Analysis of shear deformable laminated composite trapezoidal plates (original) (raw)
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European Journal of Mechanics - A/Solids, 2012
In this study, free vibration analysis of moderately thick symmetrically laminated general trapezoidal plates with various combinations of boundary conditions is investigated. The governing partial differential equations and boundary conditions for trapezoidal plate are obtained using first order shear deformation theory (FSDT) together with proper transformation from Cartesian system into trapezoidal coordinates. Generalized differential quadrature (GDQ) method is then employed to obtain solutions for the governing equations. Results of the GDQ method are compared and validated with available results in the literature which show accuracy and fast rate of convergence of the method. Effect of various parameters such as geometry, thickness, boundary condition and lay-up configuration on the natural frequency of trapezoidal and skew plates is investigated through several examples. It is also shown that the method can be used for analysis of triangular plates as special case of trapezoidal geometry with the same performance and convergence.
Composite Structures, 2018
Free vibration analysis of laminated composite and functionally graded materials (FGM) composite annular plates is investigated. The equations of motion of annular plates have been obtained via conical shell equations. Shear deformation theory is used for shell equation of motion. After the implementation of the Regularized Shannon delta (RSD) kernel and Lagrange delta sequence (LDS) kernel, the method of discrete singular convolution (DSC) is used for numerical solution of the governing equations to obtain the frequency values. To verify the accuracy of this method, comparisons of the present results are made with results available in the open literature. Some parametric results for annular plates and conical panels have depicted for isotropic, laminated composite and functionally graded composite materials. It is found that the convergence and accuracy of the present DSC method is very good for vibration problem of annular plates with functionally graded materials (FMG) and laminated composite cases. Some results about carbon nanotube reinforced (CNTR) composite plate have also been approved.
International Journal of Mechanical Sciences, 2013
A general variational formulation for the determination of natural frequencies and mode shapes of free vibration of symmetric laminated plates of trapezoidal and triangular shapes is presented in this work. The kinematics corresponding to the first-order shear deformation plate theory (FSDT) is used to take into account the effects of shear deformation and rotational inertia in the analysis. The developed approach is based on the Ritz method and the plate geometry is approximated by non-orthogonal right triangular coordinates. The transverse deflection and two rotations of the laminate are independently approximated by sets of simple polynomials. The algorithm allows obtaining approximate analytical solutions for laminated plates with different shapes, aspect ratio, number of layers, stacking sequence, angle of fiber orientation and boundary conditions including translational and rotational elastically restrained edges. The algorithm is simple to program and numerically stable.
Archive of Applied Mechanics, 2012
A global higher-order shear deformation theory is devised to obtain the governing equations of composite plates under dynamic excitation. The time-harmonic solution leads to an eigenvalue problem for the natural frequencies of plates. The eigenvalue problem for rectangular plates is converted to a set of homogenous algebraic equations using differential quadrature method. The formulation of the problem allows direct application of various boundary conditions. Therefore, rectangular plates with mixed boundary conditions are also considered. To show the validity of results, the fundamental natural frequencies of composite plates with different boundary conditions and those of isotropic plates with mixed boundary conditions are compared against the results available in the literature.
2007
In the present study, free vibration, deflection and buckling analyses of rectangular composite plates via discrete singular convolution has been presented. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. The obtained results are compared with those of other numerical methods available in the literature. Numerical calculations showed that accurate results can be achieved. It has been also shown that the DSC method yields efficient and convergence solutions and these results are in excellent agreement with the analytical solutions and other sources of numerical solutions.
Free-vibration analysis of stiffened laminated plates using higher-order shear deformation theory
Finite Elements in Analysis and Design, 1996
This paper presents the free vibration analysis of stiffened laminated plate using Finite element method. Stiffened laminated plate are commonly employed in the structures of many aerospace vehicles such as aircrafts, rockets, missiles, etc. Therefore it is necessary to determine the structural deformation and vibrational characteristics of such structures where it is desired to have high natural frequencies. The free vibration results obtained by the present finite element model are compared with previous results for the stiffened composite plate. The result shows that the present model for the stiffened plate gives quite accurate results. Effects of the eccentricity, orientation-symmetric and anti-symmetric, angle-ply and cross-ply and boundary condition are also investigated.
International Journal of Pressure Vessels and Piping, 2011
This paper presents nonlinear static analysis of a rectangular laminated composite thick plate resting on nonlinear two-parameter elastic foundation with cubic nonlinearity. The plate formulation is based on first-order shear deformation theory (FSDT). The governing equation of motion for a rectangular laminated composite thick plate is derived by using the von Karman equation. The nonlinear static deflections of laminated plates on elastic foundation are investigated using the discrete singular convolution method. The effects of foundation and geometric parameters of plates on nonlinear deflections are investigated. The validity of the present method is demonstrated by comparing the present results with those available in the literature.
