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Tutorial Sheet 3

# Tutorial Sheet 3 - Imperial College of Science Technology...

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Sheet 3 Page 1 Imperial College of Science, Technology & Medicine Department of Aeronautics Second Year Structural Mechanics and Dynamics Tutorial Sheet 3 Section a – Theory Development 1. It is common practice to estimate the effect of a suddenly applied loading on a structure by doubling the static deflections and stresses to allow for dynamic effects. Considering the undamped single degree of freedom system ) ( R kr r m τ = + ± ± subject to the step load shown in figure 1 then use the convolution integral to find the displacement response and the time variation of the spring force. Discuss the relevance of the 2*static approximation. R( τ ) Time τ R o Fig 1 2. An undamped single degree of freedom system has the equation of motion ωτ = + sin R kr r m 0 ± ± If the excitation frequency is the resonant frequency of the system, m k 2 = ω , then the steady state solution gives an infinite response. Use the convolution integral to investigate how the response increases with time and show that an infinite response is only achieved after an infinite time.

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