Extraction of Elastic, Viscous and Inertial Components From the Total Reaction of an Additional Support Attached to a Rectangular Plate

Abstract

The paper deals with a mechanical system consisting of a hinged rectangular plate and an additional viscoelastic support with considering its mass-inertia. The impact of the characteristics of additional support on the plate strained state is studied by an original approach of extracting elastic, viscous and inertial components from the total reaction. The plate is assumed to be medium thickness, elastic and isotropic. The Timoshenko hypothesis is used for deformation equations. The external non-stationary force initiates plate vibrations. The impact of the additional support is replaced by the action of three unknown independent non-stationary concentrated forces. The basic formulas for deriving system of three Volterra integral equations are proposed. The system is then solved by numerical and analytical method. By discretizing in time the system of Volterra integral equations is reduced to a system of matrix equations. The system of matrix equations is solved with using generalized Kramer’s algorithm for block matrices and Tikhonov’s regularization method. Note that the approach proposed is applicable for other objects with additional supports, such as beams, plates and shells having various boundary contour and boundary supporting. The results of computing elastic, viscous and inertial components of total reactions on the plate are given. The approach proposed is verified by matching the results of computations by two different methods, namely numerical and analytical for one total reaction and numerical for the total reaction obtained by adding elastic, viscous and inertial components.