Wave reflections in a semi infinite string due to nonlinear energy sinks at the boundary
S. Missula (TU Delft - Electrical Engineering, Mathematics and Computer Science)
W. T. van Horssen – Mentor (TU Delft - Mathematical Physics)
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Abstract
Vibrations or oscillations can be caused in overhead cable lines or bridge cables due to strong rain and winds, making the structure unstable.These vibrations can be mathematically described as a string like initial boundary value problem with non-classical boundary conditions. In this thesis, we consider a nonlinear attachment at the boundary which consists of a mass, nonlinear spring and a damper attached to a semi infinite string. In particular, we consider a weak nonlinearity and damping. In this study we used the D'Alembert solution and the multiple time scales perturbation method to obtain bounded solutions of the initial boundary value problem. We assumed travelling wave initial conditions, and obtained special cases and conducted detuning around these special cases to further study the reflected waves at the boundary and the stability of our solutions. Our main objective is to study the reflection of the incident wave on the boundary and compute how much energy is dissipated at the boundary due to the weak dissipative forces present at the boundary