Summary
In this paper, an initial-boundary value problem for a semi-infinite string is considered. A tuned-mass-damper (TMD) system is attached at one end of the string. The spring in the system is considered to be non-linear. We study the boundary reflection of waves and damping properties. The well-known D’Alembert formula is used throughout this paper to describe the general solution of the wave equation with corresponding initial velocity and displacement. A Multiple Scales Perturbation (MSP) method is used to approximate the solution of the non-linear problem. How waves are reflected depends strongly on the mass, spring and damper coefficients. Future work will focus on determining the accuracy of our approximations.
