Reflections of waves induced by a nonlinear spring at the boundary
B.M. Waasdorp (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Wim van Horssen – Mentor (TU Delft - Mathematical Physics)
C. Vuik – Graduation committee member (TU Delft - Numerical Analysis)
B. van den Dries – Graduation committee member (TU Delft - Analysis)
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Abstract
In this thesis the nonlinear spring system is considered. This system contains a semi-infinite string that is modelled by the wave equation with a pair of inititial conditions and a nonlinear boundary condition. The goal of this thesis is to find a good approximation of this system. Furthermore, the behaviour of the string is studied by plotting the reflected waves. Two methods are considered for estimating the solution. These are the Multiple Scales Perturbations method and the Fourth Order Runge Kutta method. The approximations of the two methods are compared to each other. From this, conclusions have been drawn on the accuracy of these approximations.