caa a22 4500 606167137 CHVBK 20210128100701.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10665-014-9752-z doi (NATIONALLICENCE)springer-10.1007/s10665-014-9752-z Muradova Aliki Department of Production Engineering and Management, Institute of Computational Mechanics and Optimization, Technical University of Crete, Kounoupidiana, University Campus, 73100, Chania, Greece aut A time spectral method for solving the nonlinear dynamic equations of a rectangular elastic plate [Elektronische Daten] [Aliki Muradova] The nonlinear dynamic equations of vibrations of a von Kármán thin rectangular elastic plate are solved by means of a time spectral method. External constant (compressive or stretching) forces, applied to the edges of the plate, cause oscillations of the plate. Once the initial and boundary conditions for the equations are set up, the initial-boundary value problem has a unique solution. The solution is expanded in double trigonometric series with time-dependent coefficients. Galerkin's projections are applied for spatial discretization. The Fourier coefficients are estimated, and the rate of convergence of the method is obtained. The resulting system of nonlinear ordinary differential equations is solved by a numerical scheme based on the fourth-order Runge-Kutta method. The implicit Newmark- $$\beta $$ β method is also tested. Numerical examples with various initial conditions are presented. Springer Science+Business Media Dordrecht, 2014 Dynamic equation nationallicence Fourier transform nationallicence Initial-boundary value problem nationallicence Numerical scheme nationallicence Time spectral method nationallicence Von Kármán's elastic plate nationallicence Journal of Engineering Mathematics Springer Netherlands 92/1(2015-06-01), 83-101 0022-0833 92:1<83 2015 92 10665 https://doi.org/10.1007/s10665-014-9752-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-014-9752-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Muradova Aliki Department of Production Engineering and Management, Institute of Computational Mechanics and Optimization, Technical University of Crete, Kounoupidiana, University Campus, 73100, Chania, Greece aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 92/1(2015-06-01), 83-101 0022-0833 92:1<83 2015 92 10665