Study On Vibration Isolation Performance Of Periodic Beam And Plate On Elastic Foundation

Recently material sciences research shows that periodic structures can express a unique vibration characteristic, that they can block or inhibit the propagation of elastic waves in a special frequency range, which was called'band gap'. In this paper, according to the two simplified engineering structures—beam and plate, the structures of periodic beam and plate are designed, their vibration band gaps and dynamic re-sponse analysis are solved by the combination of theoretical research and numerical analysis. The results showed that there will be an obviously vibration isolation when the frequency falls into band gaps for periodic beam and plate.The main works include three parts as following:1. Combined with engineering practice, a new concrete-steel periodic beam (a wide flanged H-section steel beam is coated by concrete in periodic positions) was developed for application purpose. At first, based on the Bloch theorem, the periodic beam was transformed into a unit cell with periodic boundary conditions, and then the DQEM was used. Thus an infinite freedom problem can be simplified into the problem of solving eigenvalues for a finite freedom structure.2. The dedicated dynamic analysis programs are work out by Matlab. Main ana-lyzing process:firstly, analysis the finite periodic beam, indicate the method in this pa-per is excellent accurate by comparing with the results from COMSOL and AN SYS. And then, detailed parameter researches for the first band gap are studied by the pro-gram, including geometric parameters (the ratio of concrete beam with steel beam, the length of a cell) and foundation parameter. All the results show that periodic beam can display a good attenuation characteristic in the range of band gaps, and the band gap frequency can be adjustment and control by the proper design.3. Be same with periodic beam, the theory equation and analysis program for pe-riodic plate on Winkler foundation are given, the geometric parameters (thickness of plate, filling rate and the size of a cell) and foundation parameter are studied for the first band gap, and the dynamic performance of vibration isolation of periodic plate is analyzed. It is found that there is a critical frequency in the band gap structure because of the existense of elastic foundation, in present, the simplified formulae of the critical frequency is given by analyzing its physical significance.