Experimental and numerical evidence for the existence of wide and deep phononic gaps induced by inertial amplification in two-dimensional solid structures

• Inertial amplification induced phononic gaps are generated in solid structures.
• The width and depth of the gaps are determined analytically and numerically.
• The inertial amplification mechanisms are optimized to yield wide and deep gaps.
• Numerically and experimentally obtained frequency responses match.
• Phononic gaps are experimentally shown for longitudinal and transverse excitations.

The aim of this paper is to show that a two-dimensional periodic solid structure with embedded inertial amplification mechanisms can possess a wide and deep phononic gap at low frequencies. The width and depth of the inertial amplification induced phononic gaps (stop bands) are determined both analytically using a distributed parameter model and numerically using one-dimensional (1D) and two-dimensional (2D) finite element models. The inertial amplification mechanisms are optimized to yield wide and deep gaps at low frequencies. These optimized mechanisms are used to form one- and two-dimensional periodic structures. Frequency responses of these periodic structures are obtained numerically using 1D and 2D finite element models. A deeper gap is generated with the two-dimensional periodic structure when compared with the one-dimensional periodic structure that has the same number of unit cells along the excitation direction. Then, the two-dimensional periodic structure is manufactured and its frequency response is determined via experimental modal analysis. The experimental and numerical frequency response results match quite well, which validate that the two-dimensional periodic solid structure has a wide and deep phononic gap.