• Structural Engineering and Mechanics
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• v.70 no.6
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• pp.711-722
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• 2019

Considering stress singularities at point support locations, buckling solutions for plates with arbitrary number of point supports are hard to obtain. Thus, new Hp-Cloud shape functions with Kronecker delta property (HPCK) were developed in the present paper to examine elastic buckling of point-supported thin plates in various shapes. Having the Kronecker delta property, this specific Hp-Cloud shape functions were constructed through selecting particular quantities for influence radii of nodal points as well as proposing appropriate enrichment functions. Since the given quantities for influence radii of nodal points could bring about poor quality of interpolation for plates with sharp corners, the radii were increased and the method of Lagrange multiplier was used for the purpose of applying boundary conditions. To demonstrate the capability of the new Hp-Cloud shape functions in the domain of analyzing plates in different geometry shapes, various test cases were correspondingly investigated and the obtained findings were compared with those available in the related literature. Such results concerning these new Hp-Cloud shape functions revealed a significant consistency with those reported by other researchers.

• Journal of Industrial Technology
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• v.16
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• pp.139-145
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• 1996

Many of the bridge systems, including the girders and cross-beams, and concrete decks behave as the special othotropic plates. A method of calculating the natural frequency corresponding to the first mode of vibration of beam and tower structures with irregular cross-sections was developed and reported by D. H. Kim in 1974. Since 1989, The author has extended this method to Vibration analysis of two dimensional problems including composite laminates, and has reported at several conferenes. Frequently, the bridge floor panels are supported by girders and cross beams. Such panels as well as some of the building floor panels can be assumed as simple supported special orthotropic plates. In this paper, the result of application of simple method of vibration analysis developed by D. H. Kim, to the simply supported sandwich panels with point Mass/Masses is presented.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.1
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• pp.166-176
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• 1994

The problem of reducing the vibration level of elastic plates driven by multiple random point forces is analyzed in this study. First, the analytical solution for the vibration level of finite thin plates with four simply supported edges under the action of multiple random point force is derived. By assuming the plates to be lightly damped, an approximate solution for the vibration level of the plate is obtained. A numerical study is carried out to determine an optimal spacing distance between the multiple point forces in order to produce a relative minimum in the plate's vibration level. The optimal spacing distance is shown to depend on the given excitation band. The effects of wave cancellation in the near field of the multiple point forces are discussed by using the equivalence of certain stationary random responses and deterministic pulse responese.

• Structural Engineering and Mechanics
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• v.62 no.4
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• pp.431-441
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• 2017

In this article, an analytical-numerical approach is presented in order to determine the dynamic response of thin plates resting on multiple elastic point supports with time-varying stiffness. The proposed method is essentially based on transforming a familiar governing partial differential equation into a new solvable system of linear ordinary differential equations. When dealing with time-invariant stiffness, the solution of this system of equations leads to a symmetric matrix, whose eigenvalues determine the natural frequencies of the point-supported plate. Moreover, this method proves to be applicable for any plate configuration with any type of boundary condition. The results, where possible, are verified upon comparison with available values in the literature, and excellent agreement is achieved.

• Advances in aircraft and spacecraft science
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• v.6 no.6
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• pp.443-461
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• 2019

This communication investigates exact and distorted similitudes and the related scaling laws for the analysis of both dynamic response and radiated power of rectangular plates. The response of a given panel in similitude from another one is determined from a generalization of the modal approach, allowing the use of mode shapes, natural frequencies and finally radiation functions in order to establish appropriate scaling laws. Analytical models of simply supported rectangular plates are used to produce both original and replica model responses under point mechanical excitation. Emphasis is then especially put on laboratory experiments which are performed on baffled simply supported aluminum panels under mechanical excitations. All the six possible scaling directions, i.e. predicting a plate vibroacoustic reponse from another plate, are reported. All obtained results show that structural response or radiated sound power of a given plate can be both recovered with satisfactory accuracy by using the related scaling laws, even if parent models are used.

