High frequency analysis of the functionally graded sandwich nanobeams embedded in elastic foundations using nonlocal quasi-3D theory

Abstract

This study focuses on the high frequency analysis of the functionally graded sandwich nanobeams resting on elastic foundations for the first time. In the current work, two types of sandwich structures, namely hard-core and soft-core sandwich beams, are considered. The elastic foundations are modeled using a two-parameter foundation model with a spring layer and a shear layer. For the size-dependent effects, the nonlocal elasticity theory is employed in conjunction with a quasi-3D theory. Hamilton's principle is applied to establish the governing equations of the motion of the nanobeams. A comprehensive parametric study is provided to demonstrate the free vibration behaviors of the sandwich nanobeams in both low and high frequency modes, with more focus on the high frequency analysis. Therefore, the present results contribute to a deeper understanding of the dynamic response of the functionally graded sandwich nanobeams in the high frequency range.