Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core

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

“…The authors' results from all three shell theories are found to be having excellent agreement with those of Fazzolari and Carrera[35] for ROM micromechanical model for shell with R y /a = 5. The results obtained from MT model are marginally lower than corresponding ROM results.…”

“…Alibeigloo and Liew [34] proposed an exact three-dimensional free vibration solution of simply supported FGM sandwich cylindrical panel using the Fourier series and state space technique. Fazzolari and Carrera [35] developed a hierarchical trigonometric Ritz formulation and employed the same to perform free vibration analysis of doubly curved shallow and deep shells with single layered FGM and sandwich shells with functionally graded core. 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.…”

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

“…A lot of literature on free vibration of laminated functionally graded structures can be found [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. However, it is evident that information available about the vibration of laminated FGM shallow shells is far from complete.…”

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.…”