Vibration Analysis of Thick Arbitrarily Laminated Plates of Various Shapes and Edge Conditions
Free vibration analysis of arbitrarily laminated plates of quad, penta and hexagonal shapes, which have combinations of clamped, simply supported and free edge conditions is performed. The finite element formulation is based on first and higher order shear deformation theories to study the free vibration response of thick laminated composite plates. A finite element code is developed incorporating shear deformation theories using an 8-noded serendipity element. The effect of plate shape, arbitrary lamination and different edge conditions on natural frequencies and mode shapes are investigated. A systematic study is carried out to determine the influence of material orthotropy and aspect ratio on free vibration response. For various cases, the comparisons of results from present study showed good agreement with those published in the literature.
This paper represents the laminated plate growing researc to dynamic loading in their working life and vibration affects working life of the structure predict of the free vibratio displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in the higher order shear deformation finding the analytical solutions. supported cross been obtained by using Layerwise HSDT. It is sh can provide accurate results. comparing it with various available results in the literature. The results show that the present model performs better than all the exist theories. ABSTRACT This paper represents the aminated plate growing researc to dynamic loading in their working life and vibration affects working life of the structure. Layerwise predict of the free vibratio displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in the higher order shear deformation finding the analytical solutions. supported cross been obtained by using Layerwise HSDT. It is sh can provide accurate results. comparing it with various available results in the literature. The results show that the present model performs better than all the exist heories. This paper represents the aminated plate. As we know that vibration and composite material are two main growing research topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the Layerwise Higher Order Shear Deformation Theory (predict of the free vibratio displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in the higher order shear deformation finding the analytical solutions. supported cross-ply and anti been obtained by using Layerwise HSDT. It is sh can provide accurate results. comparing it with various available results in the literature. The results show that the present model performs better than all the exist IJMET/index.asp This paper represents the investigation As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the Higher Order Shear Deformation Theory (predict of the free vibration characteristics of laminated composite plates. displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in the higher order shear deformation finding the analytical solutions. Non ply and anti-symmetric angle been obtained by using Layerwise HSDT. It is sh can provide accurate results. The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the present model performs better than all the exist asp 414 investigation on the response of a As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the Higher Order Shear Deformation Theory (n characteristics of laminated composite plates. displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in the higher order shear deformation theory Navier's solution method is used for Non-dimensional fundamental frequencies of simply symmetric angle-ply laminated composite plates have been obtained by using Layerwise HSDT. It is sh The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the present model performs better than all the exist the response of a As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the Higher Order Shear Deformation Theory (n characteristics of laminated composite plates. displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in theory Navier's solution method is used for dimensional fundamental frequencies of simply-ply laminated composite plates have been obtained by using Layerwise HSDT. It is shown that the present Layerwise HSDT The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the present model performs better than all the existing higher order shear deformation the response of a symmetric composite As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the Higher Order Shear Deformation Theory (HSDT n characteristics of laminated composite plates. displacements of each layer are expressed in terms of Layerwise HSDT the thickness. The displacement field of present theory contains nine unknowns, as in theory Navier's solution method is used for dimensional fundamental frequencies of simply ply laminated composite plates have own that the present Layerwise HSDT The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the ing higher order shear deformation symmetric composite As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the HSDT) is used to n characteristics of laminated composite plates. displacements of each layer are expressed in terms of Layerwise HSDT functions of the thickness. The displacement field of present theory contains nine unknowns, as in theory Navier's solution method is used for dimensional fundamental frequencies of simply ply laminated composite plates have own that the present Layerwise HSDT The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the ing higher order shear deformation symmetric composite As we know that vibration and composite material are two main h topics now a days. Almost all the structural components subjected to dynamic loading in their working life and vibration affects working life of the is used to The functions of the thickness. The displacement field of present theory contains nine unknowns, as in theory Navier's solution method is used for dimensional fundamental frequencies of simply ply laminated composite plates have own that the present Layerwise HSDT The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the ing higher order shear deformation
Recently developed inverse hyperbolic shear deformation theory by the authors is extended to analyze the free vibration response of laminated composite and sandwich plates. Euler-Lagrange equations are derived employing the principle of virtual work for the dynamic problem. A Navier type and finite element solutions are proposed to obtain the free vibration response of laminated composite and sandwich plates. A C 0 -continuous isoparametric biquadratic-quadrilateral serendipity element is used for the finite element solution of generalized higher order shear deformation theory so as to ensure its applicability to general laminates subjected to different combinations of boundary conditions. Higher modes of vibration are obtained for laminated cross-ply and angle-ply plates and efficiency of the theory is ensured by comparing the results with the existing results. It is observed that both analytical and finite element solutions with the present theory are capable for accurate prediction of the free vibration response.