The Dynamic Behaviors of a Shape Memory Polymer Membrane

As a kind of popular smart materials, shape memory polymers (SMPs) have a great potential for applications in deployable aerospace structures and other engineering structures. However, the vibration analysis of shape memory polymer structures, which would play an important role in engineering, has not gained much attention. In this study, we propose a dynamic model and establish the governing equations for characterizing the dynamic behavior of a shape memory polymer membrane subjected to time-dependent forces. The derivation of governing equations is based on a well-developed constitutive model of SMPs combined with the Euler–Lagrange equation. With the proposed model, two different loading cases are studied: the equal-biaxial sinusoidal force and the uniaxial sinusoidal force. To analyze the dynamic response of a shape memory polymer membrane and find some effective ways to control vibration, the isothermal amplitude–frequency response, the time-dependent behavior of vibration and the vibration in a variable temperature process are investigated in the numerical simulation. It is observed that temperature, mechanical force and heating rate have significant effects on the dynamic performances of a shape memory polymer membrane. We also investigate the shape memory behavior of SMP membrane involving the dynamic response. The influence of dynamics on shape fixation and shape recovery is discussed. These results and discussion may provide guidance for exploring the vibration and dynamic performances of shape memory polymer in deployable aerospace structures.