Modal Strain Based Method for Dynamic Design of Plate-Like Structures

Design optimization of dynamic properties, for example, modal frequencies, can be of much importance when structures are exposed to the shock and/or vibration environments. A modal strain based method is proposed for fast design of natural frequencies of plate-like structures. The basic theory of modal strains of thin plates is reviewed. The capability of determining the highly sensitive elements by means of modal strain analysis is theoretically demonstrated. Finite element models were constructed in numerical simulations. Firstly, the application of the proposed method is conducted on a central-massed flat plate which was topologically optimized by the Reference. The results of modal strain analysis at the first mode have good agreement with the results from the topology optimization. Furthermore, some features of the strain mode shapes (SMSs) of the flat plate are investigated. Finally, the SMSs are applied to the optimization of a stiffened plate. Attention is focused on the distributions of the SMSs of the stiffeners, which also shows good agreement with the results from the topology optimization in the previous study. Several higher orders of SMSs are extracted, which can visualize the most sensitive elements to the corresponding modal frequency. In summary, both the theory and simulations validate the correctness and convenience of applying SMSs to dynamic design of plate-like structures.

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