An analytical spectral stiffness method for buckling of rectangular plates on Winkler foundation subject to general boundary conditions

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

“…This theory provides an accurate, efficient and versatile analytical method for vibration analysis and design of rigidflexible structures. The theory is also expected to be extended to other analytical vibrational models such as membranes [72] , plates [73][74][75][76][77][78] , shells [79][80][81] , solids [82] for the vibration and buckling analysis [83,84] by using associated techniques, e.g., [85][86][87] . Besides, the analytical nature of this proposed method facilitates the consideration of uncertainties that may occur during the manufacturing and assembly procedure, such as the uncertainties in rigid bodies (mass, rotatory inertia), the beam sections [88][89][90] (Young's modulus, density, cross section and etc), their connections (relative positions) and more complex engineering problems [91] .…”

Spectral dynamic stiffness theory for free vibration analysis of plate structures stiffened by beams with arbitrary cross-sections

“…In order to remove the above restrictions in the literature, many researchers have proposed different dynamic stiffness models in recent years [30][31][32][33][34][35][36][37][38][39] . Some of these models are applicable to plate elements with more general boundary conditions, and the elements can be assembled in two directions.…”

“…Amongst these contributions, Liu, Banerjee and their coauthors [30][31][32][33][34] proposed the spectral dynamic stiffness method (SDSM) for both the transverse [30][31][32][33] and inplane [34] vibration problem of the plate by combining the spectral method with the classical dynamic stiffness method for plate with classical boundary conditions (BCs) and non-classical BCs [35,36] . The method has also been extended to buckling analysis of plates [37,38] . Nefovska-Danilovic and their coauthors proposed dynamic stiffness matrices for plate elements with general boundary conditions for the in-plane vibrations [39] and transverse vibrations based on the first-order deformation theory [40] and higher-order deformation theory [41] .…”

A modified Fourier series-based solution with improved rate of convergence for two-dimensional rectangular isotropic linear elastic solids

“…Similar methods using exact solutions for the governing PDE and Fourier series to approximate the boundary conditions has been recently developed to study out-of-plane free vibrations [11–16], in-plane free vibrations [17], and buckling [18–22] of rectangular plates or assemblies of them. In these papers, the coefficients for the Fourier series have been obtained by integrating over a domain spanning the dimensions of the plate.…”