Shape optimization of phononic band gap structures incorporating inertial amplification mechanisms

• Inertial amplification induced phononic gaps are created in 2D periodic structures.
• Size and shape optimizations are used to obtain wide and deep phononic gaps.
• The shape optimized design, which provided a wider and deeper gap, is manufactured.
• Phononic gaps are experimentally shown for longitudinal and transverse excitations.
• Out-of-plane modes are avoided within the phononic gap of the periodic structure.

The aim of this study is to obtain a wide and deep phononic gap at low frequencies in a two-dimensional periodic solid structure with embedded inertial amplification mechanisms. Size and shape optimizations are performed on the building block mechanism of the periodic structure to maximize phononic gap (stop band) width and depth. It is shown that shape optimization offers a wider and deeper gap, when both size and shape optimized mechanisms have the same mass and stiffness values. Analysis of the shape optimized mechanism is carried out using two different finite element models, one using beam elements and the other using shell elements. Both models produced similar results for the stop band width and depth. A two-dimensional periodic structure is constructed with the shape optimized building block mechanisms. Moreover, experimental and numerical frequency response results of this periodic structure are obtained. The matching frequency response results indicate that the two-dimensional periodic structure has a wide and deep phononic gap for in-plane excitations. Furthermore, due to proper selection of the out-of-plane thickness of the periodic structure, out-of-plane vibration modes do not occur within the phononic gap.