The force-deflection curve for a composite structure of mass, m = 2000 kg, is shown experimentally. a) Find the hysteresis damping ratio η, the logarithmic δ, and the equivalent damping coefficient Ceq. Need B,C,D   b) Find the value of stiffness from the graph in N/mm. c) Assume initial condition of u0 = 1.5mm, v0 = 2mm/sec, determine the free vibration response of this structure. d) Plot the response from part c. Hints: k = 165 N/mm, U (part a) = 4.3mm, η = 0.344, Ceq = 6.25 N.sec/mm, α = 14.15°, U (part b) = 1.52mm.

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.