Investigations On The Vibration Behaviors And Vibration Isolation Performances Of Periodic Structures

Vibration phenomena are always used to change the natural environment in the human’s daily life. Meanwhile, some kinds of vibrations also make people bothered. How to isolate these vibrations has been an urgent problem to be solved. With the development of science and technology, the demand for the vibration reduction technology has become increasingly urgent in the aerospace, marine and other fields. Nowadays, the vibration reduction technologies include the active vibration control, passive vibration control and semi-active vibration control. Compared with the active and semi-active vibration control technologies, the passive vibration control technology has some advantages such as its simple construction, low cost, easy maintenance and independent of external power. The design and study on the structures with passive vibration isolation performances has significant application value and it has obtained much attention of many scholars.During the long time investigations, people have noticed that there exists the frequency band gap property when elastic waves propagate in the peri odic structures, which is the natural characteristic of periodic structures. The periodic structures can realize the vibration isolation in stop bands without outer power supports. It means that the elastic waves and vibrations with stop-band frequencies cannot propagate in the periodic structures. In order to investigate the vibration isolation performance of periodic structures, the spectral element method(SEM) is adopted for the dynamics modeling, and the corresponding vibration and sound reduction performances are further analysed.For a geometrically and materially uniform simple structure, it can be considered as only one spectral element in the SEM. For the complex periodic structures containing a big amount of such simple structures, the element number of the complex structures can be reduced largely in the SEM, the degree of freedom can be also reduced and the computational cost can be decreased. O n the other hand, the SEM can obtain highly accurate results in the frequency domain, which is very convenient for the band-gap analysis in the frequency domain. In this paper, the SEM results are compared with the results from the finite element method(FEM). The high accuracy of the SEM result is validated and the superiority of this approach is also verified for solving the band-gap problem of periodic structures.The spectral stiffness matrices of the basic elements such as rod elment, torsional axis element, beam element, piezoelectric beam element, plate element and joint element are deduced by the SEM, which is the theoretical basis of the following analysis. Then the vibration isolation properties of some kinds of periodic structures such as the periodic plane rod system, space Kagome structure, periodic structure with the piezoelectric material, periodic plate structure and the periodic sandwich structure with the corrugated core are deeply investigated. In the analysis, the spectral stiffness matrix of the whole structure is established for different periodic structures, and the equation of motion of the whole structure is further obtained. The external disturbance with different frequencies is applied on one side of the periodic structure. The frequency-response curves of the pick-up point on the other side of the structure can be obtained by solving the equation of motion, and the band-gap properties of the periodic structures are further studied.For the different types of periodic structures, the effects of the structural and matrial parameters on the vibration isolation properties are discussed. The effects of the rod length on the periodic rod-joint structure, the configuration and number of the unit cell and the damping on the periodic truss structure and the unit cell number in different directions on the plane lattice structure are studied. The influences of the sub-structure number and the material parameter on the band-gap property of the space Kagome structure are also analyzed. The piezoelectric matrial is also applied in the periodic structure, and a new kind of functional material structure with both the vibration isolation and the energy harvesting performances is constructed. The effect of the component ratio of the piezoceramics on the band-gap property of the periodic structures is investigated. The defect states of the piezoelectric periodic structures with defects are analyzed. The differences of the periodic plate structures composed of the Kirchhoff and Mindlin plates are discussed. The effects of the structural and material parameters on the vibration isolation performance s of the periodic plate structures are studied. In the investigations on the vibration and sound reduction of sandwich structures with corrugated cores, the effects of the materials of the core and the upper and lower panels on the band-gap property are discussed. Considering the vibration isolation performance in the low frequency domain of the sandwich structures with corrugated cores, the effects of the width and thickness of the plate on the first stop band are also analyzed.