Stochastic Response of a Shape Memory Alloy Laminated Beam with Viscoelastic Matrix

Laminated beams with shape memory alloys (SMAs) as the surface layer and viscoelastic materials as the interlayer have been widely used in engineering applications. The stability analysis of these beams has always been a hot research topic, especially regarding the high-amplitude oscillations induced by external random disturbances. Therefore, in this paper, the stochastic response of a SMA laminated beam with viscoelastic matrix is investigated. First, a SMA laminated beam model with viscoelastic matrix under random loads is established. Here, a narrow-band noise is used to characterize the random loads that the laminated beam undergoes. Then, the steady-state amplitude response in the deterministic case, as well as the steady-state first- and second-order moments of the amplitude under random loads are discussed. These approximate analytical results obtained using the multiple-scale method are found to be consistent with the numerical results from the Monte Carlo simulation. Furthermore, multiple-values response phenomena within a certain range of the external excitation frequency or amplitude are found. Finally, the effects of noise and viscoelastic parameters on the response of the proposed SMA laminated beam model are thoroughly studied. It is found that, within the multiple-values response region, both noise and viscoelastic parameters can induce stochastic transition behaviors between desirable low-amplitude and catastrophic high-amplitude oscillations. Such undesirable vibration patterns may damage or destroy the stability and security of the SMA beam system. These findings can provide theoretical guidance for the design of laminated beams to avoid catastrophic stochastic transitions in engineering applications.