Abstract
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.
Highlights
Plate-like structures are widely used in the areas of aeronautics, automobile engineering and ship structures, due to their light weight and high structural efficiency, and so forth
The dynamic behaviours of these structures are important properties, because the natural frequencies and mode shapes of the thin plates usually need to satisfy the requirements of structural integrity, durability, and sound radiation when subjected to the shock and vibration loadings, which matters in different branches of engineering: automobile [1, 2], naval [3], aeronautics and astronautics [4], and so forth
This paper investigates the application of modal strain theory in the structural dynamic design
Summary
Plate-like structures are widely used in the areas of aeronautics, automobile engineering and ship structures, due to their light weight and high structural efficiency, and so forth. It can be seen that curvature/strain and stress mode shapes have their own advantages over displacement mode shapes due to the more sensitivity to local deformations and changes. Continuing in this line of investigation, the modal strain theory is adopted to investigate the dynamic design of platelike structures. Strain mode shapes will be demonstrated to efficiently locate the most sensitive areas and to facilitate the fast design of plate thickness and/or stiffener layout for desired modal frequencies.
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