Abstract
In this paper, the equations of motion governing the transient response of an elastomer rod with embedded shape memory alloy actuators are derived. The elastomeric flexural dynamics and elastomeric thermal dynamics are represented by a pair of parameter-dependent, coupled, partial differential equations. The response of the structural system exhibits strong hysteresis effects due to the nonlinear nature of the constitutive law of the SMA actuator. As opposed to previous work by the authors in which an explicit equation for the nonlinear constitutive law is utilized, the work herein utilizes an integral operator in a phenomenological representation of the hysteresis. Specifically, a static hysteresis operator is employed to represent the current-to-stress transformation in the SMA. The hysteresis operator consequently appears as a control influence operator in the system of governing partial differential equations. This paper presents a two-stage identification process to characterize the multivalued response associated with hysteresis. Preliminary experimental results validate the effectiveness of the method for the class of problems considered.
Rational Krylov methods for functions of matrices with applications to fractional partial differential equations
