Bandgap formation and low-frequency structural vibration suppression for stiffened plate-type metastructure with general boundary conditions

Metastructures with unique mechanical properties have shown attractive potential application in vibration and noise reduction. Typically, most of the metastructures deal with the vibration bandgap properties of infinite structures without considering specific boundary condition and dynamic behaviors, which cannot be directly applied to the engineering structures. In this research, we design a Stiffened Plate-type Metastructure (SPM) composed of a plate with periodic stiffeners and cantilever beam-type resonators subjected to general boundary conditions for low-frequency vibration suppression. The effects of boundary conditions and the number and orientation of the stiffeners on Locally Resonant (LR) type bandgap properties in SPM are further investigated. An analytical modeling framework is developed to predict the bandgap formations and vibration behaviors of SPMs in finite-size configuration. The governing equations of the SPM reinforced by various arrangements of stiffeners are derived based on the first-order shear deformation theory and Hamilton's principle, and a Fourier series combined with auxiliary functions is employed to satisfy the arbitrary boundary conditions. Finite element analysis and experimental investigations of vibration behaviors for the SPM are carried out to validate the accuracy and reliability of the present analytical model. For practical designs of the SPMs with specific boundary conditions, it is found that there exist optimal numbers of stiffeners and resonators which can produce the significant LR-type bandgap behaviors. Furthermore, various arrangements of stiffeners and resonators are explored for different boundary conditions by breaking the requirement of spatially periodicity. It is shown that for the designed SPM, the vibration modes of its host structure should be considered to widen the frequency range in which the resonators transfer and store energy, and hence improve the performance of low-frequency vibration suppression. The present work can provide a significant theoretical guidance for the engineering application of metamaterial stiffened structures.