Inertial amplification induced phononic band gaps generated by a compliant axial to rotary motion conversion mechanism

Phononic band gaps are investigated in a one-dimensional (1D) array of compliant axial to rotary motion conversion mechanisms. To create low frequency band gaps, the effective inertia of the unit cell mechanism is amplified. It is shown that 1D array of this chiral unit cell generates a stop band limited by two different types of modes of the unit cell. The lower limit is governed by the fundamental coupled axial-torsional mode and the upper limit is governed by the bending mode. To maximize the isolation bandwidth, cross flexures and spiral flexures are utilized in the unit cell, which in turn provide high bending stiffness and low stiffness for coupled axial-torsional motions. Besides, helical steel wires with finite bending stiffness and large pitch angle are used to generate large rotational motion for axial excitations. Hence, the effective inertia of the unit cell is increased. As the axial and torsional stiffnesses of the system are low, and its effective inertia is amplified, a stop band occurs at low frequencies. Phononic band structure and the frequency response characteristics of the system are obtained by using analytical and finite element models. Parametric studies are conducted to create wide band gaps at low frequencies. Prototypes of the unit cell and the periodic structure are manufactured via 3D printing and laser cutting. Then, the analytical and computational frequency response results are compared with the experimental results for validation. In the end, a very wide low frequency stop band is realized.