RESEARCH ON BAND GAP CALCULATION METHOD OF PERIODIC STRUCTURE BASED ON ARTIFICIAL SPRING MODEL

The energy method is widely used in structural dynamicsanalysis with its advantage of converting the boundary value problems fordifferential equation into the functional extreme value problem, and hasalso been introduced into periodic structure band gap computation in recentyears. However, it is difficult to construct the displacement function whenusing traditional energy methods (such as the Rayleigh-Ritz method) foranalysis because of the certain complexity in boundary conditions of theperiodic structure. Additionally, the wave number term is contained in thedisplacement function so that the mass and stiffness matrix need to berecomputed continuously in the process of calculating the band gap ofscanning wave number, which leads to a large amount of calculation. For thatreason, this paper improved the traditional energy method by introducingartificial spring model to simulate various boundary conditions includingperiodic boundaries so that boundary constraints could be transformed intothe elastic potential energy of artificial springs and only the periodicboundary elastic potential energy in energy distributions contains the wavenumber term, by which the corresponding stiffness matrix only needed to berecomputed in the scanning process of wave number and other mass andstiffness matrices need to be calculated only once and then significantlyreduced the computational burden. The research results show that the methodin this paper is accurate and reliable. The calculation efficiency of thismethod is advantageous compared with the traditional energy method. Theadvantage of calculation efficiency of this method is more obvious comparedwith the traditional energy method in the situation that the mass andstiffness matrix promote in dimension, or the scanning points of wave numberincrease. In addition, the artificial spring model is more flexible andconvenient to use, and can be further adopted to band gap analysis of morecomplex periodic composite structures.