Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates

This paper describes the analyses of the nonlinear vibrations and dynamic stability of viscoelastic orthotropic plates. The models are based on the Kirchhoff–Love (K.L.) hypothesis and Reissner–Mindlin (R.M.) generalized theory (with the incorporation of shear deformation and rotatory inertia) in geometrically nonlinear statements. It provides justification for the choice of the weakly singular Koltunov–Rzhanitsyn type kernel, with three rheological parameters. In addition, the implication of each relaxation kernel parameter has been studied. To solve problems of viscoelastic systems with weakly singular kernels of relaxation, a numerical method has been used, based on quadrature formulae. With a combination of the Bubnov–Galerkin and the presented method, problems of nonlinear vibrations and dynamic stability in viscoelastic orthotropic rectangular plates have been solved, according to the K.L. and R.M. hypotheses. A comparison of the results obtained via these theories is also presented. In all problems, the convergence of the Bubnov–Galerkin method has been investigated. The implications of material viscoelasticity on vibration and dynamic stability are presented graphically.