Statistical energy analysis of inhomogeneous systems with slowly varying properties

This paper is concerned with the analysis of high frequency vibrations of inhomogeneous systems with slowly varying properties subjected to harmonic excitation. A formula for the spatial scaling of the vibrational energy density of such systems is derived and is used to predict the mean and the variance of their vibrational energy response. The derivations are based on the assumption that waves propagate with negligible partial reflections in the systems, which holds when the relative variation of the properties of the systems is small over a wavelength of vibration. To validate the theoretical findings, numerical simulations of two plate systems are performed: a plate with a linearly varying thickness and a plate with a thickness bump.