<p>In this work, wave transmission through a rod with an attached nonlinear neutraliser is investigated. The neutraliser is a mass-spring-damper system with cubic and linear stiffness components. The wave transmission is investigated in infinite and semi-infinite rods with the neutraliser positioned near to a reflective boundary in the latter case. The equation of motion is obtained and solved with the method of varying amplitudes. First and second order harmonic solutions are compared, and stability of solutions is assessed. Two waves are incident on the neutraliser and the amplitude and phase difference of waves are assessed in terms of effect on vibration transmission. The results provide insights into the effects of incident waves on the vibration suppression behaviour of a damped neutraliser attached to a rod, with the distance between the neutraliser and the boundary affecting the behaviour.</p>