Suppose a cantilever beam stands uprigt, such as a tube attached to the floor in one end and free at the other end. Suppose then that a force is applied normal to the beam at some point along the beam causing a deflection. Then suppose that at t=0 the force disappears, and the intertia of the beam as its deflection diminishes causes an underdamped motion.(adsbygoogle = window.adsbygoogle || []).push({});

The question I cannot figure out is how to accurately determine a second order differential equation, which will describe deflection as a function of time.

All I have is the idea of assuming no damping, but then I end up with harmonic vibrations, which never change. That which I'm missing from my equation is a way to determine the damping constant or function in my second order differential equation, such that the damping force is proportional to the velocity of the beam at a given time, and is in opposite direction to the motion of the beam.

The beam is assumed to have uniform E and I.

How do I determine the damping effect theoretically?

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# Vibrating uprigt cantilever beam

Can you offer guidance or do you also need help?

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