Mathematical modeling and experimental study of damping behavior of a cantilever carbon fiber-reinforced polymer composite hollow member with metal inserts

Metal inserts are widely used particularly in bolted connections for joining composite members. In this work, a theoretical basis is provided for analyzing the damping behavior of a cantilever composite square hollow member embedded with metal inserts along its length. Analytic stress solutions around the boundaries of the insert and the member are introduced while deriving the expression of modal damping ratio. Kelvin-Voigt and amplitude-dependent damping models are considered for the formulation. Experiments are performed on the perforated composite tube reinforced with brass, copper, and steel annular inserts subjected to transverse base motion of varying amplitudes. The acceleration responses recorded from the tests are analyzed to evaluate the damping ratio of the fundamental mode. It is observed that the damping ratio evaluated from the experiments matches well with the proposed value. Furthermore, it is found that the damping ratio increases when the holes are reinforced with the inserts. The reason for the increase in damping stems from (i) frictional effect at the boundaries of the insert and the tube and (ii) material damping of the inserts. For example, the damping amplification of the tube with five steel inserts is noted to be around 3.0 and 2.1 times with respect to the unperforated and perforated (with holes) cases, respectively.