• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.721-726
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• 2004

A simplified method for the computation of first second and higher order derivatives of eigenvalues and eigenvectors derivatives associated with repeated eigenvalues is presented. Adjacent eigenvectors and orthonormal conditions are used to compose an algebraic equation whose order is (n+m)x(n+m), where n is the number of coordinates and m is the number of multiplicity of the repeated eigenvalues. The algebraic equation developed can be used to compute derivatives of both eigenvalues and eigenvectors simultaneously. Since the coefficient matrix in the proposed algebraic equation is non-singular, symmetric and based on N-space it is numerically stable and very efficient compared to previous methods. This method can be consistently applied to structural systems with structural design parameters and mechanical systems with lumped design parameters. To verify the effectiveness of the proposed method, the finite element model of the cantilever beam is considered.