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A new iterative order reduction (IOR) method for eigensolutions of large structures. (English) Zbl 1047.74024
Summary: Order reduction is a computationally efficient method to estimate some lowest eigenvalues and the corresponding eigenvectors of large structural systems by reducing the order of the original model to a smaller one. But its accuracy is limited to a small range of frequencies that depends on the selection of the retained degrees of freedom. This paper proposes a new iterative order reduction (IOR) technique to obtain accurately the eigensolutions of large structural systems. The technique retains all the inertia terms associated with the removed degrees of freedom. This hence leads to the reduced mass matrix being in an iterated form and the reduced stiffness matrix constant. From these mass and stiffness matrices, the eigensolutions of the reduced system can be obtained iteratively. On convergence the reduced system reproduces the eigensolutions of the original structure. A proof of the convergence property is also presented. Applications of the method to a practical GARTEUR structure as well as a plate have demonstrated that the proposed method is comparable to the commonly used Subspace Iteration method in terms of numerical accuracy. Moreover, it has been found that the proposed method is computationally more efficient than the Subspace Iteration method.

74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
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