Consider the longitudinally vibrating uniform beam shown in Figure 7.48. One end of the beam is fixed and the other end is free with an attached concentrated mass \(M\). Derive the frequency equation, the first three natural frequencies, and plot the first three mode shapes for axial vibration. Use \(m L / M=1\).

Transcribed Image Text:

x L m, EA M Figure 7.48: Axially vibrating cantilever beam fixed at one end with a point-mass at the other end.