• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.73-80
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• 2006

In order to examine the validity of an asymptotic solution for nonlinear interaction in asymmetric vibration modes of a perfect circular plate, we obtain the numerical solution. The motion of the plate is governed by nonlinear partial differential equation. The initial and boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution. It is found that traveling waves relating clockwise and counterclockwise as well as standing wave are depicted by the numerical solution.

• Structural Engineering and Mechanics
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• v.44 no.3
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• pp.267-288
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• 2012

Free vibration analysis of arbitrary quadrilateral thick plates with internal columns and elastic edge supports is presented by using the powerful pb-2 Ritz method and Reddy's third order shear deformation plate theory. The computing domain of arbitrary quadrilateral planform is mapped onto a standard square form by coordinate transformation. The versatile pb-2 Ritz functions defined by the product of a two-dimensional polynomial and a basic function are taken to be the admissible functions. Substituting these displacement functions into the energy functional and minimizing the total energy by differentiation, leads to a typical eigenvalue problem, which is solved by a standard eigenvalue solver. Stiffness and mass matrices are numerically integrated over the plate by using Gaussian quadrature. The accuracy and efficiency of the proposed method are demonstrated through several numerical examples by comparison and convergency studies. A lot of numerical results for reasonable natural frequency parameters of quadrilateral plates with different combinations of elastic boundary conditions and column supports at any locations are presented, which can be used as a benchmark for future studies in this area.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.6
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• pp.193-199
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• 2001

Active control of forced vibration of the cantilevered laminated composite plates using collocated piezoceramic sensor/actuator is analyzed numerically and verified experimentally for various fiber orientations. Impact on the stiffness and the damping properties is studied by varying stacking sequence of [$\theta$$_{4}$O$_{2}$90$_{2}$]s for the laminated composite plate. For the forced vibration control, the plate is excited by one pair of collocated PZT exciters in resonance and its vibrational response is suppressed by the other collocated PZT sensor/actuator using direct negative velocity feedback. It is shown that the active control of forced vibration is more effective for the smart laminated plate with higher modal damped stiffness(2ζ$\omega$/aup 2/) .

• Bulletin of the Society of Naval Architects of Korea
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• v.18 no.1
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• pp.1-8
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• 1981

To contribute to the preventive measures against local vibrations of ship's deck panels, some investigations into the prediction method of the natural frequency of the vibration of stiffened plates were done. Firstly, an analytical method based on the orthotropic plate analogy and the Rayleigh method using eigenfunctions of the Euler beam was shown, and numerical results of a regularly stiffened plate were compared with experimental results. And then, the method was extended to stiffened plates having one or two irregular stiffeners to obtain an approximate formula showing the relation between the change of the natural frequency and the size of the irregular stiffeners. The latter case was investigated for the purpose of providing a convenient design manual applicable to cure of local resonant vibrations of ships' deck panels by additional reinforcement of one or two stiffeners. In the analytical development the boundary was assumed to be rigidly supported and elastically restrained against rotation. In the experiment, however, only an extreme case i.e. simply supported boundary was investigated. The results of the investigation show that there is a fairly good conformity between the analytical results and the experimental ones in the first case, and that the approximate formula for the second case is confirmed also to be reliable for the design purpose. Considering that actual boundary conditions of deck panels in ship structures lie mostly somewhere between the simple support and the fixed, the authors discussed problems of the joint efficiency at the boundary of deck panels from the viewpoint of the practical application of the formulae.

• The Journal of the Acoustical Society of Korea
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• v.6 no.3
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• pp.5-16
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• 1987

In this paper, the sound radiation from a clamped circular plate with a viscoelastic layer excited by impact force is studied both analytically and experimentally. The composite plate vibrations are obtained by using the normal mode analysis and the eigenvalues are obtained by a Mindlin plate theory including the rotary inertia and shear deformation, The contact force developed between the ball and the plate with attached layers is obtained by Hertz contact theory. The radiated sound pressure is calculated by the Rayleigh integral. Prediction of the waveforms of sound radiating from the plate with attached layers and a method for reducing noise generation from the plate by impact force are also shown in this paper.

