In this work, transient resonant motions excited in linearised scattering interactions are approximated using a simple damped harmonic oscillator model. The scattering interactions considered involve the diffraction of an incident wave-train with a dominant regular timeharmonic component by structures which enclose a portion of the free surface. Provided a single resonant mode only is excited s...

In this paper, we present a comparative study between the Adomian decomposition method and two classical well-known Runge-Kutta and central difference methods for the solution of damped forced oscillator problem. We show that the Adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply. 

Abstract Nonlocal operators with different kernels were used here to obtain more general harmonic oscillator models. Power law, exponential decay, and the generalized Mittag-Leffler Delta-Dirac property have been utilized in this process. The aim of study was introduce into damped model nonlocalities associated these mentioned see effect each one them when computing Bode diagram obtained from L...

We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories LPTs . The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an...