Free vibration analysis and eigenvalues sensitivity analysis of composite laminates with interfacial imperfection are investigated based on the radial point interpolation method (RPIM) in Hamilton system. The governing equation of the free vibration analysis and eigenvalues sensitivity analysis are both reduced by the spring-layer model and modified Hellinger–Reissner (H–R) variational principle. The analytical method (AM), semi-analytical method (SA) and the finite difference method (FD) are used for the eigenvalues sensitivity analysis in Hamilton system. Extensive numerical results are used to show the effects of variations in the material properties and shape parameters of the composite laminates on the response quantities and sensitivity coefficients of natural frequencies. A major advantage of the governing equation sets is that the interfacial imperfection of composite laminated plates is taken into account.
Composite materials are used in almost all aspects of the industrial and commercial manufacturing fields of aircraft, ship, common vehicle and other high performance structures due to their high specific stiffness and strength, excellent fatigue resistance, longer durability as compared to metallic structures, and ability to be tailored for specific applications. The rapidly growing applications of composite materials have led to intensive study of the dynamic behavior and dynamics optimization under various conditions. Structural sensitivity concerns the relationship between design parameters and structural behaviors characterized by a response function. It is well known that the sensitivity analysis plays an important role in the general structural optimization. Using information obtained from design sensitivity analysis one can improve design greatly. Consequently, sensitivity analysis is currently one of the major research trends in computational mechanics.
Different plate theories have been developed for dynamics response analysis and sensitivity analysis of composite laminates. In these theories of dynamics for laminated thick plates, transverse shear deformation is very important such that some improved formulations which account for the deformation and rotator inertia have to be introduced in the analysis of dynamics. Since the above theories are established on some hypothesis, only partial fundamental equations can be satisfied and some of the elastic constants cannot be taken into account. Therefore, the errors will increase as the thickness of plate increases and the stress at interface cannot be exactly calculated.
In recent years, the state-vector equation in Hamilton system, which is employed in the analysis of control systems of current significance, has attracted the attention of a number of investigators who are interested in the problems of laminated structures [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15] and [16]. In the state-vector equation, two types of variables (i.e., the transverse stresses and displacements) are synchronously considered in the control equation. And the thick plates/shells or the laminated plates/shells problems can be treated without any assumptions regarding displacements and stresses. The approach to interlaminar continuity is different from some of the Zig-Zag strategies. Due to the transfer matrix technique being employed, the solution provides an exact continuous transverse stresses and displacement field across the thickness of laminated structure. Another significant difference from the classical layer-wise methods is that the scale of the final governing equation system is independent of the thickness and the number of layers of a structure. Therefore, the state-vector equation is adopted for the free vibration analysis and eigenvalues sensitivity analysis of composite laminates with bonding imperfections in this paper.
In addition, interfacial imperfection is usually not taken into account in the traditional theory of structural analysis of composite laminates. However, multifarious interlaminar debondings like microcracks, inhomogeneities, and cavities may be introduced into the bond in the process of manufacture or service. During the service lifetime, these tiny flaws can get significant. To avoid the local failure of bond or the whole collapse of structure, therefore, the effect of imperfect interfaces on the structural behavior should be accurately evaluated. Some researchers presented the theory work on this problem, but it was only focused on the analytical methods and traditional numerical methods [17], [18] and [19]. In recent years, Chen [20], [21], [22] and [23] has used the analytical methods and numerical methods to research the problem of interfacial imperfection for composite laminated plates in Hamilton system.
The objective of the present paper is to research the problem of the free vibration analysis and eigenvalues sensitivity analysis of composite laminates with interfacial imperfections based on the meshless method, the state-vector equation and the spring-layer model. Furthermore, the analytical method (AM), semi-analytical method (SA) and the finite difference method (FD) are developed for the eigenvalues sensitivity analysis in Hamilton system.
For the composite laminates with interfacial imperfections, the problem of free vibration response analysis and eigenvalues sensitivity analysis were investigated using the meshless method and the state space method in this paper. The semi-analytical governing equation sets of the free vibration analysis and eigenvalues sensitivity analysis are reduced by the spring-layer model and modified Hellinger–Reissner (H–R) variational principle. And the analytical method (AM), semi-analytical method (SA) and the finite difference method (FD) are given for the present eigenvalues sensitivity analysis approach. This free vibration analysis model accounts for the transverse shear deformation and rotary in the three-dimensional control equation. And the numerical errors and field nodes will not increase with increasing of the thickness or number of layers of the composite laminates.
