Research On The Low Frequency Band Gap Of The Complex Periodic Structure

Though the concept of the phononic crystals was proposed just a few decades,theapplication of the research for the project has a great significance.For the characteristicsof the elastic band gaps and defect states,the phononic crystals can provide a new wayof thinking for damping the application and development of the project.For referencethe phononic crystals’ theoretical study to learn the vibration characteristics of theperiodic structure,it will be conducive to the further research and to promote theapplication.However,it need to further improve the capability to inhibit the structuralvibration and the noise processing at the low frequency band.Thus,for the frequencyrange,through the optimization of the structure,changing the damping characteristics ofthe cycle structure,it become the research focus of the application of engineeringstructures in the phononic crystals.Based on the theory of phononic crystals, combined the numerical calculationmethod,two different complex periodic structure are studied on the low frequency bandgap by the finite difference method and the lumped mass method.Firstly, by the assumptions of the model, a theoretical model of the cycle dampingsheet structure has been established.Using the finite difference method, the dynamicsdifferential equation of the bidimensional binary periodic damping plate structure ischanged into a differential equation. Then according to Bloch theorem，adding to theperiodic boundary conditions, giving the wave vector, the coefficient matrix eigenvalueof the linear equations are been solved. Thereby the energy band diagram of thestructure is been obtained. By changing the lattice constant and the material parametersof the bidimensional binary periodic damping plate structure to investigate the impact ofthe corresponding change of the first band gap, the low frequency band gapcharacteristics of the bidimensional binary periodic damping plate structure can beobtained.Secondly,the three dimensional model is established by the assumptions of themodel.The simple cubic phononic crystal is be calculated by the use of the3D lumpedmass method.Through ANSYS of the modeling and meshing,and MATLAB of thenumerical calculation,the three dimensional quaternary periodic structure is beobtained.By single change of each material parameters, examine corresponding changesin the first band gap, and then come to the low-frequency band gaps of the threedimensional quaternary periodic structure.Then,using ANSYS finite element software, the model of the bidimensional binaryperiodic damping plate structure and the three-dimensional quaternary periodic structureare been created.With the dynamics harmonic response simulation,the band gap of theperiodic structure is been obtained.The theoretical calculations of band gap is beenverified.Finally,the bidimensional binary periodic damping plate structure is beenexperimental studied by the trials test.Though the comparison with finite elementsimulation results,the results is been verified correctness before.