Download Nonlinear Dynamics of Active and Passive Systems of by Mikhail Z. Kolovsky (auth.) PDF

By Mikhail Z. Kolovsky (auth.)

With development in know-how, the matter of defending human-beings, machines and technological procedures from resources of vibration and impression has develop into of extreme value. conventional "classical" equipment of safeguard, established upon utilizing elastic passive and dissipative components, turn into inefficient in lots of occasions and will now not thoroughly fulfill the complicated and infrequently contradictory claims imposed on glossy vibration safety structures which needs to supply excessive functionality at minimal dimensions. For those purposes, lively vibration security structures, that are truly platforms of computerized regulate with autonomous strength resources are generic nowadays.

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Extra info for Nonlinear Dynamics of Active and Passive Systems of Vibration Protection

Example text

Analogously, for antiresonance to occur at frequency w = r! 89) must be satisfied. 89) can be shown to be equivalent to the following T _1 1 » b (m1 + m2) 2 m2 _1 ' 71 » b (m1 + m2) 2 m2 . The latter implies that the resonant and antiresonant phenomena occur only if mass mz is not too small. 3 Efficiency conditions in the case of harmonic excitation The most important characteristic of any system of vibration protection is its efficiency. A system of vibration protection is effective when it reduces the vibration transmission to the object.

Let the forces F 1 (t), F2(t), ... ,Fk(t) act on the points A1 , A2, ... ,Ak and v1 (t), v2 (t), ... , Vk (t) denote projections of the displacement of the points Ak along the directions of the forces Fs (s = 1, ... , k), see Fig. 10. By virtue of the superposition principle which is valid for linear system we obtain k V8 (t) = L ems(p)Fm(t) (s = 1, ... , k). (1. 72) m=l Here ems(P) are the dynamic compliance operators relating forces Fm (t) to displacements V 8 (t). 72) can be written in vector form as v(t) = E(p)F(t), (1.

In other words, an active system of vibration protection is mounted between the object and the base and acts with equal forces on both the object and the base. 112) bp+c+wx(P) F(t _ ~ t mp 2 +bp+c+wx(P) ) mp2 +bp+c+wx(P) (). mp 2 (bp+c) Thus, the reduction of the system reaction after the control has been introduced depends on the nature of the dynamic excitation, too. Provided that ~(t) = 0, we have 44 1. 113) When the excitation is kinematic, we have ][1 + mp2Wx~) + p+c kR(P) = 1 kx(p). 115) can be analysed by analogy.

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