Nonlinear dynamical response of impulsively loaded structures using Ritz vector basis approach /
| Main Author: | |
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| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1990.
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| Subjects: | |
| Online Access: | Link to OAKTrust copy |
| Abstract: | The research deals with predicting the nonlinear dynamic response of a structure under impulsive loading by means of reduction methods. Techniques for reducing the number of equations to be solved, e.g., where such equations come from a finite element model, are referred to as reduction methods. The order of a dynamical system is reduced by a Rayleigh-Ritz technique using selective basis vectors. Basis vectors are Rayleigh-Ritz approximation functions used to reduce the order of a dynamical system. The physical displacement of the full system is obtained by re-expansion of the solution from the reduced system. Ritz vectors, which are not the exact eigenmodes of a given dynamical system, rather than eigenvectors, are chosen as basis vectors. Ritz vectors can be generated with less computational effort than needed to generate eigenvectors. The basis set are augmented by derivatives of Ritz vectors and updated Ritz vectors. These two vectors are added to account for the nonlinearities of the dynamical system. The proposed reduction technique is enhanced by updating the stiffness matrix with a reasonable reassembly frequency. The object of the research is to generate basis vectors in a computationally efficient manner so that nonlinear dynamical response due to an impulsive loading can be predicted with accuracy in a cost effective manner. An error norm, which is a weighted Euclidean norm of the unbalanced force vector, is utilized to determine when updating basis vectors is necessary. |
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| Item Description: | Typescript (photocopy). Vita. "Major subject: Mechanical engineering." |
| Physical Description: | xiv, 96 leaves : illustrations ; 29 cm |
| Bibliography: | Includes bibliographical references. |