• Journal of the Korean Society of Industry Convergence
• /
• v.5 no.1
• /
• pp.45-52
• /
• 2002

In this study, an exact solution of governing differential equation for the bending problem of partially loaded orthotropic rectangular plates is presented and also its computer program is developed. The method requires that two opposite edges be clamped or simply supported, or one edge clamped and the other simply supported. Any combination of boundary conditions could exist along the other edges. The plate could he subjected to uniform, partially uniform, and line loads. The solution for the deflection of rectangular plate is expressed as a Levy type single Fourier series and the loads arc expressed as a corresponding series. The advantage of the solution is that it overcomes the limitations of the previous Navier's and Levy's methods (limitation of boundary condition and loading conditions of plate), it is easy to program on a computer and it becomes fast to solve the bending problem with computer program. Calculations are presented for isotropic and orthotropic plates with different loading and boundary conditions. Comparisons are made for the isotropic plate with various boundary conditions between the result of this paper and the result of Navier, Levy and Szilard. The deflections were in excellent agreement.

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

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11b
• /
• pp.529-534
• /
• 2002

The receptance method was applied for the analysis of a cylindrical shell with a curvaturated plate attached at the top of the shell. The boundary conditions of the shell considered here were clamped at the bottom and free at the top of the shell. Before the analysis of the shell/plate combined structure, the natural frequencies of the plate and the shell were calculated separately and then they were used in the calculation of the frequencies of the combined structure by the receptance method. The frequency equation of the combined structure was derived from the continuity condition at the junction of the shell and the plate. The frequencies for various curvature factors of the plate were presented and compared with those from ANSYS to show its validity of the present method.

• Structural Engineering and Mechanics
• /
• v.52 no.1
• /
• pp.89-95
• /
• 2014

We analyze the buckling of a thin elastic plate due to intrinsic stresses in thin films attached to the surfaces of the plate. In the case of cylindrical buckling, it is shown that for a plate with clamped edges compressive intrinsic film stresses can cause flexural buckling of the plate, while tensile intrinsic film stresses cannot. For a plate with free edges, film intrinsic stresses, compressive or tensile, cannot cause buckling.

• Journal of Mechanical Science and Technology
• /
• v.17 no.1
• /
• pp.85-96
• /
• 2003

In the present investigation, the nonlinear dynamic buckling of a curved plate subjected to sinusoidal loading is examined. By the theoretical analyses, a highly nonlinear snap-through motion of a clamped-free-clamped-free plate and its effect on the overall vibration response are investigated. The problem is reduced to that of a single degree of freedom system with the Rayleigh-Ritz procedure. The resulting nonlinear governing equation is solved using Runge-Kutta (RK-4) numerical integration method. The snap-through boundaries, which vary with different damping coefficient and linear circular frequency of the flat plate are studied and given in terms of force and displacement. The relationships between static and dynamic responses at the start of a snap-through motion are also predicted. The analysis brings out various characteristic features of the phenomenon, i.e. 1) small oscillation about the buckled position-softening spring type motion, 2) chaotic motion of intermittent snap-through, and 3) large oscillation of continuous snap-through motion crossing the two buckled positions-hardening spring type. The responses of buckled plate were found to be greatly affected by the snap-through motion. Therefore, better understanding of the snap-through motion is needed to predict the full dynamic response of a curved plate.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2004.11a
• /
• pp.199-203
• /
• 2004

In this paper, a simplified model is studied to predict analytically the radiated noise from the helical gear system due to an axial excitation of helical gear. The simplified model describes gear, shaft, bearing, and housing. To obtain the axial force of helical gear, mesh stiffness is calculated in the load deflection relation. The axial force is obtained from the solution of the equation of motion, using the mesh stiffness. It is used as a longitudinal excitation of the shaft, which in turn drives the gear housing through the bearing. In this study, the shaft is modeled as a rod, while the bearing is modeled as a parallel spring and damper only supporting longitudinal forces. The gear housing is modeled as a clamped circular plate with viscous damping. For the modeling of this system, transfer function from the shaft to the clamped plate are used, using a spectral method with four pole parameters. Out-of-plane displacement for the thin circular plate with viscous damping is derived and sound pressure radiated from the plate is also derived. Using the model, parameter studies are carried out.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.18 no.1
• /
• pp.123-130
• /
• 2008

An analytical method for the free vibration of a flexible rectangular plate in contact with water is developed by the Rayleigh-Ritz method. The plate clamped along the edges is partially contacted with water at both sides. It is assumed that the contained water is incompressible and inviscid. The wet mode shape of the plate is assumed as a combination of the dry mode shapes of a clamped beam. The liquid motion is described by using the liquid displacement potential and determined by using the compatibility conditions along the liquid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict excellently the fluid-coupled natural frequencies comparing with the finite element analysis result.

• Journal of KSNVE
• /
• v.4 no.3
• /
• pp.283-295
• /
• 1994

This work presents the experimental and finite element analysis results for the free vibration of 4 edges clamped, isotropic square plates with 2 collinear circular holes. Natural frequencies of finite element analysis are obtained for the complete square plate, the square plates with a central circular hole and the square plates with 2 collinear circulare holes. And natural frequencies are experimentally measured for the complete square plate, the square plate with a central circular hole(d = 150 mm) and the square plates with 2 collinear circular holes. Agreement between experimental and FEM results is excellent. Mode shapes in special case are presented. The conclusions of the study are as follows. There is little variation of nondimensional frequency parameters for the first six mode when the aspect ratio of circular hole is less than 1/6 in the isotropic square plates with 2 collinear circular holes. And the first nondimensional frequency parameter doesn't vary as the aspect ratio of circular hole increase.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.28 no.1
• /
• pp.75-82
• /
• 1986

In this paper. the characteristics of mechanical behaviour due to various edge-ratio of uniformly loaded clamped skew-~plates has been described. In this study, the skew-plate was discretized using 8-noded isoparametric element and Mindlin's plate theory was adapted in finite element formulation. The edge-ratio 0.5,0.8,1.0,1.2,1.5,2.0 and 2.5 were considered. Hence, five cond- itions of the skew-angle, the seven levels of edge ratio were tried. When the edge-ratio was 2.5 or the edge-ratio was 2.0 and the skew-angle was less than 45 degree, the behaviour of the uniformly loaded the skew-plate with all edges clamped was independent of the skew-angle.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1996.10a
• /
• pp.237-242
• /
• 1996

A theoretical formulation for the analysis of free vibration of clamped-free cylindrical shells with plates attached at arbitrary axial positions was derived and it was programed to get the numerical results which yield natural frequencies and mode shape of the combined system of plate and shells. The frequencies and mode shapes from theoretical calculation were compared with those of commercial finite element code, ANSYS as well as modal test in order to validate the formulation. The effects of the thickness and location of the plate were evaluated.