By Wodek Gawronski
The publication offers and integrates the equipment of structural dynamics, indentification and keep an eye on right into a universal framework. It goals to create a typical language among structural and keep watch over method engineers.
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Additional info for Advanced structural dynamics and active control of structures
24) Cmv Cov ). 19) (a modal representation of a structure) is a set of uncoupled equations. Indeed, due to the diagonality of : and = , this set of equations can be written, equivalently, as qmi 2] iZi qmi Zi2 qmi yi cmqi qmi cmvi qmi , y ¦ yi , bmi u i 1,! 26) n i 1 where bmi is the ith row of Bm and cmqi , cmvi are the ith columns of Cmq and Cmv , respectively. The coefficient ] i is called a modal damping of the ith mode. In the above equations yi is the system output due to the ith mode dynamics, and the quadruple (Zi , ] i , bmi , cmi ) represents the properties of the ith natural mode.
Introduction to Structures 9 The magnitude of a flexible structure transfer function is characterized by the presence of resonance peaks; see Fig. 10(b). x The impulse response of a flexible structure consists of harmonic components, related to complex poles, or to resonance peaks; this is shown in Fig. 10(c). x The phase of a transfer function of a flexible structure shows 180 degree shifts at natural frequencies, see Fig. 10(d). x Poles of a flexible structure are complex conjugate. Each complex conjugate pair represents a structural mode.
1210 rad/s. The Standard Models 27 harmonics are shown on the impulse response plot, but are more explicit at the impulse response spectrum plot, Fig. 7, as the spectrum peaks at these frequencies. 1 can be written in time domain as n h(t ) ¦ hi (t ) i 1 where h(t) is the impulse response of a structure and hi (t ) is the impulse response of the ith mode. Thus, the structural impulse response is a sum of modal responses. This is illustrated in Fig. 8, where impulse responses of modes 1, 2, and 3 are plotted.
Advanced structural dynamics and active control of structures by Wodek Gawronski