A modified Fourier–Ritz approach for free vibration analysis of laminated functionally graded shallow shells with general boundary conditions

A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells

“…Ye et al [36] employed threedimensional shell theory of elasticity and energy based Rayleigh-Ritz procedure to carry out free vibration analysis of laminated functionally graded spherical shells under general boundary conditions. Recently, Jin et al [37] presented a modified Fourier-Ritz approach for free vibration analysis of laminated functionally graded shallow shells with general boundary conditions using first-order shear deformation shallow shell theory.…”

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

“…The modified Fourier-Ritz approach was proposed by Jin et al [49] to solve the free vibrations of laminated functionally graded shallow shells with general boundary conditions. The presented method consists of two main steps: firstly, the admissible functions of the structure elements are expanded into the modified Fourier series which consist of the two-dimensional (2D) Fourier cosine series and auxiliary functions to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions; secondly, the natural frequencies of the structure elements are obtained by using the variational operation (Ritz method) in terms of the unknown the expanded coefficient.…”

“…The method has been subsequently exploited to determine the vibration behaviors of structures [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Recently, a new method of Fourier-Ritz approach was proposed by Jin et al [49], based on the improved Fourier series method to analyze the free vibration of laminated functionally graded shallow shells with general boundary conditions. In contrast to most existing techniques, the modified Fourier-Ritz method can be universally applicable to a variety of boundary conditions including all the classical cases, elastic restraints, and their combinations without the need of making any changes of the solution procedure.…”

Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

“…Compared with the composite laminated and functionally graded sector plate, the existing results of FG sandwich sector plates are too scarce for engineering applications and comparative studies. However, we can know the importance of the FG sandwich sector plates from the existing published literature about other FG sandwich structures [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. Thus, an accurate frequency and mode shape determination are of considerable importance for the technical design of FG sandwich sector plates.…”