Harmonic And Transient Transmission Of Elastic Wave Metamaterials With Quasi-zero Stiffness

Recently,researches on elastic wave materials and periodic structure have received lots of interests.Phononic crystals,as one kind of elastic wave metamaterials,are artificial structures in which material constants change periodically and can present band gaps.In the band gaps,elastic waves cannot propagate.Then,phononic crystals and elastic wave metamaterials can be applied to vibration and noise reduction in practical engineering,e.g.aerospace,military and other national defense fields.Researches on isolation of elastic wave and vibration in the low-frequency range is currently a hot topic.But how to achieve band gaps with extremely low frequency has been still an urgent problem of elastic wave metamaterials.In this work,we propose a new kind of elastic wave metamaterials based on the mechanism of the zero-rotation stiffness.Elastic wave metamaterials with the straight linear and planar quasi-zero stiffness,as well as the theories of wave and structural dynamics,the band gaps with low frequency properties are obtained.Both the theoretical derivation and finite element simulation are applied to the calculation.Numerical results show band gaps with wide and extremely low frequency characteristics,as well as the strong attenuation effect.At the same time,we investigate the transient response of elastic wave metamaterials with the quasi-zero stiffness under shock excitation.Firstly,we design a straight linear formation with the quasi-zero stiffness and double-resonators to study band gaps in extremely low frequency range.For the flexural waves propagation,the theoretical derivation and numerical simulation are used to show the band gaps.The harmonic transmission of the finite period model is presented.Furthermore,the effects of lattice constants on the band structure are discussed.The results show that elastic wave metamaterials with the straight linear quasi-zero stiffness can produce wide band gaps in the quasi-static frequency range with 0-500 Hz and another one with 600Hz-970 Hz.As the lattice constant increases,the band gap has a little attenuation.Secondly,the elastic wave metamaterials with the planar quasi-zero stiffness is presented.And its band structure and transmission response are simulated by the finite element software.Both results are compared and discussed together.At the same time,the effects of material constants and geometry length are analyzed.The results show that both the elastic modulus and density have obvious influences on the band gap.The designed band gaps range can be achieved by tuning these parameters.Finally,the transient responses of these two kinds of elastic wave metamaterials with quasi-zero stiffness are studied.The Gaussian pulse excitation is applied to the straight linear and planar models to calculate the wave responses within the time and frequency domains.Moreover,we change material and lattice constants to illustrate their effects on the transient response.Numerical results show that elastic wave metamaterials with the quasi-zero stiffness have great isolation characteristics,in which the material and structure parameters can enhance the attenuation effect.