Localization of vibration propagation in two-dimensional systems

In this paper, a method of regular perturbation for a linear algebraic system is applied to study localization of vibration propagation in randomly disordered weakly coupled two-dimensional cantilever-spring arrays under external harmonic excitations. Localization factors, which characterize the average exponential rates of decay of the amplitudes of vibration, are defined in terms of the angles of orientation. First-order approximate results of the localization factors are obtained using a combined analytical–numerical approach.