Forced Vibration on a Cantilever Beam

[phiska]

If a cantilever beam is subject to forced vibration (from a shaker at fixed end), what will the effect be of placing a mass at a)nodes and b)between nodes?
I presume that as there is no displacement from the normal at the nodes, the mass will have little effect, but what about between the nodes?

Any textbook, or website suggestions also greatfully received!

 

[Doc Al]

Followups here: https://www.physicsforums.com/showthread.php?t=65727

 

[charng]

I can provide an explanation for the effects of placing a mass at different locations on a cantilever beam subject to forced vibration. When a cantilever beam is subjected to forced vibration from a shaker at the fixed end, it will experience oscillations in its natural frequency. The natural frequency of a cantilever beam depends on its length, material properties, and boundary conditions.

If a mass is placed at the nodes of the cantilever beam, it will not have much effect on the beam's natural frequency. This is because the nodes are points of zero displacement and the mass will not cause any change in the beam's vibration behavior. However, if the mass is placed between the nodes, it will have a significant effect on the beam's natural frequency. This is because the added mass will change the distribution of mass along the beam, causing a change in the beam's natural frequency.

Placing a mass between the nodes of a cantilever beam can also result in a phenomenon called "detuning." This occurs when the added mass causes the beam's natural frequency to shift away from the frequency of the shaker, resulting in a decrease in the amplitude of vibration. This can be seen in practical applications, where adding mass to a cantilever beam can reduce its sensitivity to external vibrations.

In terms of resources, I recommend consulting textbooks on structural dynamics or vibration analysis, as well as reputable websites such as the National Science Foundation's Engineering Virtual Library or the American Society of Mechanical Engineers. These sources can provide more detailed explanations and examples of forced vibration on cantilever beams.