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Journal ArticleDOI

Large amplitude free flexural vibrations of laminated composite skew plates

01 Dec 2004-International Journal of Non-linear Mechanics (Pergamon)-Vol. 39, Iss: 10, pp 1709-1720
TL;DR: In this paper, the large amplitude free flexural vibration behaviors of thin laminated composite skew plates are investigated using finite element approach, which includes the effects of shear deformation, in-plane and rotary inertia.
Abstract: Here, the large amplitude free flexural vibration behaviors of thin laminated composite skew plates are investigated using finite element approach. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Karman's assumptions is introduced. The non-linear governing equations obtained employing Lagrange's equations of motion are solved using the direct iteration technique. The variation of non-linear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, number of layers, fiber orientation, boundary condition and aspect ratio. The influence of higher vibration modes on the non-linear dynamic behavior of laminated skew plates is also highlighted. The present study reveals the redistribution of vibrating mode shape at certain amplitude of vibration depending on geometric and lamination parameters of the plate. Also, the degree of hardening behavior increases with the skew angle and its rate of change depends on the level of amplitude of vibration.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the free vibration analysis of multilayered laminated composite and sandwich plates using various methods available for the analysis of plates is presented and compared with other higher order shear deformation theories.

284 citations


Cites background from "Large amplitude free flexural vibra..."

  • ...Singha and Ganapathi [155] presented the large amplitude free vibration analysis of thin laminated composite skew plates using finite element approach....

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Journal ArticleDOI
TL;DR: In this article, the effect of nonlinear small-scale, angular speed, hub radius and nonlinear amplitude of rotary nanobeam on the bending vibration of a rotating cantilever was investigated.
Abstract: This study investigates the small scale effect on the nonlinear bending vibration of a rotating cantilever and propped cantilever nanobeam. The nanobeam is modeled as an Euler---Bernoulli beam theory with von Karman geometric nonlinearity. The axial forces are also included in the model as the true spatial variation due to the rotation. Hamilton's principle is used to derive the governing equation and boundary conditions for the Euler---Bernoulli beam based on Eringen's nonlocal elasticity theory. The differential quadrature method as an efficient and accurate numerical tool in conjunction with a direct iterative method is adopted to obtain the nonlinear vibration frequencies of nanobeam. The effect of nonlocal small---scale, angular speed, hub radius and nonlinear amplitude of rotary nanobeam is discussed.

90 citations

Journal ArticleDOI
Abstract: Here, the large amplitude free flexural vibration behavior of symmetrically laminated composite skew plates is investigated using the finite element method. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Karman's assumptions is introduced. The nonlinear matrix amplitude equation obtained by employing Galerkin's method is solved by direct iteration technique. Time history for the nonlinear free vibration of composite skew plate is also obtained using Newmark's time integration technique to examine the accuracy of matrix amplitude equation. The variation of nonlinear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, fiber orientation and boundary condition.

81 citations


Cites background or methods from "Large amplitude free flexural vibra..."

  • ...[20], Singha and Ganapathi [21], Sundararajana et al....

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  • ...Numerical methods such as finite element procedure is preferable over the analytical methods, as there is no need for an a priori assumption of the mode shapes, and the solution itself predict the mode shapes [21]....

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  • ...[21] are changed to cubic interpolation polynomials to describe the in-plane displacements to achieve better convergence....

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  • ...Most recently, Singha and Ganapathi [21] have employed high precision plate bending element to solve the nonlinear free vibration problem of composite skew plates....

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  • ...Though a huge body of literature exists on the linear free vibration of isotropic and composite skew plates [21], such analysis concerning the non-linear free vibration of skew plates is sparsely treated in the literature....

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Journal ArticleDOI
TL;DR: In this article, the dynamic stability characteristics of simply supported laminated composite skew plates subjected to a periodic in-plane load were investigated using the finite element approach, including the effects of transverse shear deformation, inplane and rotary inertia.
Abstract: Here, the dynamic stability characteristics of simply supported laminated composite skew plates subjected to a periodic in-plane load are investigated using the finite element approach. The formulation includes the effects of transverse shear deformation, in-plane and rotary inertia. The boundaries of the instability regions are obtained using the Bolotin's method and are represented in the non-dimensional load amplitude-excitation frequency plane. The principal and second instability regions are identified for different parameters such as skew angle, thickness-to-span ratio, fiber orientation and static in-plane load.

76 citations


Cites background from "Large amplitude free flexural vibra..."

  • ...The details of element formulation are reported earlier [13,14] and not repeated here for the sake of brevity....

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  • ...(2) is solved using finite element approach based on C(1) continuous element developed recently [13,14]....

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  • ...The covariant components of the displacement vector u (u 1⁄4 u1(1)g+u2(2)g+u3(3)g) of a shear deformable plate can be expressed in terms of the contravariant components of the position vector r (r 1⁄4 (1)rg1+(2)rg2+(3)rg3) [13,14] as u1 (1)r; (2)r; (3)r 1⁄4 u01 (1)r; (2)r þ (3)r(1)f (1)r; (2)r , u2 (1)r; (2)r; (3)r 1⁄4 u02 (1)r; (2)r þ (3)r(2)f (1)r; (2)r , u3 (1)r; (2)r; (3)r 1⁄4 u3 (1)r; (2)r , ð1Þ...

