Three-dimensional free vibration analysis of thick cylindrical shells with general end conditions and resting on elastic foundations

Three-dimensional vibration analysis of laminated functionally graded spherical shells with general boundary conditions

“…As is well-known, the selection of appropriate admissible functions is of critical importance in the Rayleigh-Ritz method because the choice of assumed functions determines the accuracy and convergence of the solution. Recently, an accurate modified Fourier series method was developed for the vibration analysis of 1-D [53,54] and 2-D [55][56][57][58] as well as 3D [59] structures with uniform elastic boundary conditions. In this method, each displacement components of a structure is constructed as a conventional cosine Fourier series with certain auxiliary functions.…”

“…More detailed information about the modified Fourier series can be seen in Refs. [55][56][57][58][59].…”

Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

“…In the practical application, the Pasternak model (also referred to as the two-parameter model) [24][25][26] is widely used to describe the mechanical behavior of the foundation, in which the wellknown Winkler model [27] is a special case. In addition, the boundary condition may not always be classical case in reality, and a variety of possible boundary conditions including classical boundary conditions, elastic boundary restraints, and the combinations of two or more conditions may be encountered [6][7][8][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. Based on the open published paper, we can know that merely Zhou et al [48,49] extended the Chebyshev-Ritz method to study the free vibration characteristics of rectangular thick plates and thick circular plates resting on elastic foundations, respectively.…”

Vibrations of Composite Laminated Circular Panels and Shells of Revolution with General Elastic Boundary Conditions via Fourier-Ritz Method

“…Later, the method fast extended to cope with other structures (i.e. beams, plates, shells and coupled structures) by the Du [27][28][29][30], Jin [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46], Wang et al [47][48][49][50][51][52] in the last ten years due to the superiority compared with other methods. The detailed theoretical analyses and mathematical principle can been seen in Refs [24][25][26].…”