Nonlinear Steady State and Dynamic Response Analysis of Focused Ultrasound Actuated Smart Biomaterials

Abstract

The nonlinear steady state and dynamic response analysis of focused ultrasound smart biomaterials is presented in this paper. The increasing demand in scientific research to develop robust governing nonlinear model with adequate boundary conditions for proper understanding of the dynamics of smart biomaterials by applying focused ultrasound excitations is of great concern particularly in remote biomedical applications. Hence, in this study, a model which describes the nonlinear steady state and dynamic response of the materials for focused ultrasound actuator which is a nonlinear partial differential equation has been developed. The Galerkin Decomposition and the Differential Transform Methods are applied to obtain the solution of the governing equations. The solutions were validated with the numerical Runge-Kutta method of fourth order and verified with results obtained in recent studies and good agreement is established among them. The effects attenuating coefficient, modal number, and damping term on the steady state response of the smart biomaterials are investigated. From the results, it is observed that the steady state deflection of the system as indicated by the attenuating coefficient is lowest for clamped-clamped boundary condition and highest for clamped-free or cantilever condition. In addition, an increase in modal number and magnitude of the damping term results in an increase in the number of nodes and anti-nodes and a decrease in the amplitude of vibration over time respectively. Hence, this study establishes the practical applications of attenuating coefficient and boundary conditions as controlling factors in the design of smart biomaterials.