Attenuation bands for flexural–torsional vibrations of locally resonant Vlasov beams

In this paper, a study on flexural–torsional vibrations of finite beams with a large number of resonators periodically attached along the length is presented. Emphasis is given in determining bandgaps, defined as frequency ranges free of resonances. The structural model is based on a modified Vlasov theory that incorporates the resonators effect by means of sectional inertial properties depending on the excitation frequency. Analyzing these last properties, the mechanism of weak and strong bandgap formation is enlightened. Analytical formulas for the edge frequencies of bandgaps are obtained. Also, an exact analytical solution for the free and forced vibration of simply supported beams is presented. This approach allows exploring, from another point of view, the location of attenuation bands.