Relationship between Structural Stiffness and Viscous Damping Coefficient in Reinforced Carbon Structure under Varying Carbon Fiber Angles

A linearized dynamic model of a carbon-fiber-reinforced plastic (CFRP) structure can be formulated using the structural stiffness and viscous damping coefficient. The carbon fiber angle is an influential factor in determining the structural stiffness of CFRP structures by serially combining the stiffness of a binding matrix and that of a carbon fiber. The viscous damping coefficient of the CFRP structure is also highly sensitive to the carbon fiber angle; that is, it assumes a parallel series between the damping coefficient of the binding matrix and that of the carbon fiber. In this study, a sensitivity formula was derived to obtain the ratio of two parameters—the structural stiffness, and the viscous damping coefficient—by dividing all parameters by the value of the reference angle. The CFRP structure was chosen for a simple rectangular specimen with five carbon fiber angles, ranging from 0° (reference) to 90°. The identified modal parameters were used from the impact modal test conducted in a previous study. Sensitivity analysis was conducted for both the structural stiffness and the viscous damping coefficient. The sensitivity results revealed that the sensitivity index of the viscous damping coefficient was proportional to that of the structural stiffness. Even a small value of the viscous damping coefficient of the carbon fiber was sensitive to the CFRP structure because the carbon-fiber damping coefficient was parallel to the large damping coefficient of the binding matrix.