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Theory of Vibro-Impact Systems and Applications by Prof. Dr V. I. Babitsky (auth.)

By Prof. Dr V. I. Babitsky (auth.)

- versions of vibro-impact structures are everyday in computer dynamics, vibration engineering, and structural mechanics. - purely monograph in this topic in English language. - Systematically provides the speculation of vibro-impact structures via research of average engineering functions. - Experimental information and laptop simulations are offered. - specific to engineers and researchers in layout and research of mechanical platforms in addition to to academics and complex scholars. Contents: - Vibro-impact structures. - similar linearisation of vibro-impact systems.- Vibro-impact strategies in structures with unmarried measure of freedom. - Vibro-impact approaches with a number of levels of freedom. - Structural synthesis of self-sustaining vibro-impact systems

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Example text

3), as amplitude is increased, their frequencies approach more cJosely to double that ofthe linear oscillator. 6) converges fairly quickly and it is interesting to discover to what extent the described nonlinear behaviour of the backbone curve is shown by the first harmonic (fundamental) of vibration. 12) This relationship is shown dotted in Fig. 3. Comparison shows that the first harmonic of the process quite accurately represents the nonlinear behaviour of the system. The situation indicated is studied in Chapters 2 to 4 using approximate methods based on analysis of the fundamental.

70) where x is the linear velocity of the striker along the bar; q, is the angular velocity of the striker; \V is the angle of the oblique profile, r is the average radius of the cam. 71) I sin\jl where 1 is the moment of inertia of the body; J I is the normal impulse during the first phase of impact. 70) we find at that instant . 73) ' § 1 Collision of solids where f-l 17 = Mr 2 / I . 61) J=J 1 +J 2 =(l+R)J , . 75) we obtain x+ = . :i:Jsin 2\jJ r(1l sin 2 \jJ + cos 2 \jJ) We note that similar relationships can be written for the impact of a free body, without a guiding bar, when the cams are symmetrical by assuming that contact of the cams occurs simultaneously.

Instead, as was shown in §2, for systems with reasonably simple structures, analytic methods can expose the approximate boundaries 01' the existence domains, and we will use these here. : O. 19) x. Hence, for th is model due to the arrangement 01' stops, within the limits 01' vibration of the linear system only one regime can exist for each ratio studied. 20) these regimes correspond to the positive sign, and when C, < I on the minus sign. : a . 15) in this case the expression below the radical is N-f} $ r - N less than or equal to unity and consequently both 1-/ values 01' ~y take the sign of the coefficient in the denominator, in other words the sign of the value of sin 3.

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