Article

Three-dimensional dynamic analysis of laminated composite plates subjected to moving load

Center of Excellence for Computational Mechanics, Shiraz University, Shiraz, Iran
Composite Structures (Impact Factor: 3.32). 09/2009; 90(2):105-114. DOI: 10.1016/j.compstruct.2009.02.008

ABSTRACT In order to accurately determine the dynamic response of cross-ply laminated thick plates subjected to moving load, a solution procedure based on the three-dimensional (3D) elasticity theory is presented. Plates with simply supported edges and subjected to point moving load are considered. The layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness of the plates. Then, the modal analysis in conjunction with the differential quadrature method is employed for the in-plane and the temporal discretization of the resulting system of differential equations, respectively. The convergence behavior of the method is demonstrated and to show its accuracy, the results are compared with those of the exact solutions obtained for the isotropic plates under moving load and other available solution. Comparisons between the results of the 3D elasticity solutions and those of the first order shear deformation theory (FSDT) and the higher order shear deformation theory (HSDT) for the cross-ply laminated plates are also made to show the effectiveness of these theories. The effects of the thickness-to-length ratio, load velocity, load eccentricity and lamina layout on the response of the plate are studied. Due to high accuracy of the method, the results can be used as benchmarks for future research.

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    • "The results compared with direct integration methods. Malekzadeh et al. [21] used layerwise theory to discretize the equations of motion and the related boundary conditions through the thickness of the plates. Then, the modal analysis in conjunction with the differential quadrature method was employed for the in-plane and the temporal discretization of the resulting system of differential equations. "
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    ABSTRACT: The present study aims to investigate the damped response of laminated Mindlin plates subjected to dynamic loads. The solutions of damped response of anti-symmetric, cross-ply and angle-ply laminates have been obtained by FEM in conjunction with the Laplace transform method using the first order shear deformation theory. The governing equations of motion of the problem are first obtained in the time domain. Subsequently, Laplace transform is applied and the linear algebraic equations are solved numerically. Materials of the laminates are assumed to be linear elastic or viscoelastic. In the viscoelastic material case the Kelvin model is employed. According to the correspondence principle the material constants are replaced with their complex counterparts in the Laplace domain. Therefore, the presented model incorporates damping very easily in the transformed domain. The solutions obtained are transformed to the time domain using the modified Durbin’s numerical inverse Laplace transform method. For the suggested model, a general-purpose finite element analysis computer program is coded. Verification of the numerical procedure is performed by comparing the results of present method with semi-analytical results available in the literature. Obtaining the equation first discretely in the time domain using FEM and then applying the Laplace transform has proved to be a procedure highly accurate and efficient compared to other numerical methods available in the literature.
    Composites Part B Engineering 04/2013; 47:107–117. DOI:10.1016/j.compositesb.2012.10.039 · 2.98 Impact Factor
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    • "However, in comparison with the extensive research works on the vibration characteristic of homogenous and laminated composite beams and plates under moving load (see for example Refs. [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]), only limited works can be found in this regard in the open literature for FG structural elements . In addition, most of these works concerned with the study of the dynamic behaviors of FG beams under moving loads. "
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    • "However, when the width of the structure is appreciable, it is more convenient to employ two-dimensional models. Therefore, many researchers have employed the plate model to examine the dynamic behavior of such structures [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49]. However, in most cases, the effects of acceleration and/or inertia of the moving load were ignored. "
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    ABSTRACT: This paper presents a combined application of the Ritz method, the Differential Quadrature (DQ) method, and the Integral Quadrature (IQ) method to vibration problem of rectangular plates subjected to accelerated traveling masses. In this study, the Ritz method with beam eigenfunctions is first used to discretize the spatial partial derivatives with respect to a co-ordinate direction of the plate. The DQ and IQ methods are then employed to analogize the resultant system of partial differential equations. The resulting system of ordinary differential equations is then solved by using the Newmark time integration scheme. The mixed scheme combines the simplicity of the Ritz method and high accuracy and efficiency of the DQ method. The accuracy of the proposed method is demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Ritz terms and DQM sampling points. Finally, the effects of following parameters having something to do with the title problem are investigated: moving load speed and acceleration, and transverse inertia of the moving load. Numerical results show that all the above-mentioned parameters have significant effects on the transient response of such structures under traveling dynamic loads.
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