A driven system responds with amplitude depending on frequency ratio and damping.
Under harmonic force F₀cosΩt, steady amplitude X=(F₀/k)/√((1-r²)²+(2ζr)²) with r=Ω/ωₙ. At low r the response is static, near r=1 it peaks, and at high r it is mass-dominated. Phase shifts from 0 to 180°.
An unbalanced washing machine shakes most near its resonance spin-up speed.
Forced vibration describes how a system responds to a continuous excitation, which is the situation in most machines and structures.
A driven system responds with amplitude depending on frequency ratio and damping.
Forced vibration describes how a system responds to a continuous excitation, which is the situation in most machines and structures.
It is the ratio of the excitation frequency to the natural frequency. Its value determines whether the response is amplified or attenuated.
Once the transient has decayed, a linear system responds at the forcing frequency, though the amplitude and phase depend on the frequency ratio.
Typical applications include predicting the vibration amplitude of a fan on a steel frame, calculating the displacement of a building under a steady wind load and estimating the response of a pump foundation to rotating unbalance.
Study "Damped vibration" first (topic 75 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Magnification factor. Transient dies out. Base excitation analogous.
An unbalanced washing machine shakes most near its resonance spin-up speed.
The next topic is "Resonance", which builds directly on this one.
It is classed as Advanced in Engineering Mechanics (topic 76 of 106). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mechanics.
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