• Smart Structures and Systems
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• v.16 no.6
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• pp.1023-1047
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• 2015

In this study, the optimal location of the MR fluid segments in a partially treated laminated composite sandwich plate has been identified to maximize the natural frequencies and the loss factors. The finite element formulation is used to derive the governing differential equations of motion for a partially treated laminated composite sandwich plate embedded with MR fluid and rubber material as the core layer and laminated composite plate as the face layers. An optimization problem is formulated and solved by combining finite element analysis (FEA) and genetic algorithm (GA) to obtain the optimal locations to yield maximum natural frequency and loss factor corresponding to first five modes of flexural vibration of the sandwich plate with various combinations of weighting factors under various boundary conditions. The proposed methodology is validated by comparing the natural frequencies evaluated at optimal locations of MR fluid pockets identified through GA coupled with FEA and the experimental measurements. The converged results suggest that the optimal location of MR fluid pockets is strongly influenced not only by the boundary conditions and modes of vibrations but also by the objectives of maximization of natural frequency and loss factors either individually or combined. The optimal layout could be useful to apply the MR fluid pockets at critical components of large structure to realize more efficient and compact vibration control mechanism with variable damping.

• Earthquakes and Structures
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• v.14 no.2
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• pp.117-128
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• 2018

In this research work, free vibrations of simply supported functionally graded plate resting on a Winkler-Pasternak elastic foundation are investigated by a new shear deformation theory. The influence of alternative micromechanical models on the macroscopic behavior of a functionally graded plate based on shear-deformation plate theories is examined. Several micromechanical models are tested to obtain the effective material properties of a two-phase particle composite as a function of the volume fraction of particles which continuously varies through the thickness of a functionally graded plate. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. The energy functional of the system is obtained using Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Finally, the numerical results are provided to reveal the effect of explicit micromechanical models on natural fundamental frequencies.

• Smart Structures and Systems
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• v.29 no.3
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• pp.395-420
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• 2022

A new hybrid quasi-3D and 2D high-order shear deformation theory is studied in this mathematical formulation, for an investigation of the bending, free vibrations and buckling influences on a functionally graded material plate. The theoretical formulation has been begun by a displacement field of five unknowns, governing the transverse displacement across the thickness of the plate by bending, shearing and stretching. The transverse shear deformation effect has been taken into consideration, satisfying the stress-free boundary conditions, especially on plate free surfaces as parabolic variation through its thickness. Thus, the mechanical properties of the functionally graded plate vary across the plate thickness, following three distributions forms: the power law, exponential form and the Mori-Tanaka scheme. The mechanical properties are used to develop the equations of motion, obtained from the Hamilton principle, and solved by applying the Navier-type solution for simply supported boundary conditions. The results obtained are compared with other solutions of 2D, 3D and quasi-3D plate theories have been found in the literature.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.327-333
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• 1998

A method for analysis of the free vibrations of the composite cylindrical shell with a longitudinal, interior rectangular plate is developed by using the receptance method. This method is based on the ratio of a deflection(or slope) response to a harmonic force(or moment) at an joint point. The natural frequencies of the combined shells calculated numerically. The results are compared with the experiment and a finite, element analysis results in order to validate the formulation. The effects of the location and thickness of the plate on the frequencies are also investigated.

• Structural Engineering and Mechanics
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• v.68 no.2
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• pp.203-213
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• 2018

This paper presents a study of geometric nonlinear forced vibration of carbon nano-tubes (CNTs) reinforcement composite plates on nonlinear elastic foundations. The plate is bonded with piezoelectric layers. The von Karman geometric nonlinearity assumptions with classical plate theory are employed to obtain the governing equations. The Galerkin and homotopy perturbation method (HPM) are utilized to investigate the effect of carbon nano-tubes volume fractions, large amplitude vibrations, elastic foundation parameters, piezoelectric applied voltage on frequency ratio and primary resonance. The results indicate that the carbon nano-tube volume fraction, applied voltage and elastic foundation parameters have significant effect on the hardening response of carbon nanotubes reinforced composite (CNTRC) plates.