By Mikhail Z. Kolovsky (auth.)
With development in know-how, the matter of shielding human-beings, machines and technological techniques from assets of vibration and effect has develop into of extreme value. conventional "classical" equipment of security, established upon making use of elastic passive and dissipative parts, develop into inefficient in lots of events and will no longer thoroughly fulfill the advanced and sometimes contradictory claims imposed on smooth vibration safeguard structures which needs to supply excessive functionality at minimal dimensions. For those purposes, energetic vibration safeguard structures, that are really structures of computerized regulate with self sufficient strength resources are generic nowadays.
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Extra info for Nonlinear Dynamics of Active and Passive Systems of Vibration Protection
The displacements of points Ak and Ck coincide in the case of the rigid attachment. Let R(t) denote the vector of forces acting on the base which results in TJ (t) = -E0 (p)R(t). 165) Here E 0 (p) is the matrix of the dynamic compliance operator of the base at points Ck. 165) give ((t) = -[Eo(P) + EA(p)]R(t). 166) 54 1. Dynamic characteristics and efficiency of vibration protection systems Let the vibration isolators be mounted between the base and the object. Let ZA (t) and zc (t) denote the displacement vectors at points Ak and Ck.
15. where w(iw) = eAB(iw)wz(iw)[1 + eA(iw)wz(iw)]- 1 . 102) This enables one to determine the amplitude of ( B ( t) which is ZBo = V((Ao Rew(iw)- (Eo cos a:)2 + ((Ao Im w(iw)- (no sin a:) 2 . 103) 3. Let us apply the equations obtained to deriving the conditions for an efficient active vibration protection system of a single-degree-of-freedom system. The system is assumed to consist of a mass m, an elastic element of stiffness c and a dashpot b, see Fig. 15. Let us assume that the mass m is driven by a prescribed force F (t) and the displacement of the base is ~(t).
Let force U (t) be applied at point A of the object in a prescribed direction. In general, the goal of the control is to influence some parameter of the vibration field, for example the displacement ZB of another point B. Let the displacement of this point without control be ( 8 (t). 90) with eAB(P) being the dynamic compliance operator. e. U(t) = -wz(P)ZB (t). 91) In other words, the control is realised by means of feedback, the minus sign implying a negative feedback. 93) expresses the displacement of point B in the system with control in terms of that in the system without control.