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# Inverse vibration problem for un-damped 3-dimensional multi-story shear building models

## Dolatshahi, K. M ; Sharif University of Technology

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- Type of Document: Article
- DOI: 10.1016/j.jsv.2013.08.045
- Abstract:
- Various researchers have contributed to the identification of the mass and stiffness matrices of two dimensional (2-D) shear building structural models for a given set of vibratory frequencies. The suggested methods are based on the specific characteristics of the Jacobi matrices, i.e., symmetric, tri-diagonal and semi-positive definite matrices. However, in case of three dimensional (3-D) structural models, those methods are no longer applicable, since their stiffness matrices are not tri-diagonal. In this paper the inverse problem for a special class of vibratory structural systems, i.e., 3-D shear building models, is investigated. A practical algorithm is proposed for solving the inverse eigenvalue problem for un-damped, 3-D shear buildings. The problem is addressed in two steps. First, using the target frequencies, a so-called normalized eigenvector matrix, which is a banded matrix containing the information related to the frequencies and mode shapes of the target structural system, is determined. In this regard, similar to the solution of inverse problem for 2-D shear building structural models in which an auxiliary structure is constructed by adding constraints (or springs) to the original system, three auxiliary structures are proposed to solve the problem for 3-D cases. In the second step, the normalized eigenvector matrix is utilized to obtain the normalized stiffness matrix; in turn, this matrix is decomposed into the stiffness and mass matrices of the system. Finally, a numerical example is presented to demonstrate the efficiency of the proposed algorithm in determining the mass and stiffness matrices of a 3-D structural model for a given set of target vibrational frequencies
- Keywords:
- Eigenvector matrices ; Inverse eigenvalue problems ; Inverse vibration problem ; Shear-building model ; Solution of inverse problems ; Structural modeling ; Target frequencies ; Vibratory frequency ; Algorithms ; Auxiliary equipment ; Buildings ; Eigenvalues and eigenfunctions ; Inverse problems ; Jacobian matrices ; Stiffness matrix ; Three dimensional
- Source: Journal of Sound and Vibration ; Volume 333, Issue 1 , 6 January , 2014 , Pages 99-113 ; ISSN: 0022460X
- URL: http://www.sciencedirect.com/science/article/pii/S0022460X13007335