Research On The Band Gaps And Tunability Of Beams And Plates Based On The Theory Of Phononic Crystals

Phononic crystals are periodic materials or structures with elastic wave band gaps in which the propagation of vibration and sound are blocked.In this dissertation,the vibration band gap characteristics and propagation characteristics of elastic wave in periodic Euler beams and two types of negative Poisson’s ratio lattice structures are mainly studied by combining theories of phononic crystals.The basic theory of phononic crystals and the calculation method of elastic wave band gap were first introduced.Then,the band structure of periodic Euler beam was calculated using the transfer matrices method,and its band gap characteristics were studied in combination with the transmission characteristics of the finite period beam.The influence of beam length ratio,structure parameters,period length,material properties and other parameters on the band gap boundary frequency was analyzed.It is found that the geometric parameters of the beam have a large effect on the band gap boundary frequency and the band gap width;the elastic modulus has a greater effect on the upper edge of the band gaps,and the density change has a greater effect on the lower edge of band gap.The vibration gaps of periodic beams containing shape memory alloys can be controlled by temperature.For two-dimensional periodic lattices structures,the work concentrated on star-shaped and reentrant hexagonal periodic lattices structures,which with the negative Poission’s ratio.The eigenvalue problem including dispersion relationship was established using the spatial beam element model and Bloch’s theorem.The phase constant surfaces and Comsol Multiphysics software were used to systematically study the characteristics of band gap and elastic wave propagation about both in-plane and out-of-plane modes in the lattice structures.It is found that these periodic lattices with negative Poisson’s have richer band gaps and the propagation direction of the elastic wave is related to the topological configuration of the structure.Changes of the band gaps affected by the structural parameters were studied.These parameters included the angle of the lattice structures cell,the length ratio of different beams,the width of the beam.The band gap mechanism was analyzed in combination with the vibration mode.All the work provides a reference for lattice structures design to generate lowfrequency and wide band gap.At the end of the article,a preliminary study on the bending vibration band gap of periodic grid sandwich plates with different topologies was also done.