• Structural Engineering and Mechanics
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• v.51 no.2
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• pp.333-347
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• 2014

Nonlinear bending of super-elliptical plates of uniform thickness under uniform transverse pressure was investigated by the Ritz method. The material was assumed to be homogeneous and isotropic. The contribution of the boundary conditions at the point supports was introduced by the Lagrange multipliers. The solution was obtained by the Newton-Raphson method. The influence of the location of the point supports on the central deflection was highlighted by sensitivity analysis. An approximate relationship between the central deflection and the super-elliptical power was obtained using the method of least squares. The critical points where the maximum deflection may develop, and the influence of nonlinearity were highlighted. The nonlinearity was found to be sensitive to the aspect ratio. The accuracy of the algorithm was validated by comparing the central deflection with the solutions of elliptical and rectangular plates.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.6
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• pp.607-613
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• 2009

A new formulation of NDIF method to the algebraic eigenvalue problem is introduced to efficiently extract natural frequencies of arbitrarily shaped plates with the simply supported boundary condition. NDIF method, which was developed by the authors for the free vibration analysis of arbitrarily shaped membranes and plates, has the feature that it yields highly accurate natural frequencies compared with other analytical methods or numerical methods(FEM and BEM). However, NDIF method has the weak point that it needs the inefficient procedure of searching natural frequencies by plotting the values of the determinant of a system matrix in the frequency range of interest. A new formulation of NDIF method developed in the paper doesn't require the above inefficient procedure and natural frequencies can be efficiently obtained by solving the typical algebraic eigenvalue problem. Finally, the validity of the proposed method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate compared to other exact, analytical, or numerical methods.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.9
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• pp.830-836
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• 2012

The NDIF method based on a sub-domain technique is introduced to extract highly accurate natural frequencies of arbitrarily shaped plates with the simply-supported boundary condition. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped plates with various boundary conditions, has the feature that it yields highly accurate natural frequencies thanks to its effective theoretical formulation, compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that it can be applicable for only convex plates. It was revealed that the NDIF method offers very inaccurate natural frequencies or no solution for concave cavities. To overcome the weak point, the paper proposes the sub-domain method of dividing a concave plate into several convex domains. Finally, the validity of the proposed method is verified in various case studies, which indicate that natural frequencies obtained by the proposed method are very accurate compared to the exact method and FEM(ANSYS).

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.4
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• pp.91-96
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• 2001

In this paper, an investigation was performed on the dynamic interlaminar fracture toughness of CFRP(carbon filber rein-forcement plastics). Specimens used in this experiments are CF/PEEK laminated plates. In this experiments, Split Hopkin-sons Bar(SHPE) tes was apply to dynamic and notched flexure test. The model II fracture toughness of each unidirectional CFRP was estimated by the analyzed deflection of the specimen and J-integral with the measured impulsive load and reac-tions at the supported points. As an experimental results the vibration amplitude of [$0^{\circ}_10 /F_4 0^{\circ}_10 $] j-aminates appear more than that of [$0^{\circ}_10 /F_2 0^{\circ}_10 $ laminates for the j-integral and displacement velocity at a measuring point. Also, it is thought that the dynamic fracture toughness of two kind specimen(CF/PEEK) with the crease of displacement velocity becomes great at a measuring point with in the range of measurement.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.675-678
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• 2001

In this paper, an investigation was performed on the dynamic interlaminar fracture toughness of CFRP(carbon fiber reinforcement plastics). Specimens used in this experiment are CF/EPOXY laminated plates. In this experiments, Split Hopkinson s Bar test was applied to dynamic and notched flexure test. The mode II fracture toughness of each unidirectional CFRP was estimated by the analyzed deflection of the specimen and J-integral with the measured impulsive load and reactions at the supported points. As an experimental result, the vibration amplitude of 〔$0_{10}F_4/0_{10}$〕laminates appear more than that of 〔0_{10}/F_2/0_{10}$〕laminates for the J-integral and displacement velocity at a measuring point. Also, it is thought that the dynamic fracture toughness of two kind specimen with the increase of displacement velocity becomes great at a measuring point with in range of measurement.