Hambric Vibroacoustic Demonstrators

The simple harmonic oscillator is the most basic system of vibration. A mass is mounted on a spring and dashpot, or a complex spring with internal damping. The resonance frequency is simply the square root of the ratio of the mass and stiffness (divide by 2π for the frequency in Hz). The vibration response is set by the spring constant at low frequencies (below resonance), by the damping at and near resonance, and by the mass at high frequencies (after it has been 'sprung' and becomes effectively free in space).

This demonstrator starts by showing the displacement response normalized by the driving force. The four plots show the real, imaginary, magnitude, and phase of the response/input force. Start by examining the magnitude of the response at the upper left. Notice that the low frequency d/F is just the inverse of the stiffness. This is the static response, where the mass and damping have no influence, only the spring. At resonance (the sharp peak near 500 Hz) the peak response is determined solely by damping, and d_peak/d_static is just the inverse of the loss factor (sometimes called the 'Q'). Notice also how the phase (lower left) between the displacement and input force is 0 at low frequencies (the displacement and force are completely in phase), and jumps to 180 degrees above resonance (the mass is perfectly out of phase with the force).

Now switch the response type to 'Acceleration'. The curves all look quite different! The y axis scales have also changed since the a/F levels are much higher than the d/F levels. This is because for harmonic response acceleration is -ω²(displacement). Now, the high frequency response of the magnitude is constant with frequency - this is the inverse of the mass. The phase plot shows that for high frequency (above resonance) response the acceleration is in phase with the input force. Now a_peak/a_{high frequency} is the inverse of loss factor (or Q).

Finally, switch the response to velocity. The amplitudes are different again. Velocity is iω(displacement) and (acceleration)/(iω). There are no constant low or high frequency trends for v/F. However, we can see that v/F at resonance is just the inverse of the equivalent viscous damping (b=ηk/ω). Check the title for the value of b at the current resonance frequency. Hover over the peak |v/F| or Re(v/F) response and confirm that the value displayed is 1/b.

Adjust the mass, stiffness, and damping loss factor to view the effects on the oscillator vibration response. The resonance peak shifts as you change stiffness and mass (watch the title to see the changing resonance frequency). The peak amplitude changes as you adjust damping loss factor (the title shows the equivalent viscous damping coefficient at the current resonance frequency). Switch between the response types. You can hover your mouse over the plots to display actual values.