Optimal design of vibrating composite plate considering discrete–continuous parameterization model and resonant peak constraint

Many discrete design variables in broadband dynamic optimization cause intensive computational and storage burdens in both frequency response and sensitivity analysis. One solution is to adopt the continuous angle design model. However, a local optimum solution is more likely to be obtained due to its high non-convex character. Consequently, this paper develops an integrated optimization model for minimizing composite plate’s local response in a given frequency band by the discrete–continuous parameterization model (DCP). The DCP is adopted to optimize fiber angles where it divides the total angle range into several subranges and combines the discrete and continuous variables. Thus, it offers a wide and flexible design space for selecting the fiber angle and is useful to find better-optimized results. In addition, the solid isotropic material with penalty scheme (SIMP) is used to optimize the layout of the damping material. Additionally, due to the dominant role of the low-order resonant peak on the structural vibration, the low-order resonant peak constraint is also considered. The mode acceleration method (MAM) and the decoupled sensitivity analysis method are incorporated for frequency and sensitivity analysis. Several numerical examples are employed to investigate the validity of the developed model.