Postprint version. Published in Proceedings of the 14th Annual ASCE Engineering Mechanics Division 2000: Austin, Texas, May 21, 2000. ©American Society of Civil Engineers.
A significant amount of research in the last few years has greatly advanced the field of structural control through the use of smart materials. Smart materials have the ability to change shape, stiffness, natural frequency, damping and other mechanical characteristics in response to environmental condition changes. One of he new class of materials with promising applications in structural and mechanical systems are Shape Memory Alloys (SMAs). However, there are few studies where the random response of mechanical systems containing shape memory components has been conducted. Such study is important to verify the feasibility on the use of SMAs in structural components. The present contribution reports on the operator split technique applied to random vibration of single-degree-of-freedom (SDOF) mechanical system with a shape memory helical spring. A constitutive theory originally developed by Fremond with internal variables that must satisfy internal constrains is used to model the restoring force provided by the spring. The operator split technique has been used on the solution of well-posed nonlinear dynamic problem and its basic idea is to promote a partition of state space in sub-spaces that may be solved separately. Results in terms of root-mean-square for both zero and non-zero mean random vibration is presented for SDOF shape memory oscillator. Numerical simulations of the system under a wide range of white noise excitation are presented.