Time-domain flexural wave intensity estimation in orthotropic Kirchhoff plates

In this paper, a method for estimating the vibrational energy flow associated with the flexural vibration of an orthotropic Kirchhoff plate, in the time-domain, is presented. The approach is based on the plane propagating wave solution to the equation of motion, and uses a Fourier series approximation of the wave field. The various linear and angular velocities, shear forces and moments that are needed to calculate the energy flow are estimated by digitally filtering and combining the outputs of an array of sensors. A similar approach is used to reconstruct the local wave field to provide an estimate of the wave propagation direction.The theoretical basis of the approach is described, and design considerations for the sensor array and for the filters used for parameter estimation are discussed. Simulations are presented for plane flexural waves and for transient transverse point force excitation of a range of orthotropic plates having different material properties, using a simulated array of velocity sensors. These simulations show that the method can provide accurate estimates of the magnitude and direction of the vibrational energy flow, as well as of the propagation direction of a single wave train or ‘burst’, provided that the sensor array is sufficiently distant from the excitation point. This is consistent with preliminary experimental measurements, also presented in this paper, performed on a composite orthotropic plate.