• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.19 no.2
• /
• pp.208-216
• /
• 2009

In this paper, we present the equations of motion by which the natural vibration of a rotating annular disk can be analyzed accurately. These equations are derived from the theory of finite deformation and the principle of virtual work. The radial displacements of annular disk at the steady state where the disk is rotating at a constant angular velocity are determined by non-linear static equations formulated with 1-dimensional finite elements in radial direction. The linearlized equations of the in-plane vibrations at the disturbed state are also formulated with 1-dimensional finite elements in radial direction along the number of nodal diameters. They are expressed as in functions of the radial displacements at the steady state and the disturbed displacements about the steady state. In-plane static deformation modes of an annular disk are used as the displacement functions for the interpolation functions of the 1-dimensional finite elements. The natural vibrations of an annular disk with different boundary conditions are analyzed by using the presented model and the 3-dimensional finite element model to verify accuracy of the presented equations of motion. Its results are compared and discussed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2011.10a
• /
• pp.244-249
• /
• 2011

The potential hazards resulting from a low-velocity impact (bird-strike, tool drop, runway debris, etc.) on aircraft structures, such as engine nacelle or a leading edges, has been a long-term concern to the aircraft industry. Certification authorities require that exposed aircraft components must be tested to prove their capability to withstand low-velocity impact without suffering critical damage. In most of the past research studies unloaded specimens have been used for impact tests, however, in reality it is much more likely that a composite structure is exposed to a certain stress state when it is being impacted, which can have a significant effect on the impact performance. And the radiated impact sound induced by impact is analyzed for the damage detection evaluation. In this study, an investigation was undertaken to evaluate the effect in-plane loading on the impact force and sound of composite laminates numerically.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.27 no.9
• /
• pp.1486-1491
• /
• 2003

A modeling method for the modal analysis of a composite trapezoidal plate undergoing in-plane translational acceleration is presented in this paper. The equations of motion for the plate are derived and transformed into a dimensionless form. The effects of the inclination angles, fiber orientation angle and the acceleration on the modal characteristics of the plate are investigated.

• Computational Structural Engineering
• /
• v.7 no.4
• /
• pp.103-111
• /
• 1994

Based on a variational principle of the consistent shear deformable discrete laminate theory derived in the companion paper Part I, a finite element procedure for the vibration analysis of laminated composite plates is presented. The present formulation takes the in-plane displacements of an arbitrary layer, the rotations of the cross section of each layer and transverse displacement of the plate as the state variables at a nodal point of finite element, resulting in total nodal degree of freedom of 2(n+l) +1 for the n-layered laminate. Thus, it allows to specify displacement boundary conditions of layer stretching and/or rotation of layer cross sections around the plate edge and/or lateral displacement. The developed procedure is applied to the free vibration problem for sandwich-type hybrid laminates composed of layers with drastically different material properties whose elasticity solutions are known. Comparison of analysis results with other FEM solutions showed that the present formulation yields better accuracy.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2000.11a
• /
• pp.649-654
• /
• 2000

The non-linear differential equations of motion of a fluid conveying curved pipe are derived by making use of Hamiltonian approach. The extensible dynamics of the pipe is based on the Euler-Bernoulli beam theory. Some significant differences between linear and nonlinear equations and the basic analysis results are discussed. Using eigenfrequency analysis, it can be shown that the natural frequencies are changed with flow velocity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11a
• /
• pp.383.2-383
• /
• 2002

In this paper, an experimental technique using a reference accelerometer has been developed to measure the in-plane vibration intensity of a beam. It has the advantages of shortening measurement time and reducing accelerometer phase error comparing with the cross spectral Intensity measurement technique using an accelerometer array. The distribution of the in-plane vibration Intensity over the beam has been measured. (omitted)

• Journal of Power System Engineering
• /
• v.11 no.4
• /
• pp.78-85
• /
• 2007

In order to analyze accurately the vibration of a structure by using the finite element method (FEM), we have to model a analytical structure as a numerical model with many degrees-of-freedom. However, in this case, the FEM needs much computation time and storage. The authors developed the finite element-transfer stiffness coefficient method (FE-TSCM) for overcoming the drawback of the FEM. In this paper, the authors apply the FE-TSCM to the in-plane vibration analysis of general plates with various shapes. Two numerical examples, a rectangular plate and a triangular plate, are used to compare the results of the FE-TSCM and the FEM. Through the numerical calculation, we confirm that the FE-TSCM can be applied to the in-plane free or forced vibration analysis of the general plates with various shapes and is effective to in-plane vibration analysis of general plates.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2007.05a
• /
• pp.1181-1184
• /
• 2007

The differential equations governing free, in-plane vibrations of linearly elastic circular arches with rotationally flexible supports, including the effects of rotatory inertia, shear deformation and axial deformation, are solved numerically using the corresponding boundary conditions. The lowest four natural frequencies and the corresponding mode shapes are obtained over a range of non-dimensional system parameters: the subtended angle, the slenderness ratio, and the rotational spring stiffness.

• Journal of Korean Association for Spatial Structures
• /
• v.6 no.4 s.22
• /
• pp.81-92
• /
• 2006

This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon Poisson's ratio ( V ), results are shown for $0{\leq}v{\leq}0.5$, valid for isotropic materials.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1997.10a
• /
• pp.609-612
• /
• 1997

This paper deals with in-plane vibration analysis of curved beams. The exact dynamic element method is applied to obtain the dynamic model for curved beams. Numerical examples are provided to validate the proposed modeling and analysis method. The numerical results show that the proposed method is useful for the dynamic analysis of curved beams.