- Todd, M.D. and Virgin, L.N., Natural frequency considerations of an impact oscillator,
Journal of Sound and Vibration, vol. 194 no. 3
pp. 452 - 460  .
(last updated on 2007/03/23)
This paper studies an experimental linear oscillator with one-sided displacement constraint. Due to the mobility of the constraint, the natural frequency of the system changes as the impact point changes, and the analytical calculations are performed to describe this dependence for pure elastic rebound and for a bilinear oscillator. Bilinear results show that a general decrease in the natural frequency is seen for all constraint locations when compared to elastic rebound results, which is expected since the mass spends a non-zero amount of time in the stiffer region. A series solution is partially obtained for the corresponding non-linear experimental system. The experimental results correlated very well with analytical calculations based on a pure elastic rebound.
Natural frequencies;Constraint theory;Calculations;Equations of motion;Dynamics;Lagrange multipliers;Vibrations (mechanical);