• 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.

• 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 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.

• 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.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.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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.10
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• pp.653-659
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• 2015

A new formulation of the non-dimensional dynamic influence function method, which is a type of the meshless method, is introduced to extract highly accurate eigenvalues of clamped plates with arbitrary shape. Originally, the final system matrix equation of the method, which was introduced by the author in 1999, does not have a form of algebraic eigenvalue problem unlike FEM. As the result, the non-dimensional dynamic influence function method requires an inefficient process to extract eigenvalues. To overcome this weak point, a new approach for clamped plates is proposed in the paper and the validity and accuracy is shown in verification examples.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.10
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• pp.1069-1074
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• 2009

A sub-domain method for free vibration analysis of arbitrarily shaped, concave membranes with a deep groove is proposed in the paper. The proposed method divides the concave membrane of interest into two convex regions. The vibration displacement(approximate solution) of each convex region is assumed by linearly superposing plane waves generated at edges of the region. A sub-system matrix for each convex region is extracted by applying a provisional boundary condition to the approximate solution. Finally, a system matrix, which of the determinant gives eigenvalues of the concave membrane, is made by considering the fixed boundary condition(displacement zero condition) at edges and the compatibility condition(the condition of continuity in displacement and slope) at the interface between the two regions. Case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed are compared to those by NDIF method, FEM, or the exact method.

• 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.22 no.8
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• pp.742-747
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• 2012

A modified NDIF method using a sub-domain approach is introduced to extract highly accurate eigenvalues of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, has the feature that it yields highly accurate eigenvalues 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 cavities. It was revealed that the solution of the NDIF method is very inaccurate or is not suitable for concave cavities. To overcome the weak point, the paper proposes the sub-domain method of dividing a concave domain into several convex domains. Finally, the validity of the proposed method is verified in two case studies, which indicate that eigenvalues obtained by the proposed method are more accurate compared to the exact method, the NDIF method, or FEM(ANSYS).