A unified accurate solution for vibration analysis of arbitrary functionally graded spherical shell segments with general end restraints

Free vibration analysis of laminated composite and functionally graded sector plates with general boundary conditions

“…Since the restriction of geometric boundary conditions is relaxed by the boundary spring, any linear dependence and complete basis functions can be employed. In this paper, a modified Fourier series is adopted to represent the displacement and rotation components of sector plates [30][31][32] …”

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].…”

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

“…However, from the literatures review, we also know that the most existing numerical solutions for the title problem usually take account of a onefold computational model instead of unified computational model. For instance, Su et al [7][8][9] divided the open and closed functionally graded cylindrical, conical, spherical shells to study and resort different admissible functions by means of the modified Fourier series technology. However, in practical project application, the structural forms are generally unknown.…”

“…Aragh and Hedayati [6] dealt with the free vibration and static response of a twodimensional functionally graded (2D FGM) metal/ceramic open cylindrical shell with classical boundary conditions by using 2D generalized differential quadrature method. Su et al [7][8][9] applied the modified Fourier series and Rayleigh-Ritz method to analyze the free vibrations of functionally graded open and closed shells including cylindrical, conical, and spherical ones with general boundary conditions based on first-order shear deformation theory. Sofiyev and Kuruoglu [10][11][12][13] presented a theoretical approach on the basis of the Galerkin method to solve vibration problems of functionally graded (FG) truncated and complete conical shells under mixed classical boundary conditions and resting on elastic 2 Mathematical Problems in Engineering foundations.…”

“…In order to check the present method, the numerical results reported by Su et al [7][8][9], Qu et al [27], and Tornabene et al [1,3,52] are also given in the above tables for comparison. From the comparisons, we can see a consistent agreement of present results taken from the current proposed unified approach and referential data.…”