By George J. Simitses
Dynamic instability or dynamic buckling as utilized to constructions is a time period that has been used to explain many periods of difficulties and plenty of actual phenomena. it's not remarkable, then, that the time period unearths numerous makes use of and interpretations between structural mechanicians. difficulties of parametric resonance, follower-force, whirling of rotating shafts, fluid-solid interplay, common reaction of constructions to dynamic rather a lot, and several other others are all categorised less than dynamic instability. Many analytical and experimental stories of such difficulties are available in different books as both really good subject matters or the most subject matter. such sessions, parametric resonance and balance of nonconservative platforms less than static quite a bit (follower-force problems), shape the most subject matter of 2 books through V. V. Bolotin, that have been translated from Russian. additionally, remedy of aero elastic instabilities are available in different textbooks. eventually, analytical and experimental reports of structural components and platforms subjected to severe rather a lot (of very brief length) are the point of interest of the hot monograph via Lindberg and Florence. the 1st bankruptcy makes an attempt to categorise some of the "dynamic instability" phenomena through making an allowance for the character of the reason, the nature of the reaction, and the historical past of the matter. additionally, some of the suggestions and methodologies as built and utilized by some of the investigators for estimating serious stipulations for all of sudden loaded elastic structures are totally defined. bankruptcy 2 demonstrates the ideas and standards for dynamic balance via uncomplicated mechanical versions with one and levels of freedom.
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Extra resources for Dynamic Stability of Suddenly Loaded Structures
Geometry and sign convention for model A. FIGURE equilibrium is characterized by dui =0 (1) de where U T is the total potential, and the character of equilibrium (stable or unstable) by the sign of the second derivative. 40 ,I ! 35 / o _--- K,,--_ " "- , --" a. 2 Load-displacement curves (model A). PTS. 26 2. Simple Mechanical Models where p = 2PjkL and (J~ denotes the nondimensionalized total potential. " The static equilibrium points are characterized by p=[Jl+sinO-Jl+sinO o] Note that, for 00 = ° cotO for 00 #0.
Critical conditions for model B: constant load of infinite duration. (a) Total potential curves. (b) The phase plane. 38 2. Simple Mechanical Models Use of eqs. 9, p. 36). Clearly, if (47) eq. (46) denotes a closed curve about the null position (8 = () = 0) in the phase plane. 9). When [proeY = 1, eq. (46) denotes a curve that can escape the closed loop and thus the motion becomes buckled. Therefore, L 1 (pro)cr = - =-:::.. e (48) e Clearly, the result is the same as before, eq. (39). Next, the case of a sudden constant load of infinite duration is considered.
Pro) = _2_ sin eo dr 90 (13) The zero-load static equilibrium positions are obtained by requiring the total potential, eq. (8), to have a stationary value, or d[J~ =O=[jl +sine-jl +sineo]cot el j l +sine de for eo#o. (14) This requirement yields e = eo and e = ± n12. 3) are unstable. A critical condition exists when T7 = [J~ (e = nI2), or T~r = [J2 - j l + sineoy (16) J2 - j (17) From eqs. _2_ Tjl/2 = 2[ sm eo cr 1 + sin eo]/sin eo. Two observations are worth mentioning at this point: (1) Because this is a one-degree-of-freedom model, the critical impulse (prO)er given by eq.