Nonlinear Vibration Analysis of the Composite Cable using Perturbation Method and the GreenLagrangian Nonlinear Strain

In this study, nonlinear vibration of a composite cable is investigated by considering nonlinear stressstrain relations. The composite cable is composed of an aluminum wire as reinforcement and a rubber coating as matrix. The nonlinear governing equations of motion are derived about to an initial curve and based on the fundamentals of continuum mechanics and the nonlinear GreenLagrangian strain, using the Hamilton’s principle. The equations of motion of the system are reduced into the ordinary differential equations using the Galerkin method, and solved by the perturbation method (multiple scales). Timeresponse diagrams are presented for the composite cable with different volume fractions of the matrix and the reinforcement. It is predicted that the more volume fraction of the matrix is, the more nonlinear quadratic and cubic terms in the governing equations of motion affects the vibration of the cable. Results indicate that increasing the length of the cable would decrease the amplitude of the time response of the system.