Boundary beam characteristics orthonormal polynomials in energy approach for vibration of symmetric laminates — I: Classical boundary conditions

Free vibration of two-side simply-supported laminated cylindrical panels via the mesh-free kp-Ritz method

“…The products of eigenfunctions of vibrating beams [3][4][5][6][7] are the most commonly used two-dimensional trial functions. Other frequently used functions include degenerated beam functions [8], orthogonal characteristic beam polynomials [9][10][11][12][13][14], and spline functions [15]. The use of two-dimensional polynomials as basic functions has attracted special attention in recent years, and noteworthy works in the vibration analysis of general two-dimensional structures of arbitrary boundary conditions include those of Bhat [16], Liew and Lam [17], Liew et al [18] and Liew and Wang [19,20].…”

An efficient meshfree method for vibration analysis of laminated composite plates

“…Other approaches have been also successfully applied to vibration analysis of laminated composite plates, e.g. the Rizt, p-Ritz and Rayleigh-Ritz methods [5][6][7][8][9][10][11][12][13], the strip element method [14,15], and the discrete singular convolution (DSC) method [16,17]. Bellman et al [18] introduced the differential quadrature technique initially for solving nonlinear partial differential equations, which was later applied to vibration problems of composite laminates [19][20][21][22][23].…”

Explicit local buckling analysis of rotationally restrained composite plates under uniaxial compression

“…(17) into Eqs. (6), (8) and (10) and summing them according to Eq. (11), the solution of an eigenvalue problem for the local buckling of the elastically restrained plate subjected to the in-plane compression along the X -axis is obtained.…”

“…Similar to the local buckling problems, the effects of boundary constraints on the vibration characteristics of symmetrically laminated rectangular plates were first investigated by Hung et al [8,9]. The problem of free vibration of a moderately thick rectangular plate with edges elastically restrained against transverse and rotational displacements was studied by Xiang et al [31] using the Ritz method combined with a variational formulation and Mindlin plate theory.…”