• Structural Engineering and Mechanics
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• v.21 no.2
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• pp.169-184
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• 2005

This study deals with the free vibration of a circular plate in contact with a fluid; submerged in fluid, beneath fluid or on fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. The proposed method is verified by the finite element analysis using commercial program with a good accuracy. The normalized natural frequencies are obtained in order to estimate the relative added mass effect of fluid on each vibration mode of the plate. Also, the location of plate coupled with fluid and the cases of free and bounded fluid surface are studied for the effect on the vibration characteristics.

• Journal of the Korean Society for Advanced Composite Structures
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• v.2 no.3
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• pp.42-47
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• 2011

A method of calculating natural frequencies corresponding to the modes of vibration of beams and tower structures with irregular cross sections and arbitrary boundary conditions was developed. The result is compared with that of the beam theory. Finite difference method is used for this purpose. The influence of the $D_{22}$ stiffness on the natural frequency is rigorously investigated. In this paper, the relation between the applied loading sizes and the natural frequency of vibration of some structural elements is presented. The results of application of this method to steel bridge and reinforced concrete slab bridge by using specially orthotropic plate theory is presented.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1899-1909
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• 1994

This work presents the experimental and FEM results for the free vibration of cantilevered, symmetrically and antisymmetrically laminated composite rectangular plates. The natural frequencies, mode shapes and contour plots of a number of CFRP, GFRP, DFRP-Aluminum, GFRP-Aluminum and DFRP-GFRP hybrid composite plates are experimentally obtained. Determination of Young's modulus and test procedures are described. The natural frequencies are determined for a wide range of parameters : e.g. , composite material constants, fiber angles and stacking sequences. Natural frequency and nondimensional frequency parameter results are compared with the finite element analysis and existing literatures. Agreement between experimental and calculated frequencies is excellent. The effects of varing the parameters upon the free vibration frequencies and mode shapes are discussed.

• Journal of KSNVE
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• v.2 no.4
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• pp.305-315
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• 1992

In order to investigate the effects of layer-wise in-plane displacements on vibration and damping characteristics of composite laminated plates, the finite element method based on the generalized laminated plate theory(GLPT) has been formulated. Specific damping capacity of each mode was obtained by modal strain energy method. To see the effect of transverse shear on deformation, the strain energy of stress components was computed. The accuracy of this study was examined for the cylindrical bending vibration of cross-ply plate strip. The results were very accurate compared with 3-D solutions. The numerical results show that through-thickness variation of in-plane displacements has not so much influence on the natural frequency, but has a great influence on the damping of composite plates, especially on the damping of thick composite plates since the damping is affected by local behavior while the natural frequency is affected by global behavior.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.1-4
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• 2001

A new non-destructive fatigue prediction model of the composite laminates is developed. The natural frequencies of fatigue-damaged laminates under extensional loading are related to the fatigue lift of the laminates by establishing the equivalent flexural stiffness reduction as a function of the elastic properties of sublaminates. The flexural stiffness is derived by relating the $90^{\circ}$-ply elastic modulus reduction, and using the laminate plate theory to the degraded elastic modulus and the intact elastic modulus of other laminate. The natural frequency reduction model, in which the dominant fatigue mode can be identified from the sensitivity scale factors of sublaminate elastic properties, provides natural frequency vs. fatigue cycle curves for the composite laminates. Vibration tests were also conducted on $[\textrm{90}_{2}\textrm{0}_{2}]_s$ carbon/epoxy laminates to verify the natural frequency reduction model. Correlations between the predictions of the model and experimental results are good.

• Wind and Structures
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• v.24 no.4
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• pp.307-331
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• 2017

Free transverse vibration of shear deformable super-elliptical plates with uniform thickness was studied based on Mindlin plate theory using finite element method. Quadrilateral isoparametric elements were used in the paper. Sensitivity analysis was made to determine the influence of the thickness, the aspect ratio, and the shape of the plate on the natural frequency. Accuracy of the results computed in the current study was validated by comparing them with the solutions available in the literature. The results reveal that the frequencies of clamped super-elliptical plates lie in the range bounded by elliptical and rectangular plates irrespective of the aspect ratio, and furthermore, the frequency decreases if the super-elliptical power increases. A similar trend was observed for simply supported plates with high aspect ratio. The free vibration response for the first and the second symmetric-antisymmetric (SA) modes were found to be different for high aspect ratio. The results reveal that using insufficient number of degrees of freedom results in finding a totally different relation between the super-elliptical power and the frequency.

• Steel and Composite Structures
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• v.28 no.4
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• pp.509-516
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• 2018

The differential quadrature (DQ) and teaching-learning based optimization (TLBO) methods are coupled to introduce a hybrid numerical method for maximizing fundamental natural frequency of laminated composite skew plates. The fiber(s) orientations are selected as design variable(s). The first-order shear deformation theory (FSDT) is used to obtain the governing equations of the plate. The equations of motion and the related boundary conditions are discretized in space domain by employing the DQ method. The discretized equations are transferred from the time domain into the frequency domain to obtain the fundamental natural frequency. Then, the DQ solution is coupled with the TLBO method to find the maximum frequency of the plate and its related optimum stacking sequences of the laminate. Convergence and applicability of the proposed method are shown and the optimum fundamental frequency parameter of the plates with different skew angle, boundary conditions, number of layers and aspect ratio are obtained. The obtained results can be used as a benchmark for further studies.

• Journal of Industrial Technology
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• v.16
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• pp.123-129
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• 1996

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and tower structures with irregular cross-sections and with arbitrary boundary conditions was developed and reported by D. H. Kim in 1974. In order to obtain the natural frequency by the presented method, the first step to take is to obtain the deflection influence surfaces. In design and analysis of any structure, the first step to be taken is to obtain this deflection influence surfaces. Any method can be used for this purpose. Then using this surfaces, deflections, slopes, moments, shears, and natural frequencies can be obtained by differentiating either the continuous function or discrete function defined at certain points. The merit of the presented method is that the natural frequency can be obtained by the deflection influence surfaces obtaining which is the first step in structural analysis.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.143-146
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• 2003

A finite element based on the efficient higher order zig-zag theory with multiple delaminations Is developed to refine the predictions of frequency and mode shapes. Displacement field through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions including delaminated interfaces as well as free hounding surface conditions of transverse shear stresses. Thus the proposed theory is not only accurate but also efficient. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Throught the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Through the natural frequency analysis and time response analysis of composite plate with multiple delaminations, the accuracy and efficiency of the present finite element are demonstrated. The present finite element is suitable in the predictions of the dynamic response of the thick composite plate with multiple delaminations.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.11
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• pp.779-786
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• 2015

The Kansa method, which is used for various free vibration problems of arbitrarily shaped plates including membranes, discretizes the domain of a plate using only nodes without elements unlike FEM. The method requires a small amount of computation relative to FEM thanks to this discretization scheme but has limit in the accuracy of its solution. This paper reveals the reason of the limit and, to overcome the limit, proposes the practical method of calculating the singularity of a system matrix and extracting accurate natural frequencies. Case studies for a rectangular plate and an arbitrarily shaped plate validate the proposed method.