Higher-order trigonometric series-based analytical solution to free transverse vibration of suspended laminated composite slabs

Abstract

Suspended floors can be designed as effective pendulum seismic isolators for high-rise buildings. However, research studies on the free vibration of suspended laminated composite slabs are relatively limited. This paper presents a comprehensive analytical solution to the free vibration problem of suspended laminated composite slabs. The equations of elasticity are used to establish the equation of motion. The critical factors influencing free vibration are explicitly considered, including the material anisotropy, number of layers, elastic properties, rotatory inertia, and transverse shear of plates. The higher-order trigonometric series are utilized to solve the dynamic equations. The developed analytical solution is a complete and realistic form of the existing analytical solutions in literature and has the capability of converging fast. The proposed analytical solution does not have a dependency on the shape function as well as separate-of-variable forms unlike the Finite Element Method (FEM). Moreover, the FEM requires an in-depth mesh convergence analysis, particularly for higher-magnitude natural frequencies, which is not the case for the proposed analytical solution for any infinite range of eigenfrequencies. The proposed solution procedure is first verified by the simplified problems available in the literature. For more complex problems, the finite element analysis results obtained from Abaqus are employed to validate the analytical solution. The comparison demonstrates that the proposed analytical solution is accurate and reliable for a wide range of case-study examples. It is found that the natural frequencies of suspended laminated composite slabs are significantly influenced by the crucial factors under investigation.