The Finite Difference Scheme for the Suspended String Equation with the Nonlinear Damping Term

A numerical solution of the initial boundary value problem of the suspended string vibrating equation with the particular nonlinear damping term based on the finite difference scheme is presented in this paper. The investigation of how the second and third power terms of the nonlinear term affect the vibration characteristic. We compare the vibration amplitude as a result of the third power nonlinear damping with the second power obtained from previous report provided that the same initial shape and initial velocities are assumed. The comparison results show that the vibration amplitude is inversely proportional to the coefficient of the damping term for the third power nonlinear damping case, while the vibration amplitude is proportional to the coefficient of the damping term in the second power nonlinear damping case.

Authors:

• Jaipong Kasemsuwan

Keywords:

• Finite-difference method
• the nonlinear damped equation
• the numerical simulation
• the suspended string equation

References:

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