Bi-axial flexural vibration attenuation in periodic asymmetric beam and study of the effect of geometry on stopband sensitivity: An analytical, FEA and experimental study

The Bragg scattering phenomenon for vibration attenuation has been extensively explored. However, most of the existing literature deals with symmetric beam cross-sections undergoing uniaxial bending. In contrast, asymmetric beam cross-sections are commonly used in aerospace structures. Such beams exhibit coupled biaxial bending behavior. This paper presents an analysis of flexural wave propagation through such a beam using a transfer matrix-based approach with biaxial bending incorporated in the governing differential equation. The results were validated using the frequency response function obtained from both the 1D and 3D finite element analyses. Experimental impact hammer test results were also obtained for a periodic beam constructed using an L-section beam of aluminum. The results were found to be in close agreement. A parametric study was performed to investigate the effects of beam configuration, material properties, and orientation of the periodic beam on the stopbands. The results revealed that asymmetric beam structures yield partial and full stopbands and better flexibility in controlling the stopbands for vibration suppression.