics of double beam system, the effect of gradient parameter, foundation parameters, axial loading and connecting stiffness on the frequency and buckling load is compared, and the influence of damping factor is also investigated. Finally, dynamic response of double-beam system is studied using Fourier transformation. [ABSTRACT FROM AUTHOR]