• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.10a
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• pp.658-663
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• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate eigenvalues of concave acoustic cavities with arbitrary shapes. It is said that the MNDIF method cannot yield accurate eigenvalues for concave cavities. To overcome this weak point, a new approach of dividing a concave cavity into two convex domains is proposed. The validity of the proposed method is shown through a case study.

• 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).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.04a
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• pp.601-602
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• 2014

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.184.2-184.2
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• 2005

• 한국신재생에너지학회:학술대회논문집
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• 2005.06a
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• pp.534-537
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• 2005

Free Vibration Analysis using Non-dimensional Dynamic Influence Function (NDIF) is extended to arbitrarily shaped plates including polygonal plates. Since the corners of polygonal plates have indefinite normal directions and additional boundary conditions related to a twisting moment at a corner along with moment and shear force zero conditions, it is not easy to apply the NDIF method to polygonal plates wi th the free boundary condition. Moreover, owing to the fact that the local polar coordinate system, which has been introduced for free plates with smoothly varying edges, cannot be employed for the straight edges of the polygonal plates, a new coordinate system is required for the polygonal plates. These problems are solved by developing the new method of modifying a corner into a circular arc and setting the normal direction at the corner to an average value of normal direct ions of two edges adjacent to the corner. Some case studies for plates with various shapes show that the proposed method gives credible natural frequencies and mode shapes for various polygons that agree well with those by an exact method or FEM (ANSYS).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.180-185
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• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate natural frequencies of concave plates with arbitrary shape. Originally, the MNDIF method cannot yield accurate natural frequencies for concave plates. To overcome this weak point, a new approach of dividing a concave plate into two convex domains is proposed and the validity and accuracy is shown in a verification example.

• 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.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.23 no.8
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• pp.725-733
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• 2013

An improved formulation of the MNDIF method is introduced to extract highly accurate natural frequencies of concave plates with arbitrary shape. Originally, the MNDIF method cannot yield accurate natural frequencies for concave plates. It can be applicable to only convex plates. To overcome this weak point, a new approach of dividing a concave plate into two convex domains and applying the MNDIF method to each domain is proposed and the validity and accuracy are shown in verification examples.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.11
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• pp.1003-1011
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• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate eigenvalues of concave acoustic cavities. Since the MNDIF method, which was introduced by the author, can be applicable for only convex acoustic cavities, a new approach of dividing a concave cavity into two convex domains and formulating an algebraic eigenvalue problem is proposed in the paper. A system matrix equation, which gives eigenvalues, is obtained from boundary conditions for each domain and the condition of continuity in the interface between the two domains. The validity and accuracy of the proposed method are shown through example studies.