Bandgaps and damping of four-component phononic crystals with planar tension–torsion coupling effect

Abstract In the conventional phononic crystal, the torsion local resonance cannot open new bandgaps due to the absence of coupling between the torsion of core and the tension/compression of matrix. Also, the soft coating may greatly reduce the overall stiffness due to the direct contact between the coating and the matrix. By introducing the planar tension–torsion coupling (TTC) effect and the rigid strain isolation interphase, the four-component phononic crystal with higher stiffness and damping properties is developed in this study, and the general mechanism of the TTC effect on the bandgap and energy attenuation properties of TTC phononic crystal is investigated based on Bloch–Floquet theory. The effects of stiffness coefficients including tension stiffness, torsion stiffness and TTC stiffness on the location and width of bandgaps in the TTC phononic crystals are presented, it is found that the introduced TTC effect is beneficial for opening new bandgaps that cannot be created in the conventional locally resonant phononic crystals (LRPCs). The spatial and temporal energy attenuation properties of TTC phononic crystal are evaluated via ‘harmonic wave’ approach ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> ) and ‘free wave’ approach ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> ), respectively. Meanwhile, the TTC effect can help some damping phononic crystals to increase the temporal energy attenuation via the modal strain energy approach. Furthermore, the maximum spatial energy attenuation of TTC phononic crystal is triggered by the TTC local resonance of the core. This study provides some guidelines for high-damping and high-stiffness phononic crystals, which are ideal candidates for vibration reduction of engineering structures.