Linear and Nonlinear Dynamic Responses of Various Shaped Laminated Composite Plates

2009 ◽  
Vol 4 (4) ◽  
Author(s):  
Muhammad Tanveer ◽  
Anand V. Singh
Keyword(s):  
Fourier Transforms ◽  
Numerical Procedure ◽  
Laminated Composite ◽  
Composite Plates ◽  
Dynamic Responses ◽  
Published Data ◽  
Laminated Composite Plates ◽  
Displacement Fields ◽  
Linear And Nonlinear ◽  
Displacement Based

A unified approach to study the forced linear and geometrically nonlinear elastic vibrations of fiber-reinforced laminated composite plates subjected to uniform load on the entire plate as well as on a localized area is presented in this paper. To accommodate different shapes of the plate, the analytical procedure has two parts. The first part deals with the geometry which is interpolated by relatively low-order polynomials. In the second part, the displacement based p-type method is briefly presented where the displacement fields are defined by significantly higher-order polynomials than those used for the geometry. Simply supported square, rhombic, and annular circular sector plates are modeled. The equation of motion is obtained by the Hamilton’s principle and solved by beta-m method along with the Newton–Raphson iterative scheme. Numerical procedure presented herein is validated successfully by comparing present results with the previously published data, convergence study, and fast Fourier transforms of the linear and nonlinear transient responses. The geometric nonlinearity is seen to cause stiffening of the plates and in turn significantly lowers the values of displacements and stresses. Also as expected, the frequencies are increased for the nonlinear cases.

Nonlinear Forced Vibrations of Laminated Piezoelectric Plates

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Muhammad Tanveer ◽  
Anand V. Singh
Keyword(s):  
Electric Fields ◽  
Mechanical Load ◽  
Numerical Procedure ◽  
Laminated Composite ◽  
Composite Plates ◽  
Forced Vibrations ◽  
Homogeneous Material ◽  
Displacement Fields ◽  
Electrical Loads ◽  
Piezoelectric Plates

A numerical approach is presented for linear and geometrically nonlinear forced vibrations of laminated composite plates with piezoelectric materials. The displacement fields are defined generally by high degree polynomials and the convergence of the results is achieved by increasing the degrees of polynomials. The nonlinearity is retained with the in-plane strain components only and the transverse shear strains are kept linear. The electric potential is approximated layerwise along the thickness direction of the piezoelectric layers. In-plane electric fields at the top and bottom surfaces of each piezoelectric sublayer are defined by the same shape functions as those used for displacement fields. The equation of motion is obtained by the Hamilton’s principle and solved by the Newmark’s method along with the Newton–Raphson iterative technique. Numerical procedure presented herein is validated by successfully comparing the present results with the data published in the literature. Additional numerical examples are presented for forced vibration of piezoelectric sandwich simply supported plates with either a homogeneous material or laminated composite as core. Both linear and nonlinear responses are examined for mechanical load only, electrical load only, and the combined mechanical and electrical loads. Displacement time histories with uniformly distributed load on the plate surface, electric volts applied on the top and bottom surfaces of the piezoelectric plates, and mechanical and electrical loads applied together are presented in this paper. The nonlinearity due to large deformations is seen to produce stiffening effects, which reduces the amplitude of vibrations and increases the frequency. On the contrary, antisymmetric electric loading on the nonlinear response of piezoelectric sandwich plates shows increased amplitude of vibrations.

scholarly journals Damping mathematical modelling and dynamic responses for FRP laminated composite plates with polymer matrix

2018 ◽  
Vol 5 (1) ◽  
pp. 35-42 ◽  
Author(s):  
Qimao Liu
Keyword(s):  
Polymer Matrix ◽  
Initial Conditions ◽  
Laminated Composite ◽  
Composite Plates ◽  
Dynamic Responses ◽  
Inversion Method ◽  
Laminated Composite Plates ◽  
Governing Equations ◽  
Damping Force ◽  
Time Domains

Abstract This paper proposes an assumption that the fibre is elastic material and polymer matrix is viscoelastic material so that the energy dissipation depends only on the polymer matrix in dynamic response process. The damping force vectors in frequency and time domains, of FRP (Fibre-Reinforced Polymer matrix) laminated composite plates, are derived based on this assumption. The governing equations of FRP laminated composite plates are formulated in both frequency and time domains. The direct inversion method and direct time integration method for nonviscously damped systems are employed to solve the governing equations and achieve the dynamic responses in frequency and time domains, respectively. The computational procedure is given in detail. Finally, dynamic responses (frequency responses with nonzero and zero initial conditions, free vibration, forced vibrations with nonzero and zero initial conditions) of a FRP laminated composite plate are computed using the proposed methodology. The proposed methodology in this paper is easy to be inserted into the commercial finite element analysis software. The proposed assumption, based on the theory of material mechanics, needs to be further proved by experiment technique in the future.

Wave Propagation in Laminated Composite Plates Using Higher Order Theory

2000 ◽  
Vol 68 (3) ◽  
pp. 503-505 ◽  
Author(s):  
M. R. Chitnis ◽  
Y. M. Desai ◽  
T. Kant
Keyword(s):  
Wave Propagation ◽  
Laminated Composite ◽  
Composite Plates ◽  
Transversely Isotropic ◽  
Order Theory ◽  
Higher Order ◽  
Numerical Results ◽  
Laminated Composite Plates ◽  
Layered Plates ◽  
Displacement Based

A higher order displacement based formulation has been developed to investigate wave propagation in fiber-reinforced polymer composite laminated (FRPCL) plates. The formulation has been applied, as an illustration, to a plate made up of transversely isotropic laminae with the axes of symmetry lying in the plane of the lamina. Results for the plane as well as the antiplane strain cases are shown to be in excellent agreement with the exact solutions for isotropic and transversely isotropic single layered plates. Also, numerical results have been obtained for crossply (0 deg/90 deg/0 deg/90 deg) laminated composite plates, which agree very well with the previously published numerical results. The formulation can be employed to expeditiously investigate the dispersion characteristics of waves propagating in a plate with an arbitrary number of anisotropic laminae.

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