Theoretical model of guided waves in a bone-mimicking plate coupled with soft-tissue layers

Quantitative ultrasound has shown a significant promise in the assessment of bone characteristics in the recent reports. However, our understanding of wave interaction with bone tissues is still far from complete since the propagation of ultrasonic waves in bones is a very challenging topic due to their multilayer nature. The aim of the current study is to develop a theoretical model for guided waves in a bone-mimicking plate coupled with two soft-tissue layers. Here, the bone plate is modeled as an isotropic solid layer while the soft tissues are modeled as fluid layers. Based on the boundary conditions set for the three-layered structure, a characteristic equation is obtained which results in dispersion curves of the phase and group velocities. New expressions for free guided waves propagating in the trilayered plate are introduced. The amplitudes of wave modes generated by time-harmonic loads applied in the plate are theoretically computed by reciprocity consideration. As an example of calculation, the normalized amplitudes of the lowest wave modes are presented. The obtained results and equations discussed in this study could be, in general, useful for further applications in the area of bone quantitative ultrasound.