Numerical analysis of SDOF random vibration response. Computes response spectrum, response RMS, and 3-sigma values from PSD input in real time. Applicable to vibration durability design for spacecraft, aircraft, and automotive components.
Input PSD / Response PSD / Transfer Function (Log Scale)
Theoretical Background
In random vibration analysis, the response PSD is obtained from the input power spectral density (PSD) and the transfer function of the single-degree-of-freedom system. The response RMS is the square root of the integral of the response PSD.
Transfer function: $|H(f)|^2 = \dfrac{1}{\left[1-\left(\dfrac{f}{f_0}\right)^2\right]^2 + \left[2\zeta\dfrac{f}{f_0}\right]^2}$
Resonance peak factor: $Q = \dfrac{1}{2\zeta}$ (transfer function maximum $\approx Q^2$)
The Miles equation is an approximate solution that assumes a constant PSD level $G_0$ near $f_0$. When the PSD varies significantly around $f_0$, the numerical integration result is more accurate. Widely used in vibration durability assessment of spacecraft and aircraft components.