Nonlinear vibration analysis of carbon nanotube-reinforced composite beams resting on nonlinear viscoelastic foundation

Nonlinear vibration analysis of composite beam reinforced by carbon nanotubes resting on the nonlinear viscoelastic foundation is investigated in this study. The material properties of the composite beam is considered as a polymeric matrix by reinforced carbon nanotubes according to different distributions. With using Hamilton's principle, the governing nonlinear partial differential equations are derived based on the Euler-Bernoulli beam theory. In the nonlinear kinematic assumption, the Von Karman nonlinearity is used. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The nonlinear natural frequency and the nonlinear free response of the system is obtained. In addition, the effects of different patterns of reinforcement, linear and nonlinear damping coefficients of the viscoelastic foundation on the nonlinear vibration responses and phase trajectory of the carbon nanotube reinforced composite beam are investigated.

Automated summary

Nonlinear vibration analysis of a carbon nanotube-reinforced composite beam resting on a nonlinear viscoelastic foundation is investigated. The material properties of the composite beam are considered based on different distributions of reinforced carbon nanotubes in a polymeric matrix. Nonlinear partial differential equations are derived using Hamilton's principle and the Euler-Bernoulli beam theory. The Galerkin's decomposition technique is used to discretize the equations and solve the resulting nonlinear ordinary differential equation using the multiple time scale method. The study explores the effects of different reinforcement patterns and linear and nonlinear damping coefficients on the nonlinear vibration responses and phase trajectory of the carbon nanotube-reinforced composite beam.