Handbook of Friction-Vibration Interactions

2.3.2 Response of a SDOF system to an arbitrary function input

Next we consider the response of a SDOF vibration system to arbitrary function input. The equation of motion is given by

$\ddot{\mathit{y}}\left(\mathit{t}\right)+2\mathit{\xi }{\mathit{\omega }}_{\mathit{n}}\dot{\mathit{y}}\left(\mathit{t}\right)+{\mathit{\omega }}_{\mathit{n}}^2\mathit{y}\left(\mathit{t}\right)=\mathit{x}\left(\mathit{t}\right)$ [2.156]

[2.156]

where x(t) = F(t)/m, ${\mathit{\omega }}_{\mathit{n}}=\sqrt{\mathit{k}/\mathit{m}}$, ξ = c/c_c and ${\mathit{c}}_{\mathit{c}}=2\sqrt{\mathit{km}}$. The arbitrary function x(t) is plotted in Figure 2.13. There are two different ways to obtain the solution of Eq. 2.156. The first one used is the impulse response method. In this ...