By Wodek Gawronski
The e-book provides and integrates the equipment of structural dynamics, indentification and keep watch over right into a universal framework. It goals to create a standard language among structural and keep watch over process engineers.
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Extra resources for Advanced structural dynamics and active control of structures
30) i i and the structural transfer function at the ith resonant frequency is approximately equal to the ith modal transfer function at this frequency (b) G (Zi ) # Gmi (Zi ) ( jcmqi Zi cmvi )bmi 2] iZi2 , i 1, ! , n. Proof. 28). Structural Poles. 26). The equation s 2 2] iZi s Zi2 0 is the characteristic equation of the ith mode. For small damping the poles are complex conjugate, and in the following form: s1 ] iZi jZi 1 ] i2 , s2 ] iZi jZi 1 ] i2 . 32) The plot of the poles is shown in Fig.
32) The plot of the poles is shown in Fig. 1, which shows how the location of a pole relates to the natural frequency and modal damping. 2. 1. 5910 » . 7370 »¼ ) The modes are shown in Fig. 2. 1. Pole location of the ith mode of a lightly damped structure: It is a complex pair with the real part proportional to the ith modal damping; the imaginary part approximately equal to the ith natural frequency; and the radius is the exact natural frequency. 0156 0 º «0 ». 3280 » . 2. Modes of a simple system: For each mode the mass displacements are sinusoidal and have the same frequency, and the displacements are shown at their extreme values (see the equation (a)).
1210 rad/s. The phase plot shows a 180-degree phase change at each resonant frequency. 4. 87 Hz). For each mode the nodal displacements are sinusoidal, have the same frequency, and the displacements are shown at their extreme values. Gray color denotes undeformed state. 28), and their magnitudes and phases are shown in Fig. 6. 1, the transfer function of the entire structure is a sum of the modal transfer functions, and this is shown in Fig. 6, where the transfer function of the structure was constructed as a sum of transfer functions of individual modes.