Exact and approximate analytical solutions of oscillator with piecewise linear asymmetrical damping

The objective of this work is to present exact and approximate analytical solutions of a 1-DOF oscillator with asymmetrical damping under harmonic excitation, and to explore the role of asymmetrical damping in the response of such oscillator. The response of the case with overdamped expansion and underdamped compression is shown in details to illustrate the effect of the asymmetry ratio (β) on the transition time, the mean position and energy dissipation. The solutions for all other cases are also shown, indicating similar effects. Higher asymmetry ratio (β>1) provides lower peak acceleration in high frequency, while (β