M.F. Liu¹

CMC-Computers, Materials & Continua, Vol.22, No.2, pp. 97-128, 2011, DOI:10.3970/cmc.2011.022.097

Abstract A new invented Orthogonal Tapered Beam Functions (OTBFs) have been introduced in this paper and used in accordance with the Rayleigh-Ritz method to determine the natural frequencies and mode shapes of the non-uniform rectangular isotropic plates with varying thickness in one or two directions. The generation of the OTBFs is based on the static solution of a one-dimensional beam problem subjected to constant applied load, and then extends to an orthogonal or orthonomal infinite set of admissible functions by performing the three-term recurrence scheme. A wide range of non-uniform rectangular plate whose domain is referenced by a so-called truncation factor… More >

Chih-Ping Wu^1,2, Hao-Yuan Li²

CMC-Computers, Materials & Continua, Vol.19, No.2, pp. 155-198, 2010, DOI:10.3970/cmc.2010.019.155

Abstract The Reissner mixed variational theorem (RMVT)- and principle of virtual displacements (PVD)-based finite layer methods (FLMs) are developed for the quasi-three-dimensional (3D) free vibration analysis of simply-supported, multilayered composite and functionally graded material (FGM) plates. The material properties of the FGM layers are assumed to obey either an exponent-law exponentially varied with the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In these formulations, the plate is divided into a number of finite layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of… More >