Coupled damping vibrations of composite structures

This paper summarizes the results of a series of papers on developing methods for deter-mining elastic-dissipative characteristics of polymer composite materials (PCM) and predicting the corresponding dynamical responses from structures. For a prismatic anisotropic bar which is arbitrarily oriented with respect to the axes of elastic symmetry of an orthotropic plate, a mathematical model and a method for solving the problem of damping bending-torsional vibrations are developed. The interaction between the vibration modes of a composite bar is examined. Basic provisions of an iterative method for determining elastic and dissipative characteristics of PCM are formulated. Mathematical models of damping vibrations of fibrous composite thin-walled bars and plates are developed, and a two-stage method for solving the resulting complex eigenvalue problems is put for-ward. The effect of the composition and the reinforcement structure on the eigenfrequencies and the coefficients of mechanical losses of the structures in question is discussed. Controlability of the values of resonance frequencies and the coefficients of the mechanical losses due to variation of the degree of anisotropy of fiber materials and the degree of inhomogeneity of the structure over thickness has been demonstrated. The widely used method of potential energy of eigenforms is shown as being capable of providing correct values of the coefficients of mechanical losses only up to η = 0.02–0.03, resulting in significant errors for higher dissipative characteristics of composite structures. For the method presented, examples of practical implementation in developing vibration absorptive composite structures are given.