Analytical study and multi-objective optimization of low-frequency flexural vibration band gaps of periodic orthogonal stiffened meta-plates

In this paper, the low-frequency flexural vibration band gap characteristics of periodic orthogonal stiffened meta-plates with local resonators are analytically investigated. A theoretical model of periodic orthogonal stiffened meta-plate is established considering the coupling effect of Timoshenko beam and Kirchhoff plate. The flexural vibration band gaps of periodic orthogonal stiffened meta-plates are calculated by using the plane wave expansion method and Bloch theorem. In addition, numerical calculation and experimental tests were conducted to verify the proposed theoretical model. Results show that the proposed theoretical model of periodic orthogonal stiffened meta-plates can be effectively and efficiently applied to predict the low-frequency flexural wave band gaps and vibration isolation performance in a specific frequency range, which shows a good agreement with numerical simulation and experimental results. Furthermore, the multi-objective Non-dominated Sorting Genetic Algorithms-II combination with the theoretical model of periodic orthogonal stiffened meta-plates is utilized to achieve the optimization design of low-frequency broadband flexural vibration band gaps.