TY - JOUR
T1 - Application of the nondimensional dynamic influence function method for free vibration analysis of arbitrarily shaped membranes
AU - Kang, Sang Wook
AU - Atluri, Satya N.
AU - Kim, Sang Hyun
PY - 2012
Y1 - 2012
N2 - A new formulation for the NDIF method (the nondimensional dynamic influence function method) is introduced to efficiently extract eigenvalues and mode shapes of arbitrarily shaped, homogeneous membranes with the fixed boundary. The NDIF method, which was developed by the authors for the accurate free vibration analysis of arbitrarily shaped membranes and plates including acoustic cavities, has the feature that it yields highly accurate solutions compared with other analytical methods or numerical methods (the finite element method and the boundary element method). However, the NDIF method has the weak point that the system matrix of the method is not independent of the frequency parameter and as a result the method needs the inefficient procedure of searching eigenvalues by plotting the values of the determinant of the system matrix in the frequency parameter range of interest. An improved formulation presented in the paper does not require the above-mentioned inefficient procedure because a newly developed system matrix is independent of the frequency parameter. Finally, the validity of the proposed method is shown in several case studies, which indicate that eigenvalues and mode shapes obtained by the proposed method are very accurate compared to those calculated by exact, analytica, or numerical methods.
AB - A new formulation for the NDIF method (the nondimensional dynamic influence function method) is introduced to efficiently extract eigenvalues and mode shapes of arbitrarily shaped, homogeneous membranes with the fixed boundary. The NDIF method, which was developed by the authors for the accurate free vibration analysis of arbitrarily shaped membranes and plates including acoustic cavities, has the feature that it yields highly accurate solutions compared with other analytical methods or numerical methods (the finite element method and the boundary element method). However, the NDIF method has the weak point that the system matrix of the method is not independent of the frequency parameter and as a result the method needs the inefficient procedure of searching eigenvalues by plotting the values of the determinant of the system matrix in the frequency parameter range of interest. An improved formulation presented in the paper does not require the above-mentioned inefficient procedure because a newly developed system matrix is independent of the frequency parameter. Finally, the validity of the proposed method is shown in several case studies, which indicate that eigenvalues and mode shapes obtained by the proposed method are very accurate compared to those calculated by exact, analytica, or numerical methods.
KW - NDIF method
KW - algebraic eigenvalue problem
KW - arbitrarily shaped membrane
KW - eigenvalue
KW - free vibration
KW - nondimensional dynamic influence function method
UR - http://www.scopus.com/inward/record.url?scp=84863809318&partnerID=8YFLogxK
U2 - 10.1115/1.4006414
DO - 10.1115/1.4006414
M3 - Article
AN - SCOPUS:84863809318
SN - 1048-9002
VL - 134
JO - Journal of Vibration and Acoustics, Transactions of the ASME
JF - Journal of Vibration and Acoustics, Transactions of the ASME
IS - 4
M1 - 041008
ER -