Free vibration of in-plane bi-directional functionally graded materials rectangular plates with geometric imperfections and general elastic restraints - Chen, Xiaochao; Lu, Yixin; Wu, Zhangbin; Shao, Yichuan; Xue, Xin; Wu, Yiwan (Aerospace science and technology, 2023)
This research addresses the free vibration performance of bi-directional functionally graded materials (BDFGMs) rectangular plate with general boundary restraints and geometrical imperfections. The symmetric/asymmetric material distributions subject to power-law along in-plane two directions are considered. Two types of geometric imperfections are formulated employing transcendental functions, including the sine-type imperfection which is global eccentric/symmetrical and depicted by sine and exponential functions, and the cosine-type global/localized imperfections which is simulated by hyperbolic and cosine functions. The general boundary restraints are imitated by artificial virtual springs. The Lagrangian energy function is formulated, and then vibration characteristics of plates are acquired with the Ritz method and improved Fourier series. Verifications are carried out for accuracy of theoretical model and reliability of solution method. A comprehensive numerical investigation are exhibited to explore the influencing mechanism of material distribution patterns, geometrical imperfection modal and elastic boundary restraints on vibration performance of rectangular plates. The results show that the in-plane material gradient can function as regulatory measures for dynamic characteristic of plates. In addition, geometric imperfections may cause singularity in vibration performance of plate. These innovative results may serve as a benchmark for future studies on design or analysis of plates.