Influence of 2 secondary effects on shear failure of cantilever with attached mass block under impulsive loading

The influence of two secondary effects, rotatory inertia and presence of a crack, on the dynamic plastic shear failure of a cantilever with an attached mass block at its tip subjected to impulsive loading is investigated. It is illustrated that the consideration of the rotatory inertia of the cantilever and the presence of a crack at the upper root of the beam both increase the initial kinetic energy of the block required to cause shear failure at the interface between the beam tip and the tip mass, where the initial velocity has discontinuity Therefore, the influence of these two secondary effects on the dynamic shear failure is not negligible.

Basic equations for suspension flows with interphase mass-transfer

In the case of suspension flows, the rate of interphase momentum transfer M(k) and that of interphase energy transfer E(k), which were expressed as a sum of infinite discontinuities by Ishii, have been reduced to the sum of several terms which have concise physical significance. M(k) is composed of the following terms: (i) the momentum carried by the interphase mass transfer; (ii) the interphase drag force due to the relative motion between phases; (iii) the interphase force produced by the concentration gradient of the dispersed phase in a pressure field. And E(k) is composed of the following four terms, that is, the energy carried by the interphase mass transfer, the work produced by the interphase forces of the second and third parts above, and the heat transfer between phases. It is concluded from the results that (i) the term, (-alpha-k-nabla-p), which is related to the pressure gradient in the momentum equation, can be derived from the basic conservation laws without introducing the "shared-pressure presumption"; (ii) the mean velocity of the action point of the interphase drag is the mean velocity of the interface displacement, upsilonBAR-i. It is approximately equal to the mean velocity of the dispersed phase, upsilonBAR-d. Hence the work terms produced by the drag forces are f(dc) . upsilonBAR-d, and f(cd) . upsilonBAR-d, respectively, with upsilonBAR-i not being replaced by the mean velocity of the continuous phase, upsilonBAR-c; (iii) by analogy, the terms of the momentum transfer due to phase change are upsilonBAR-d-GAMMA-c, and upsilonBAR-d-GAMMA-d, respectively; (iv) since the transformation between explicit heat and latent heat occurs in the process of phase change, the algebraic sum of the heat transfer between phases is not equal to zero. Q(ic) and Q(id) are composed of the explicit heat and latent heat, so that the sum Q(ic) + Q(id)) is equal to zero.

Physical Modeling And Parametric Study On Two-Degree-Of-Freedom Viv Of A Cylinder Near Rigid Wall

Unlike most previous studies on the transverse vortex-induced vibration(VIV) of a cylinder mainly under the wallfree condition (Williamson & Govardhan,2004),this paper experimentally investigates the vortex-induced vibration of a cylinder with two degrees of freedom near a rigid wall exposed to steady flow.The amplitude and frequency responses of the cylinder are discussed.The lee wake flow patterns of the cylinder undergoing VIV were visualized by employing the hydrogen bubble technique.The effects of the gap-to-diameter ratio (e0/D) and the mass ratio on the vibration amplitude and frequency are analyzed.Comparisons of VIV response of the cylinder are made between one degree (only transverse) and two degrees of freedom (streamwise and transverse) and those between the present study and previous ones.The experimental observation indicates that there are two types of streamwise vibration,i.e.the first streamwise vibration (FSV) with small amplitude and the second streamwise vibration (SSV) which coexists with transverse vibration.The vortex shedding pattem for the FSV is approximately symmetric and that for the SSV is alternate.The first streamwise vibration tends to disappear with the decrease of e0/D.For the case of large gap-to-diameter ratios (e.g.e0/D = 0.54～1.58),the maximum amplitudes of the second streamwise vibration and transverse one increase with the increasing gapto-diameter ratio.But for the case of small gap-to-diameter ratios (e.g.e0/D = 0.16,0.23),the vibration amplitude of the cylinder increases slowly at the initial stage (i.e.at small reduced velocity V,),and across the maximum amplitude it decreases quickly at the last stage (i.e.at large Vr).Within the range ofthe examined small mass ratio (m＜4),both streamwise and transverse vibration amplitude of the cylinder decrease with the increase of mass ratio for the fixed value of V,.The vibration range (in terms of Vr ) tends to widen with the decrease of the mass ratio.In the second streamwise vibration region,the vibration frequency of the cylinder with a small mass ratio (e.g.mx = 1.44) undergoes a jump at a certain Vr,.The maximum amplitudes of the transverse vibration for two-degree-of-freedom case is larger than that for one-degree-of-freedom case,but the transverse vibration frequency of the cylinder with two degrees of freedom is lower than that with one degree of freedom (transverse).