Derive the equation of motion and boundary conditions for a transversely vibrating beam using Hamilton's principle. Assume small deflections. Let \(I_{p}\) equal the mass moment of inertia per unit length of the beam about its neutral axis. Figure 7.60 provides a sketch of the beam along with positive sign conventions.

Transcribed Image Text:

Mo y p(x,t) 20 y L x M Figure 7.60: Transversely vibrating beam subjected to an arbitrary continuous load p(x, t) along with boundary moments and shears.