A Unified Transient Vibration Analysis of FGM Sandwich Plates in Thermal Environment Based on a Further Refined Zigzag Plate Theory

Abstract

In this study, a simple and unified process is established for transient vibration analysis of functionally graded material (FGM) sandwich plates in thermal environment. The temperature field, considered constant in the plane, is distributed along the thickness with uniform, linear and nonlinear profiles. For the material properties, both temperature and position dependence are taken into account. A further refined zigzag plate theory accounting for partitioned transverse displacements and piecewise-continuous in-plane displacements is developed within the framework of Hamilton’s principle including thermal effects. Appropriately and simplicity representation of the deformation states is provided in the governing equations. A spectral analysis technique, namely, method of reverberation ray matrix (MRRM), is employed to calculate the transient vibration responses of FGM sandwich plates with general boundary conditions and arbitrary external loadings. The artificial spring technology and the equivalent wave source vector are introduced to improve the numerical stability and parametric adjustability of MRRM. The accuracy, flexibility and efficiency of the proposed process are discussed using many numerical examples. On this basis, the effects of the boundary parameters, FGM gradient index, core-to-facesheet thickness ratio, thermal properties and external loadings on the transient vibration behaviors of FGM sandwich plates are thoroughly investigated.

New Accomplishments on the Equivalence of the First-Order Displacement-Based Zigzag Theories through a Unified Formulation

“…Based on Cho and Parmerter's model, Nguyen et al [39,40] addressed the viscoelastic study of laminated composite plates. In the RZT-based framework, various problems and study cases have been addressed, including functionally graded and carbonnanotube-reinforced structures [41][42][43], the transient response of innovative multilayered plates [44,45], delamination and damage assessment [46][47][48][49][50], thermal and buckling load conditions [51,52], linear and non-linear analyses [53][54][55], laminated shell problems [56][57][58], angle-ply lamination schemes [59][60][61], laminates with viscoelastic layers [62,63], solutions using the peridynamic differential operator [64,65], optimisation [66], isogeometric analysis (IGA) [67,68] and inverse FEM studies [69][70][71][72][73] for structural health monitoring purposes.…”

Acoustic field characteristic analysis of the rotary acoustic cavity coupled system

“…Shi et al 8 proposed a method for the analysis of acoustic modals and steady-state responses of arbitrary triangular prism and quadrangular prism acoustic cavities with impedance walls based on the three-dimensional improved Fourier series. Within the framework of Hamilton's principle, Shao et al 9 established a simple and unified process for transient vibration analysis of functionally graded material (FGM) sandwich plates in thermal environment.…”