Modeling of a perforated plate with hysteresis type characteristics under kinematic excitations
Abstract
In this study, the energy expressions of a perforated plate with hysteresis-type elastic-dissipative characteristics subjected to kinematic excitations are determined, and based on them, the differential equation of motion is formulated using the second-order Lagrange equation. The dissipative properties of the plate material are described using the expressions derived from the Pisarenko-Boginich hypothesis, and are incorporated through coefficients in explicit form by means of the harmonic linearization method. The cut-out extracted from the rectangular plate is also assumed to be rectangular in shape, with its sides parallel to those of the plate, and its location considered arbitrary within the plate domain. The kinetic and potential energies are expressed separately for the plate and the corresponding cut-out region, and, based on the equality of displacements along the cut-out boundary, the necessary compatibility relations are established. As a result, both the kinetic and potential energies are ultimately expressed solely in terms of the plate deflection. The mode shapes of the perforated plate are assumed to be orthogonal, and by applying the Bubnov-Galerkin method, the governing differential equation of motion is reduced to a simplified form.