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3.Flexureanalysis - 25 we can measure the static response...

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3. Flexure Analysis Consider a simple cantilevered beam in bending ( i.e. steal the equations from your structures book): W σ σ ε = = = = U V | | | W | | | My I M WL E I bh 3 12 where W = Weight or applied force L = Unsupported length of the beam b = Width of beam h = Height (in y ) of beam M = Applied moment y = Distance from neutral axis Combine equations above to get : ε = 6 2 WL Ebh , which is perhaps more commonly written as ε y My EI = . (25) Eq. (25) can be thought about in terms of two components that determine how the strain, ε , depends on the applied moment, M . I y is the section modulus ; it is a geometric parameter and EI is the flexural stiffness So, using a strain gage to monitor the strain, which is directly proportional to the applied moment (eq. 25), we can measure the static response
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Unformatted text preview: 25), we can measure the static response of the beam to an applied load. For the purposes of measuring the frequency response , one can model the vibration of a cantilevered beam as a second order system. A damped second order system response can be characterised by two parameters, the undamped natural frequency, ω , and the damping ratio, ζ (eq. 3). By measuring the frequency and amplitude decay in free vibration, both parameters can be estimated by experiment. 2 BUT . ...... enquiring minds might want to know: Why? What does the damping ratio correspond to, physically? Why should the damping be proportional to the velocity? Why is it like viscous damping? Think....
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