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73) u rel, max ---------------------- = V(ω) 2 ·· ( y go ⁄ ω n ) • For further cases check the literature. 2) by cos ( jω 0 t ) first, and then integrating it over the period T 0 . 2) by sin ( jω 0 t ) and then integrating it over the period T 0 . 19) • The steady-state response u ( t ) of a damped SDoF system under the periodic excitation force F ( t ) is equal to the sum of the terms of the Fourier series. 2 Half-sine An-Najah 2013 2 A series of half-sine functions is a good model for the force that is generated by a person jumping.

2 Half-sine An-Najah 2013 2 A series of half-sine functions is a good model for the force that is generated by a person jumping. 22) The static term a 0 = 2Aτ ⁄ π = G corresponds to the weight of the person jumping. 44kN natural frequency f n of the beam, the magnification factor V is small. - Taking into account the higher harmonics can be important! 0000 • Notes Total (6 harmonics) • The damped case can be solved in the exact same way. On the web page of the course there is an Excel file to illustrate this excitation.

6 Time Zeit [s] -4 0 10 20 Zeit [s] Time [s] 30 40 4 2 x [m/s ] ü An-Najah 2013 From the previous figure it can be clearly seen that the time-history of an earthquake ground acceleration can not be described by a simple mathematical formula. 1) must therefore be solved numerically. 5s SDoF system 2 0 -2 -4 0 10 20 30 40 Zeit [s] Time [s] 7 Seismic Excitation Page 7-1 The sample values of the ground acceleration u··g ( t ) are known from beginning to end of the earthquake at each increment of time Δt (“time step”).

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Fundamentals of Structural Dynamics - IUSS School


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