Modeling and Forced Vibration Analysis of Rod-Like Solid-State Actuators

Solid-state smart actuators are widely utilized in a variety of micro and nano-positioning applications. Most of today’s modeling frameworks adopt lumped-parameter representation for system dynamics due to its more straightforward analysis and control. In this article, a distributed-parameters rod-like configuration is considered for free and forced motion analysis of structure. To include the effects of widely-used flexural mechanisms, a mass-spring-damper boundary condition is considered for the system. Moreover, the effect of electromechanical actuation is included as a concentrated force at the boundary. The problem is then divided into two parts: first part deals with free motion analysis of system to obtain eigenvalues and eigenfunctions using the expansion theorem and a standard eigenvalue problem procedure. The effects of different boundary mass and spring values on the natural frequencies and mode shapes are demonstrated, which indicate their significant contribution to system dynamical properties. In the second part, forced motion analysis of system and its state-space conversion tools are presented. It is shown that distributed-parameters modeling is inevitable when precision high frequency motions are demanded. This can enhance control bandwidth and performance of rod-like solid-state actuators such as piezoelectric and magnetostrictive positioners with moving to next generation digital signal processing systems which enable ultrahigh-frequency sampling rates.