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Question: The EOM for a cantilevered beam with a thin disk supported at its free end is
The beam has length l = 1 m and a circular cross section with diameter d = 25 mm. It is made from steel with modulus of elasticity E = 2.1 × 1011 Pa. The disk supported at the end of the beam has radius r = 250 mm and thickness b = 25 mm and is also made from steel (density = γ = 7830 kg/m3 ).
Tasks: (a) Determine the inertia and stiffness matrices and state the matrix EOM.
(b) Determine the eigenvalues, natural frequencies, and matrix of eigenvectors [A]. Draw the eigenvectors.
(c) Without normalizing your eigenvectors, show that [A]T[L][A] and [A]T[K][A] are diagonalized, where [L] is the inertia matrix and [K] is the stiffness matrix.
(d) State the modal differential equations and the transformation from modal to physical coordinates.
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