Dynamic deflection

Covers density, indentation-force deflection, compressionforce deflection, constant deflection, compression set, tension, tear resistance, air-flow, resilience (ball rebound), static-force loss at constant deflection, dynamic fatigue, steam autoclave aging, and dry-heat aging. 

Deflection. Dynamic shaft deflection at the impeller centerline shall not exceed 0.005 in. (0.13 mm) anywhere within the design region as specified... 

TABLE 7.57 Deflection dynamics under a 100 lb load (a third-point load), a 5.5 in. X 1.25 in. Trex board, support span 22 in. 

The END trajectories for the simultaneous dynamics of classical nuclei and quantum electrons will yield deflection functions. For collision processes with nonspherical targets and projectiles, one obtains one deflection function per orientation, which in turn yields the semiclassical phase shift and thus the scattering amplitude and the semiclassical differential cross-section... 

A deflected shaft is absolutely straight when rotated in a lathe or dynamic balancer. The deflection is the result of a problem induced either by operation or. system design. The deflected shaft also will fail prematurely in the pump, leaving similar, but different evidence on the elo.se tolerance rubbing parts in the pump. The next two pictures show how a bent shaft appears when rotated 180 degrees (Figure 9-9 and Figure 9-10). 

Again, the characteristics of the system need to be considered. The weight of the machine and the frequency will determine the static and dynamic deflections of the mounts and hence the material of which the mount is to be constructed. At very high frequencies mats may be placed under machinery, and these may consist of mbber, cork or foam. At middle frequencies it is usual to use mbber in-shear mounts. At low frequencies metal spring mounts are employed. 

There are plastics such as TP elastomers that are frequently subjected to dynamic loads where heat energy and motion control systems are required. One of the serious dynamic loading problems frequently encountered in machines and vehicles is vibration-induced deflection (Chapter 4, DYNAMIC LOAD ISOLATOR). 

The most common conditions of possible failure are elastic deflection, inelastic deformation, and fracture. During elastic deflection a product fails because the loads applied produce too large a deflection. In deformation, if it is too great it may cause other parts of an assembly to become misaligned or overstressed. Dynamic deflection can produce unacceptable vibration and noise. When a stable structure is required, the amount of deflection can set the limit for buckling loads or fractures. 

D = dynamic range = log(maximal meter deflection/sensitivity). 

The complex island structure in Fig. 7 is a consequence of the complicated dynamics of the activated complex. When a trajectory approaches a barrier, it can either escape or be deflected by the barrier. In the latter case, it will return into the well and approach one of the barriers again later, until it finally escapes. If this interpretation is correct, the boundaries of the islands should be given by the separatrices between escaping and nonescaping trajectories, that is, by the time-dependent invariant manifolds described in the previous section. To test this hypothesis, Kawai et al. [40] calculated those separatrices in the vicinity of each saddle point through a normal form expansion. Whenever a trajectory approaches a barrier, the value of the reactive-mode action I is calculated. If the trajectory escapes, it is assigned this value of the action as its escape action . 

Resistance-Deflection Function. The resistance-deflection function establishes the dynamic resistance of the trial cross-section. Figure 4a shows a typical design resistance-deflection function with elastic stiffness, Kg (psi/in), elastic deflection limit, Xg (in) and ultimate resistance, r.. (psi). The stiffness is determined from a static elastic analysis using the average moment of inertia of a cracked and uncracked cross-section. (For design... 

The load-mass factor, K, transforms the actual dynamic system to the equivalent SDOF system. The value is usually between 2/3 and 3/4 and depends on the geometry, end conditions, support conditions, and range of behavior (i.e. elastic, elasto-plastic, or plastic). The maximum deflection, X, is then compared to the allowable ultimate deflection to determine the adequacy of the trial section. 

The shear loads, V, are based on the ultimate bending resistance, r, of the structural element. Shear resistance is provided to support the resulting shear stresses, v. This allows the element to reach its full dynamic flexural loacf carrying capacity and not fail prematurely, in shear, at small deflection. Two major shear stresses must be checked diagonal tension at a distance from the support, and direct shear at the support. 

Rebound Response to the dynamic blast load, will cause the window to rebound with a negative (outward) deflection. The outward pane displacement and the stresses produced by the negative deflection must be safely resisted by the window while positive pressures act on the window. Otherwise, the window which safely resists stresses... 

In many cases, the dynamic amplification factor or the ratio of static load to dynamic load capacity will exceed two. This is because of the concave up shape of the resistance function and the mobilization of membrane resistance at large deflection to thickness ratios. Because of this phenomenon, it is unconservative to assume the blast capacity of polycarbonate glazing to be no less than one half of its static pressure load capacity. 

During the transient load phase of an accidental explosion, when the shock duration is less than the time of maximum response of the structural elements, member end rotations are limited to one degree. Maximum inelastic deformation is limited to three times the member elastic limit deflection. Since this loading phase is suddenly applied, use of material dynamic increase factors based on strain rate of loading are also used. 

As mentioned above, it is common practice to separate a structure into its major components for purposes of simplifying the dynamic analyses. This uncoupled member by member approach approximates the actual dynamic response since dynamic iteration effects between major structural elements are not considered. Resulting calculated dynamic responses, which include deflections and support reactions, may be underestimated or overestimated, depending on the dynamic characteristics of the loading and the structure. This approximation occurs regardless of the solution method used in performing the uncoupled dynamic analyses. 

In order to determine the dynamic response of a system, one needs to develop generalized force versus deflection relationships for the overall structure or each member. 

Revise size to get closer to the target deflection. Try a lighter channel. Use dynamic reactions. 

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