A method is described for determining the stiffness and mass modifications required in order to modify the natural frequencies of undamped discrete nongyroscopic vibrating systems in a prescribed manner. The method is based upon a new perturbation formulation. Structural changes are represented by perturbed stiffness and mass matrices defined in terms of linear design parameters of the discrete model. The equations are subject to frequency constraints defined by the analyst, and the modified mode shapes are assumed confined to a subspace of the baseline modes. The proposed method provides a complete solution of the perturbation equations without deleting or approximating coupling terms in the unknowns and is therefore suitable for large and small changes alike. Numerical results demonstrate that the new method is superior to the predictor-corrector method for determining large structural changes and that solutions of a high accuracy can be obtained provided a sufficiently rich subspace of baseline modes is used.
A Perturbation Method for Inverse Frequency Modification of Discrete, Undamped Systems
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Smith, M. J., and Hutton, S. G. (December 1, 1994). "A Perturbation Method for Inverse Frequency Modification of Discrete, Undamped Systems." ASME. J. Appl. Mech. December 1994; 61(4): 887–892. https://doi.org/10.1115/1.2901573
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