Design of elastic metamaterials with ultra-wide low-frequency stopbands via quantitative local resonance analysis

Abstract

Elastic metamaterials (EMMs) with engineered bandgaps have numerous applications in medical, transport, and aerospace domains due to their extraordinary performance in manipulating elastic waves. Nevertheless, developing an efficient method to guide designs of EMMs with low-frequency and wide frequency stopband is still a challenging problem in this field. In this paper, a quantitative local resonance analysis scheme is proposed for efficient design of three-dimensional (3D) latticed EMMs with broad and complete wave attenuation band at low frequency. To acquire a low starting frequency, a diatomic mass spring analytic model is applied to guide the modification of structure and adjustment of geometrical parameters of the EMM, and thus its effective stiffness and mass values affecting the starting frequency are altered desirably. With the aim of enlarging stopband, a strategy to analyze stopband formation mechanism is proposed by virtue of modal superposition principle. Dominant vibration modes developed on the EMM are found with modal superposition principle and these modes are further characterized with the aid of a quantitative local resonance measurement method aiming at exploring vibration features on the EMM. Upon the revealing of wave attenuation mechanism, we show the low-frequency stopband for the EMM can be widened via altering vibration characteristics of dominant modes that are responsible for stopband closing. The proposed new analysis scheme as well as the EMM structure facilitate the development of structure designs for elastic wave attenuation.