Research On Low-frequency Vibration Reduction Characteristics Of Locally Resonant Plate

The thin plate is widely used in various engineering structures,and it is easy to produce vibration under the excitation loads,which has an adverse effect on the engineering structure.Traditional active vibration reduction structures are complex and costly,and are prone to failure during work.While the passive vibration reduction method is not effective at low frequency,and the damping material is easy to aging,which need to be replaced regularly,causing inconvenience to the project.The active vibration reduction method has the problems of complex structure,high cost and easy to failure in the work.In recent years,new concepts such as "phononic crystals" and "acoustic metamaterials" have been put forward,which provide a new theoretical basis and technical approach for the realization of low-frequency vibration and noise reduction.The locally resonant(LR)plate is one of them.It is a new artificial periodic structure,which is composed of periodic dynamic vibration absorbers(DVAs)attached to the thin plate structure.In this paper,the LR plate is taken as the research object,and the calculation,analysis and design of its low-frequency vibration reduction characteristics are studied on the four-sided simply supported boundary conditions.The research work in this paper is helpful to improve the theoretical calculation of LR plates,and it can provide a simple and effective theoretical calculation method for the design and analysis of the LR plate vibration reduction.The main contents of this paper are as follows:(1)the calculation method of the band structure of the damped LR plate is established,and the influence of the damper on the structure band gap is discussed;(2)the calculation method of the vibration reduction characteristics of the finite-period LR plate under four-sided simply-supported boundary conditions is established;(3)the influence of the parameters of the local oscillator and the base plate on the low-frequency vibration reduction characteristics of the LR plate is analyzed The energy band structure of infinite-period and the displacement transfer rate of finite-period are compared and analyzed.The research results show that the analytical expression derived in this paper can accurately calculate the vibration reduction characteristics of the LR plate under four-sided simply-supported boundary conditions.By adjusting the parameters of the local oscillator and the base plate,a good vibration reduction performance can be achieved.The main contribution of this paper is:It is proved that when the number of periodically arranged DVAs in the X and Y directions is greater than or equal to the modal truncation order,the modal superposition method can be used to obtain the LR plate at any simple harmonic excitation.The analytical solution of the forced vibration response is obtained,and the analytical expressions of the transmission characteristics and total kinetic energy of the system are obtained.