Exact analytical modeling of power and energy for multimode lamb waves excited by piezoelectric wafer active sensors

This article presents an analytical model for power and energy transfer between excited piezoelectric wafer active sensors and host structure. This model is based on exact multimodal Lamb waves, normal mode expansion technique, and orthogonality of Lamb waves. Modal participation factors are presented to show the contribution of every mode to the total energy transfer. The model assumptions include the following: (1) straight-crested multimodal ultrasonic guided wave propagation, (2) propagating waves only, (3) ideal bonding (pin-force) connection between piezoelectric wafer active sensors and structure, and (4) ideal excitation source at the transmitter piezoelectric wafer active sensors. Constrained piezoelectric wafer active sensor admittance is reviewed. Electrical active power, mechanical converted power, and Lamb wave kinetic and potential energies are derived in closed-form formulae. Numerical simulations are performed for the case of symmetric and antisymmetric excitation of thin aluminum structure. The simulation results are compared with axial and flexural approximation for the case of low-frequency Lamb waves. In addition, a thick steel structure example is considered to illustrate the case of multimodal guided waves. A parametric study for different excitation frequencies and different transducer sizes is performed to show the best match of frequency and piezoelectric wafer active sensor size to achieve maximum energy transfer into the excited structure.