MULTIPLE VIBRATION BAND GAPS IN LOCALLY RESONANT BEAM CARRYING SINGLE PERIODIC ARRAY OF CANTILEVER BEAM TYPE RESONATORS

摘要

In this paper, the property of multiple vibration band gaps in locally resonant beam carrying beam type resonators is investigated. Small sized beams are attached to one host beam to combine into a locally resonant beam containing cantilever beam type resonators. Numerical and experimental analyses show that this type of locally resonant beam can generate a plurality of locally resonant band gaps. Equivalent multiple resonators model of the cantilever beam type resonator is established according to modal superposition theory. Each mode of the cantilever beam type resonator is equivalent to a single degree of freedom spring-mass oscillator system while effective modal mass and effective modal stiffness of each mode are as the lumped mass and stiffness of the oscillator system respectively. Equivalent multiple resonators model is verified by dynamic stiffness and dispersion relation results. The multi-band gaps induced by cantilever beam type resonator are verified theoretically and experimentally. The band structure of the locally resonant beam containing equivalent multiple resonators model is consistent with the one of the locally resonant beam containing cantilever beam type resonators model indicating the high accuracy of equivalent method. Experimental work also verified that locally resonant band gap could be broadened effectively after laying damping layer on the cantilever beam type resonator while greater damping can be achieved at higher order modes.