Low frequency bandgap enhancement in dual graded metastructure beam with negative capacitance circuits and light-weight mass-spring resonators

In this work bandgap formation and vibration attenuation properties in graded metastructure beams are studied. By using negative capacitance circuits and different grading laws on frequency spacing and arrangement of the piezoelectric and mechanical resonators, hybrid graded metamaterial beams are formed. This study emphasizes the potential of spatially graded metamaterials as a promising solution for improving vibration attenuation in low-frequency applications. It is found that graded distribution of light-weight mechanical (<10 % mass of the host structure) and negative capacitance resonators, enhance the width of the bandgap especially at low frequency (lower than the first structural frequency). Moreover, the spatially graded resonators enhance vibration attenuation along the entire length of the beam, unlike the periodic configuration where suppression mainly occurs near the free end. It is also demonstrated that by tuning grading variation parameters in dual graded hybrid metamaterial beam, wide and effective attenuation bandgaps in desired positions can be achieved. To this end, the governing equations of the vibrations of hybrid meta-beams are derived using Hamilton principle. Initially, a Floquet solution is developed for the repetitive unit-cell of a periodic structure and its band structures are investigated through dispersion analysis. Then for the frequency response analysis, the governing equations are discretized using the Galerkin method and solved for various grading laws in mechanical, electromechanical, and dual graded meta-beams. Based on the obtained frequency response results, the bandgap properties of the meta-beams are analyzed and compared.