Question: The cantilever beam shown in Figure P5.76 has length L and a rectangular cross section with width a and height b. The rectangular thin plate mounted on the end of the beam has weight w and dimensions A = 16 in. and B = 18 in.
(a) For motion within the plane of the paper, draw a free-body diagram for the plate and state the equations of motion. Determine the inertia and stiffness matrices, and state the matrix EOM.
(b) Determine the eigenvalues, natural frequencies, and eigenvectors for the following data: a = 2 in., b = 1 in., L = 10 in., w = 200 lbs. The beam is made from steel, E = 30E6 psi.