Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method

By D. Zhou, Y. Cheung, F. Au, S. H. Lo. 2002

176 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e9af8be29286022f759b62417c2fa1b9566abf29

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In Biomedical Engineering

In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Three-dimensional vibration analysis of functionally graded material plates in thermal environment (2009, background): “The three displacements of rectangular plates are expanded by Chebyshev polynomial series multiplied by boundary functions [10,11].”
Exact characteristic equations for some of classical boundary conditions of vibrating moderately thick rectangular plates (2005, methodology): “More recently Zhou et al. (2002) investigated the free vibration of rectangular plates with any thickness using three-dimensional analysis and selecting the Chebyshev polynomials as the admissible functions of the plate in the Ritz method.”
On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results (2015, methodology): “[208,209] presented three-dimensional vibration analysis of thick rectangular plates using Ritz method.”
Three‐dimensional vibration analysis of rectangular thick plates on Pasternak foundation (2004, methodology): “Comparing the present results with those of square thick plates without foundation [29], one can find out that most of the eigenfrequencies which remain fairly constant correspond to the symmetric modes in the thickness direction.”
Post-buckling analysis of functionally graded rectangular plates (2007, unknown): “[21], and many others.”
Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT (2019, unknown): “The obtained results are compared with those given by exact 3D solution developed by Zhou et al .”
Three-dimensional analysis of an all-round clamped plate made of functionally graded materials (2005, methodology): “Remarkably, the Chebyshev polynomials employed as admissible functions have been proven to be highly efficient, as well as stable and accurate in many numerical applications (see Zhou et al. [ 8 ] for the isotropic case).”
Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials (2015, unknown): “[43, 44] used Chebyshev polynomials in studying the three-dimensional vibration of thick rectangular and circular plates.”
Free vibration of tapered isotropic rectangular plates (2012, background): “…inspection of the excellent review articles by Leissa (1969, 1977a,b, 1981a,b, 1987a,b) and Liew et al. (1995) and other comprehensive works by Cheung and Zhou (2000), Dickinson and Blasio (1986), Leissa (1973), Liew et al. (1990), Lim et al. (1989), Yamada and Irie (1987) and Zhou et al. (2002).”