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  • ...In the present paper, a four-noded shear flexible quadrilateral high-precision plate-bending element developed recently [13,14] is extended to analyze the dynamic stability behavior of perfect laminated composite skew plates....

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  • ...The efficacy of the present element for the buckling and vibration analysis of composite skew plates has already been established earlier [13,14] and are not presented here for the sake of brevity....

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Journal ArticleDOI
TL;DR: In this paper, a nonlinear free vibration analysis of thin-to-moderately thick laminated composite skew plates is presented based on the first order shear deformation theory (FSDT) using differential quadrature method (DQM).

75 citations

References
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Book
24 May 2005
TL;DR: Linear Elastic Stress-Strain Relations Elastic Constants Based on Micromechanics, Plane Stress, Global Coordinate System, Elastic Constant Based on Global Coordinated System, Laminate Analysis - Part I- Laminate analysis - Part II- Effective Elastic Constant of a Laminate- Failure Theories of a Laminating System, Homogenization of Composite Materials, to Damage Mechanics of composite Materials as discussed by the authors.
Abstract: Linear Elastic Stress-Strain Relations- Elastic Constants Based on Micromechanics- Plane Stress- Global Coordinate System- Elastic Constants Based on Global Coordinate System- Laminate Analysis - Part I- Laminate Analysis - Part II- Effective Elastic Constants of a Laminate- Failure Theories of a Lamina- to Homogenization of Composite Materials- to Damage Mechanics of Composite Materials

851 citations


"Large amplitude free flexural vibra..." refers background in this paper

  • ...For a composite laminate of thickness h, comprising of N layers with stacking angles i (i=1; 2; : : : ; N ) and layer thicknesses hi (i = 1; 2; : : : ; N ), the necessary expression to compute the sti3ness coeKcients are available in the literature [30]....

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Journal ArticleDOI
Abstract: A review of the recent developments in the analysis of laminated beams and plates with an emphasis on shear effects and buckling is presented. A discussion of various shear-deformation theories for plates and beams is given. The available theories are derived assuming a variation of either the in-plane displacement components or the stress components or both in the thickness coordinate. A review of the recently developed finite elements to analyze thin and thick laminated beams and plates is given next. These elements have been derived using the displacement methods, or the mixed methods or the hybrid methods. Recent studies on the buckling and postbuckling behavior of perfect and geometrically imperfect plates are described next. These behaviors have been studied using analytical, numerical, and experimental techniques. Finally, a review of the various studies on the delamination buckling and growth in beams and plates is given. Once again, the studies have been conducted using analytical, numerical, and experimental techniques. The energy release rates have been determined using closed-form solutions or using numerical differentiation. Mention also is made of studies on multiple delaminations and on dynamic response of composite laminates under impact loads.

490 citations


"Large amplitude free flexural vibra..." refers methods in this paper

  • ...These studies are reviewed and are well documented by Leissa [1,2], Bert [3], Sathyamoorthy [4], Chia [5], and Kapania and Raciti [6]....

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Journal ArticleDOI
TL;DR: A review of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations is presented in this paper, where a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials.
Abstract: A summary of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations in presented. First, a review of the recent studies on the free-vibration analysis of symmetrically laminated plates is given. These studies have been conducted for various geometric shapes and edge conditions. Both analytical (closed-form, Galerkin, Rayleigh-Ritz) and numerical methods have been used. Because of the importance of unsymmetrically laminated structural components in many applications, a detailed review of the various developments in the analysis of unsymmetrical ly laminated beams and plates also is given. A survey of the nonlinear vibrations of the perfect and geometrically laminated plates is presented next. It is seen that due to the bending-stretching coupling, the nonlinear behavior of the unsymmetrically laminated perfect and imperfect plates, depending upon the boundary conditions, may be hardening or softening type. Similar behavior also is observed for imperfect isotropic and laminated plates. Lastly, the developments in studying the wave propagation in laminated materials are reviewed. It is seen that a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials. Some recent studies on the linear and nonlinear transient response of laminated materials also are described.

288 citations


"Large amplitude free flexural vibra..." refers methods in this paper

  • ...These studies are reviewed and are well documented by Leissa [1,2], Bert [3], Sathyamoorthy [4], Chia [5], and Kapania and Raciti [ 6 ]....

    [...]

Journal ArticleDOI

191 citations


"Large amplitude free flexural vibra..." refers methods in this paper

  • ...Prathap and Varadan [22], and Sathyamoorthy and Chia [23] have investigated large amplitude vibration of anisotropic skew plates using the Galerkin method on the basis of a single term assumed vibration mode....

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  • ...These studies are reviewed and are well documented by Leissa [1,2], Bert [3], Sathyamoorthy [4], Chia [5], and Kapania and Raciti [6]....

    [...]