Natural Frequency Analysis and Optimization Design of Rectangular Thin Plates With Nonlinear Variable-Thickness

Abstract

Variable-thickness thin plate structures have been widely employed in many engineering applications, such as the automotive industry, aviation industry and civil structures. In this paper, natural frequency and optimization design of nonlinear variable-thickness rectangular thin plates are performed. For this purpose, theoretical solutions of dimensionless natural frequency of the bidirectional linear variable-thickness thin plates are conducted on the three classical boundaries to verify the correctness of a conducted numerical model. Then the natural frequencies of variable thickness plates with different forms including bidirectional and unidirectional nonlinear were compared. Additionally, the difference in vibration characteristics between the thin plate of variable thickness and the corresponding thin plate of equal mass are compared and analyzed, and the results show that when the middle part of the thin plate is thick, the natural frequency increases by a greater percentage. Finally, a new bidirectional stepped variable-thickness plate is proposed to improve the natural frequency of variable-thickness thin plates. Inspired by the stepped idea, the square and circle division methods are employed to improve the natural frequency of variable thickness thin plates, as the optimal design is carried out. The results show that the nonlinear variable thickness after performing an optimal design could significantly improve the natural frequency of thin plates. The finding provides useful insight into the structural design of variable thickness plates for free vibration.