TY - JOUR
T1 - Improved non-dimensional dynamic influence function method for vibration analysis of arbitrarily shaped plates with clamped edges
AU - Kang, Sang Wook
AU - Atluri, Satya N.
N1 - Publisher Copyright:
© SAGE Publications Ltd, unless otherwise noted. Manuscript content on this site is licensed under Creative Commons Licenses.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2016/3
Y1 - 2016/3
N2 - A new formulation for the non-dimensional dynamic influence function method, which was developed by the authors, is proposed to efficiently extract eigenvalues and mode shapes of clamped plates with arbitrary shapes. Compared with the finite element and boundary element methods, the non-dimensional dynamic influence function method yields highly accurate solutions in eigenvalue analysis problems of plates and membranes including acoustic cavities. However, the non-dimensional dynamic influence function method requires the uneconomic procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues because it produces a non-algebraic eigenvalue problem. This article describes a new approach that reduces the problem of free vibrations of clamped plates to an algebraic eigenvalue problem, the solution of which is straightforward. The validity and efficiency of the proposed method are illustrated through several numerical examples.
AB - A new formulation for the non-dimensional dynamic influence function method, which was developed by the authors, is proposed to efficiently extract eigenvalues and mode shapes of clamped plates with arbitrary shapes. Compared with the finite element and boundary element methods, the non-dimensional dynamic influence function method yields highly accurate solutions in eigenvalue analysis problems of plates and membranes including acoustic cavities. However, the non-dimensional dynamic influence function method requires the uneconomic procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues because it produces a non-algebraic eigenvalue problem. This article describes a new approach that reduces the problem of free vibrations of clamped plates to an algebraic eigenvalue problem, the solution of which is straightforward. The validity and efficiency of the proposed method are illustrated through several numerical examples.
KW - Non-dimensional dynamic influence function method
KW - algebraic eigenvalue problem
KW - arbitrarily shaped plate
KW - free vibration
KW - mode shape
KW - natural frequency
UR - http://www.scopus.com/inward/record.url?scp=84962637052&partnerID=8YFLogxK
U2 - 10.1177/1687814016638586
DO - 10.1177/1687814016638586
M3 - Article
AN - SCOPUS:84962637052
VL - 8
SP - 1
EP - 8
JO - Advances in Mechanical Engineering
JF - Advances in Mechanical Engineering
SN - 1687-8132
IS - 3
ER -