Laminated composite is common to replace traditional metals in today's industries due to its high specific strength. Shape memory alloy has been used to improve structural behaviours such as buckling, vibration and fatigue through its well‐ known property of shape memory effect. This ability of shape memory alloy to improve the parametric instability behaviour of laminated composite plate has not been studied in the past and as such, this study is conducted. Here, shape memory alloy wires are embedded within the outer layers of the laminated composite plates. The Mathieu‐Hill equation for the parametric instability of the shape memory alloy composite plate has been developed using finite element method based on the first order shear deformation theory. The formulation is validated and parametric studies have been conducted to investigate the effect of shape memory alloy on the dynamic instability behaviour of the composite that corresponds to factors such as static load factor, thickness of the plate and boundary conditions. The study shows that shape memory alloy improves significantly the dynamic instability behaviour of the laminated composite plate by shifting the instability chart to the right. The effect of shape memory alloy can increase the frequency centre of the instability chart by more than 100 %.
The parametric resonance or instability challenge in designing laminated composite is crucial in areas such as aeronautical and marine where structures experience dynamic loading. Shape memory alloy (SMA), a type of smart material, has been used to improve the structural behaviours of composite plate using its well-known property of shape memory effect. It is also known that mechanical couplings that exist in unsymmetric composite can increase the instability of the composite. In this study, the SMA property has been exploited to generate recovery stress in the composite to improve its parametric instability problem. The unsymmetric composites were embedded with SMA fibres, and the formulation for the dynamic instability of this composites was developed using finite element method. The third-order shear deformation theory of composite was applied. The results were initially validated for the case of composite without SMA. Following that, the parametric instability behaviour of unsymmetric composites was studied under the effect of several parameters. It was found that the mechanical couplings that exist in the unsymmetric composite have increased the instability of the composite, but the presence of the SMA can significantly reduce this instability.
Today’s design of machine rotor requires the rotor to operate at a high rotational speed to improve the efficiency of the machine. However, the existence of disturbances such as periodic axial load may cause parametric resonance to the rotor system in addition to the common force resonance. Previous studies on this parametric resonance of shaft typically included the element of translational and rotary inertia, gyroscopic moments and bending and shear deformation but surprisingly neglected the effect of the axial torque. This paper investigated the parametric instability behaviour of the shaft rotating at high speed while considering the torsional effect of the shaft. Based on the finite element method, a shaft model that includes torsional deformation as one of its degree of freedom was established. The Mathieu-Hill equation was derived, and then the Bolotin’s method was used to solve the equation by establishing the parametric instability chart. Two types of the rotary system were studied: a shaft with different boundary conditions and shaft with different bearing types. The results were initially validated with past findings. Following that the results were compared to the results correspond to the Timoshenko’s beam formulation that omits the torsional degree of freedom. The effect of axial torsional deformation was found to be very significant especially at high speed. The developed model in this study shows that at the shaft speed of 40000 rpm, the effect of torsional deformation has given the difference of more than 100% in the frequency ratios correspond to the 4DOF and 5DOF models for the case of fix-free boundary condition.
Abstract. The application of laminated sandwich composite in machine structures is attractive due to the low specific and tailorable properties of the composites. As such a study on the parametric instability that often occurs in machine structures should be crucially conducted on composite plates. In this paper, finite element method (FEM) has been used to model laminated composite plate subjected to periodic compressive loading for the parametric instability analysis. The FEM formulation is based on the first order shear deformation theory. Eight noded serendipity element that requires 5 degrees of freedom per node is used in this study. The developed Mathieu-Hill type equation that represents the parametric instability of the composite plate has been solved using the Bolotin's method that reduces the Mathieu-Hill equation to a couple of eigen-value problems. The FEM source codes have been developed to determine the instability charts for several configurations of composite plates. While the formulation and codes have been found to give results that agree well with past results, it has been also been found that as the static load factor is increased, the frequency center for dynamic instability region is shifted to the left while the degree of instability is increased.
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