The active strain energy tuning on the parametric resonance of composite plates using finite element method

Abstract

Studies on the effect of shape memory alloy (SMA) on structural behaviours of laminated composite that include mechanical and thermal buckling, vibration and deflection are numerous. However studies on such effect of SMA on parametric instability of composite plates are hardly to be found in literatures. The parametric instability is an important design consideration for structures that are loaded periodically as to avoid the possible occurrence of fatigue failure to the structures due to the parametric resonance. This paper is to report on a study conducted to investigate the improvement made by the SMA on the parametric instability behaviour of laminated composite plates subjected to periodic compressive load. SMA, well-known for having the shape memory effect property that is capable of inducing recovery stress in the SMA, in wire form is embedded within laminated composite plates. Brinson's model is used to predict the amount of recovery stress induced and the new property of the SMA after the phase transformation occurs in the SMA. Based on the third order shear deformation theories (TSDT), the governing equation for the parametric instability of the SMA composite plate is developed using finite element method (FEM). The Mathieu-Hill type of parametric instability equation is derived and solved using the Bolotin's method. The results due to the TSDT have been found to correlate well with the results due to the first order shear deformation theory (FSDT). Furthermore it is found that the SMA causes a significant improvement of delaying the parametric instability from occurring by shifting to the instability chart to the right. The effect of SMA on the dynamic instability of laminated composite plate depends greatly on the activation temperature and the initial stress of the SMA that determine the amount of recovery stress induced by the SMA.