Analytical study of low-frequency flexural vibration band gaps of lightweight stiffened meta-plates with inertial amplified resonators

Abstract

In this paper, a two-dimensional periodic stiffened meta-plate structure with inertial amplified resonators is proposed to achieve the engineering structure design with lightweight high-strength performance and low-frequency broadband flexural vibration isolation characteristics simultaneously. A theoretical model of periodic stiffened meta-plate with inertial amplified resonators is established, based on the Lagrange equation and the beam-plate coupling theory. The flexural band gap and vibration isolation properties of the periodic stiffened meta-plates are studied by using the plane wave expansion method. Numerical calculation and experimental tests were conducted to verify the proposed theoretical model. Results show that the proposed lightweight high-strength stiffened meta-plate with inertial amplified resonators can significantly enhance the low-frequency broadband flexural bandgap compared to the existing periodic stiffened plate and stiffened meta-plate with local resonators. The performance enhancement mechanism is mainly attributed to the coupling effect of stiffened plate and inertial amplified resonators. The flexural bandgap and low-frequency broadband vibration reduction performance of the proposed lightweight stiffened meta-plates with inertial amplified resonators can be significantly enhanced based on the theoretical model and the multi-objective NSGA-II algorithm.