Question

PROBLEM: A simply supported beam is subjected to a harmonic load F(t)-Fo sin ณ at mid-span as a result of the operation of a mechanical system that rotates at a constant speed n rev/min. The beam is made from steel with an elasticity modulus E 29x103 ksi and specific weight 490 lb/ft3. The beam has a cross-sectional area A = 1.59 in, a moment of inertia 1 = 3.85 in, and an approximate viscous damping factor 0.05. The length between supports is L-12 ft. E, A, I, γ Fo sin 2t 2 u(t) L/2 a. Plot the magnitude of the frequencyresponse IG (Q)| as a function of the frequency ratio Ω/ where on is the natural frequency of the beam b. Plot the phase angle of the frequency re c. If we want to limit the magnitude of the frequency response to a maximum value of 4, what should be the maximum allowed rotation speed (in rev/min) of the mechanical system mounted on the beam? sponse ф as a function of the frequency ratio /ch. d. Find the maximum transverse displacement umax of the beam mid-span for IG2) 1000 lb. 4 and Fo

Answer 1

In this solution some basic concepts and formulas of Vibration Mechanics are used. For more information, refer to any standard textbook or drop a comment below. Please give a Thumbs Up, if solution is helpful.

Solution :

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atan (0.1ナリ冫 plot ( r, φ kt 1亓り n 173.gl, Λ 12-17ヶ Scanned with CS amscanner

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