Abstract
In this research, free and forced vibration of functionally graded sandwich beams is considered using Timoshenko beam theory which takes into account the significant effects of transverse shear deformation and rotary inertia. The governing equations of motion are formulated from Lagrange's equations and they are solved by using The Ritz and Newmark methods. The results are presented in both tabular and graphical forms to show the effects of layer thickness ratios, boundary conditions, length to height ratios, etc. on natural frequencies and dynamic deflections of the beams. According to the numerical results, all parametric studies considered in this research have significant impact on free and forced behaviour of the beams; for example, the frequency is low and the dynamic deflection is large for the beams which are hinged at both ends.
Highlights
Functionally graded (FG) sandwich structures play a vital role in modern structural engineering with excellent properties in high strength-to-weight ratio
In the literature, buckling and vibration of functionally graded (FG) sandwich beams with the combination of general and non-general boundary conditions were considered by Tossapanon and Wattanasakulpong [1] and Trinh et al [2]
In the study of Vo et al [6], the development of finite element model was presented for vibration and buckling of FG sandwich beams under various general boundary conditions
Summary
Functionally graded (FG) sandwich structures play a vital role in modern structural engineering with excellent properties in high strength-to-weight ratio. In the literature, buckling and vibration of FG sandwich beams with the combination of general and non-general boundary conditions were considered by Tossapanon and Wattanasakulpong [1] and Trinh et al [2]. A quasi-3D theory was employed to deal with static bending, buckling and vibration problems of FG sandwich beams in Refs. In the study of Vo et al [6], the development of finite element model was presented for vibration and buckling of FG sandwich beams under various general boundary conditions. The relationship between fundamental natural frequency and in-plane loading was presented in the study. This investigation aims to extend research work to deal with dynamic behaviour of FG sandwich beams under various kinds of different dynamic loadings. Many important parametric studies such as boundary condition, layer thickness ratio, material volume fraction index, etc. are investigated
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