• Smart Structures and Systems
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• v.15 no.5
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• pp.1345-1362
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• 2015

The present paper deals with the free vibration analysis of the functionally graded solid and annular circular plates with two functionally graded piezoelectric layers at top and bottom subjected to an electric field. Classical plate theory (CPT) is used for description of the all deformation components based on a symmetric distribution. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness direction of the plate. The properties of plate core can vary from metal at bottom to ceramic at top. The effect of non homogeneous index of functionally graded and functionally graded piezoelectric sections can be considered on the results of the system. $1^{st}$ and $2^{nd}$ modes of natural frequencies of the system have been evaluated for both solid and annular circular plates, individually.

• Composite Materials and Engineering
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• v.3 no.3
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• pp.179-199
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• 2021

A simple solution for free vibration of cross-ply and angle-ply laminated composite plates in a thermal environment is investigated using a basic trigonometric shear deformation theory. By application of trigonometric four variable plate theory, the transverse displacement is subdivided into bending and shear components, the present theory's number of unknowns and governing equations is reduced, making it easier to use. Hamilton's Principle is extended to derive the equations of motion of the plates using Navier's double trigonometric series, a closed-form solution is obtained; the primary conclusion is that simple solution is obtained with good results accuracy when compared with previously published results, and the natural frequency will differ depending on, environment temperature, thickness ratio, and lamination angle, as well as the aspect ratio of the plate.

• Advances in aircraft and spacecraft science
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• v.9 no.6
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• pp.507-523
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• 2022

This study is aimed to accurately predict the vibration response of two types of functionally graded sandwich plates, one with FGM core and another with FGM face sheets. The gradation in FGM layer is quantified by exponential method. An efficient zig-zag theory is used and the zigzag impacts are established via a linear unit Heaviside step function. The present theory fulfills interlaminar transverse stress continuity at the interface and zero condition at the top and bottom surfaces of the plate for transverse shear stresses. Nine-noded C-0 FE having 8DOF/node is utilized throughout analysis. The present model is free from the obligation of any penalty function or post-processing technique and hence is computationally efficient. Numerical results have been presented on the free vibration behavior of sandwich FGM for different end conditions, lamination schemes and layer orientations. The applicability of present model is confirmed by comparing with published results. Several new results are also specified, which will serve as the benchmark for future studies.

• Proceedings of the KSR Conference
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• 2010.06a
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• pp.13-17
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• 2010

This presentation examines the characteristics of torsional vibration in axisymmetric out-of-plane vibrations of an annular Mindin plate. The out-of-plane vibration of circular or annular plates have been investigated since a long years ago by many researchers. When the classical Kirchhoff plate theory neglecting the effect of transverse shear deformation is applied to a thick plate, its out-of-plane natural frequencies are much different from reality. And so, since Minlin presented a plate theory considering the effect of rotary inertia and transverse shear deformation, many researches for the out-of-plane natural vibration of circular or annular Mindin plates have been performed. But almost all researchers missed the torsional vibration due to transverse shear deformation in axisymmetric out-of-plane vibrations of the circular or annular Mindin plate. Therefore, in this presentation, we verify the existence of torsional vibration of an annular plate and present the natural frequencies of an annular plate with free outer boundary surface.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.8
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• pp.1331-1337
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• 2003

Linearized equations of motion for the vibration analysis of rotating cantilever plates with arbitrary orientation angle are derived in the present work. Two in-plane stretch variables are introduced to be approximated. The use of the two in-plane stretch variables enables one to derive the equations of motion which include proper motion-induced stiffness variation terms. The equations of motion are transformed into dimensionless forms in which dimensionless parameters are identified. The effects of the dimensionless parameters on the modal characteristics of rotating cantilever plates are investigated through numerical study. The natural frequency loci veering along with the associated mode shape variations, which occur while the rotating speed increases, are also presented and discussed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.4 s.97
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• pp.395-403
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• 2005

The dynamic characteristics of delaminated smart composite laminates are studied using animproved layerwise laminate theory. The theory is capable of capturing interlaminar shear stresses that are critical to delamination. The presence of discrete delamination is modeled through the use of Heaviside unit step functions. Stress free boundary conditions are enforced at all free surfaces. Continuity in displacement field and transverse shear stresses are enforced at each ply level. In modeling piezoelectric composite plates, a coupled piezoelectric-mechanical formulation is used in the development of the constitutive equations. Numerical analysis is conducted to investigate the effect of nonlinearity in the transient vibration of bimodular behavior caused by the contact impact of delaminated interfaces. Composite plates with delamination, subject to external loads and voltage history from surface bonded sensors, are investigated and the results are compared with corresponding experimental results and plates without delamination.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.469-475
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• 2004

The transient analysis of delaminated smart composite laminates is studied using an improved layerwise laminate theory. The theory is capable of capturing interlaminar shear stresses that are critical to delamination. The presence of discrete delamination is modeled through the use of Heaviside unit step functions. Stress free boundary conditions are enforced at all fee surfaces. Continuity in displacement field and transverse shear stresses are enforced at each ply level. In modeling piezoelectric composite plates, a coupled piezoelectric-mechanical formulation is used in the development of the constitutive equations. Numerical analysis is conducted to investigate the effect of nonlinearity in the transient vibration of bimodular behavior caused by the contact impact of delaminated interfaces. Composite plates with delamination, subject to external loads and voltage history from surface bonded sensors, are investigated and the results are compared with corresponding experimental results and plates without delamination.

• Structural Engineering and Mechanics
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• v.37 no.4
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• pp.367-383
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• 2011

In this paper, nonlinear partial differential equations of motion for a hybrid composite plate subjected to initial stresses on elastic foundations are established to investigate its nonlinear vibration behavior. Pasternak foundation and Winkler foundations are used to represent the plate-foundation interaction. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the example problems. The governing equations of motion are reduced to the time-dependent ordinary differential equations by the Galerkin's method. Then, the Runge-Kutta method is used to evaluate the nonlinear vibration frequency and frequency ratio of hybrid composite plates. The nonlinear vibration behavior is affected by foundation stiffness, initial stress, vibration amplitude and the thickness ratio of layer. The effects of various parameters on the nonlinear vibration of hybrid laminated plate are investigated and discussed.

• Geomechanics and Engineering
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• v.11 no.2
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• pp.289-307
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• 2016

A simple hyperbolic shear deformation theory taking into account transverse shear deformation effects is proposed for the free flexural vibration analysis of thick functionally graded plates resting on elastic foundations. By considering further supposition, the present formulation introduces only four unknowns and its governing equations are therefore reduced. Hamilton's principle is employed to obtain equations of motion and Navier-type analytical solutions for simply-supported plates are compared with the available solutions in literature to check the accuracy of the proposed theory. Numerical results are computed to examine the effects of the power-law index and side-to-thickness ratio on the natural frequencies.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.668-671
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• 1997

In order to investigate the vibration characteristics of fluid-structure interaction problem, we modeled two identical rectangular plates coupled with bounded fluid. The fixed boundary condition along the plate edges and an ideal fluid were assumed. A commercial computer code, ANSYS was used to perform finite element analysis and FEM solutions were compared with the experimental results to modify the finite element model. As a result, comparison of FEM and experiment showed good agreement, and the transverse vibration modes, in-phase and out of-phase. were observed alternately in the tluid-coupled system. The effects of distance between two rectangular plates and width to length ratio on the fluid-coupled natural frequency were investigated. And it was found that the ormalized natural frequency of the fluid-coupled system monotonically increased with an increase in the number of modes.