A time-domain formulation of flexural vibrations in damped rectangular orthotropic plates has been developed, in order to investigate transient and nonlinear excitation of plates. The model includes three basic mechanisms of damping: thermoelasticity, viscoelasticity, and radiation. As a consequence, the four rigidity factors are modified by perturbation terms, each perturbation term corresponding to one specific damping mechanism. The thermoelastic term is derived from the coupling between the thermoelastic stress-strain relationships and the heat diffusion equation. The second perturbation term is obtained from the standard generalized partial differential equation formulation of viscoelasticity. The third term is obtained through a Pade approximant of the damping factor which governs the radiation of an infinite plate coupled with a light fluid. The flexural equations are solved numerically in the particular case of a sphere impacting the plate with the help of a finite difference scheme of second order in time and fourth order in space. A simulated sound pressure is then obtained by a simple discrete form of the Rayleigh integral. The simulated tones show the relative relevance of the three damping mechanisms, for four different materials: aluminium, glass, carbon fibers, and wood.