Phononic crystals can be defined as artificial materials that exhibit a periodic arrangement of unit-cells made with a combination of parts with a high impedance discrepancy. Due to its periodic structure, some frequency ranges may exist where elastic waves are forbidden to propagate. By applying this concept to design an elastic beam, significant attenuation in the vibration behavior may be obtained. For some cases, this problem can be solved in terms of mechanical energy flow analysis, by using the Energy Spectral Element (ESE) method. ESE uses the mechanical energy to formulate vibration problems via energy density and flow. In this work, ESE is used to analyze an elastic phononic crystal beam in order to verify, in terms of energy, whether it is possible to identify bandgaps. Simulated examples are presented and the results are compared and verified using the Spectral Element (SEM) method and the Wave Finite Element (WFE) method.
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