• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.3 s.120
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• pp.220-225
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• 2007

Free vibration analysis using the method of NDIF (non-dimensional dynamic influence function), which was developed by the author, is extended to arbitrarily shaped polygonal plates with free edges. Local Cartesian coordinate systems are employed to apply the free boundary condition to nodes distributed along the edges of the plate of interest. Furthermore, a new way for applying the free boundary condition to nodes located at corners of the plate is for the first time introduced by considering the phenomenon of stress concentration at the corners. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM(ANSYS).

• 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 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.21 no.2
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• pp.186-193
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• 2011

The NDIF method(non-dimensional dynamic influence function method) for free vibration analysis of arbitrarily shaped plates with the simply supported edge is newly developed in the paper. In order to extract the system matrix that gives the natural frequencies and natural modes of the plate of interest, the difficulty of measuring higher differential terms involved in the simply supported boundary condition is successfully overcome. Finally, the excellence of the characteristics of convergence and accuracy of the proposed method is shown through two verification examples, which indicate that natural frequencies and natural modes obtained by the proposed method are very accurate and swiftly converged even though a small number of nodes are used compared with FEM.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.6
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• pp.674-680
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• 2008

A new meshless method for obtaining natural frequencies of arbitrarily shaped plates with the free boundary condition is introduced in the paper. In order to improve the characteristics of convergence and accuracy of the method, a special local polar coordinates system is devised and located for each of nodes distributed along the boundary of the plate of interest. In addition, a new way of decreasing the size of the system matrix that gives natural frequencies of the plate is employed to reduce the amount of numerical calculations, which is needed for computing the determinant of the system matrix. Finally the excellence of the characteristics of convergence and accuracy of the method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate and converged swiftly to exact values as the number of boundary nodes increases.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.6 s.123
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• pp.531-538
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• 2007

A new method for free nitration analysis using series functions is proposed to obtain the eigenvalues of arbitrarily shaped, polygonal plates with clamped edges. Since a general solution used in the method satisfies the equation of motion for the transverse vibration of a plate, the method offers very accurate eigenvalues, compared to FEM or BEM results. In addition, the method can minimize the amount of numerical calculation because it has the advantage of not needing to divide the plate of interest. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM (NASTRAN) or another analytical method.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.740-745
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• 2003

The so-called boundary node method (or NDIF method) that was developed by the authors has been extended for free vibration analysis of arbitrarily shaped plates with free edges. Since the proposed method is based on the collocation method, no integration procedure is needed on boundary edges of the plates and only a small amount of numerical calculation is required. A special coordinate transformation has been devised to consider the complicated free boundary conditions at boundary nodes. By the use of the special coordinate transformation, the radius of curvature involved in the free boundary conditions can be successfully dealt with. Finally, verification examples show that natural frequencies obtained by the present method agree well with those given by exact method and other analytical methods.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.10
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• pp.821-827
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• 2003

The so-called boundary node method (or NDIF method) that was developed by the authors has been extended for free vibration analysis of arbitrarily shaped plates with free edges. Since the proposed method requires no interpolation functions. no integration Procedure is needed on boundary edges of the plates and only a small amount of numerical calculation is involved, compared with FEM and BEM. In order to explain tile reason why spurious eigenvalues are generated when the NDIF method is applied to free plates, the NDIF method has been considered for free vibration analysis of both a fixed string and a free beam. Finally, verification examples show that natural frequencies obtained by the present method agree well with those given by an exact method or a numerical method (ANSYS).

• Advances in aircraft and spacecraft science
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• v.1 no.2
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• pp.145-175
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• 2014

The results of a series of numerical experiments are presented to verify some of the important developments made in the first part of this paper. Firstly, the static solution of an algebraic system obtained through Strong Formulation Finite Element Method (SFEM) is presented. Secondly, the stress and strain recovery procedure is descripted for the present technique. It will be clear that the present approach is suitable for any strong formulation finite element methodology, due to the presented general approach based on the unknown displacements and on the elasticity equations. Thirdly, the numerical solutions for some classical and other numerical results found in literature are exposed. Finally, an arbitrarily shaped composite plate is solved and good agreement is observed for all the presented cases.