Static deflection

Damping reduces the transmissibihty at the natural frequency, but increases the transmissibihty at higher frequencies. The natural frequency of isolators made from most materials also can be expressed as a function of the static deflection of the isolator due to the load imposed by the supported equipment that is, / = 5/v where 5 is the static deflection of the isolator, cm (5). 

Elastomeric materials, which provide relatively low practical static deflections and have relatively high natural frequencies, are used only to isolate higher frequencies. The volume compressibiUty of elastomeric materials is relatively low, therefore the shape of the elastomeric isolator must be taken into account, and space must be provided for lateral expansion. Because of their inherent resistance to chemical and environmental deterioration, neoprene and other synthetic materials often can be used in severe environments where natural materials would deteriorate. 

Products. Vibration isolators typically are selected to have a static deflection, under load, that yields a natural frequency no more than one-third the lowest driving frequency that must be isolated (see Eig. 7). The supporting stmcture must have sufficient stiffness so it does not deflect under the load of the supported equipment by more than one-tenth the deflection of the isolator itself (6). In addition to static deflection requirements, vibration isolators are selected for a particular appHcation according to their abiHty to carry an imposed load, and to withstand the environment in which they are used (extreme temperatures, chemical exposure, etc). 

The undamped critical speed is proportional to the static deflection nf a sii shaft as seen by the following equation for a mass concent at a le point [6],... 

Gel strength, in units of lbf/100 ft , is obtained by noting the maximum dial deflection when the rotational viscometer is turned at a low rotor speed (usually 3 rpm) after the mud has remained static for some period of time. If the mud is allowed to remain static in the viscometer for a period of 10 s, the maximum dial deflection obtained when the viscometer is turned on is reported as the initial gel on the API mud report form. If the mud is allowed to remain static for 10 min, the maximum dial deflection is reported as the 10-min gel. 

When all possible vibration reduction has been obtained, the machine must be isolated from the structure. Some form of spring mounting achieves this. Spring mounts have a resonant frequency dependent on the stiffness of the spring and the weight of the object placed on it. It will be apparent that the static deflection of the spring will also be proportional to the resonant frequency. 

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. 

Although these are loosely termed mbber mounts, they are often composed of synthetic mbbers, which are not readily attacked by oils and can operate over a much wider temperature range. Typical maximum static deflections are 12.5 mm. 

The relationship between the weight of mass M and the static deflection of the spring can be calculated using the equation W = ZZ,. If the spring is displaced downward some distance, Zo, from Zj and released, it will oscillate up and down. The force from the spring, F, can be written as follows, where a is the acceleration of the... 

X = Spring displacement at time, t Zst = Static spring deflection under constant load, Fo Cl) = Forced frequency ci)o = Natural frequency of the oscillation t = Time... 

FolK = Deflection of the spring under load, (also called static deflection, Zst) a> = Forced frequency ft)jj = Natural frequency of the oscillation = Frequency ratio... 

Figure 6. Vacuum mixer for lead paste 1, mixing compartment 2, fast-rotating mixing tools 3, material-deflecting plate 4, discharge opening 5, static, vacuum-sealed enclosure [21J.

FEA is applicable in several types of analyses. The most common one is static analysis to solve for deflections, strains, and stresses in a structure that is under a constant set of applied loads. In FEA material is generally assumed to be linear elastic, but nonlinear behavior such as plastic deformation, creep, and large deflections also are capable of being analyzed. The designer must be aware that as the degree of anisotropy increases the number of constants or moduli required to describe the material increases. 

In many cases, a product fails when the material begins to yield plastically. In a few cases, one may tolerate a small dimensional change and permit a static load that exceeds the yield strength. Actual fracture at the ultimate strength of the material would then constitute failure. The criterion for failure may be based on normal or shear stress in either case. Impact, creep and fatigue failures are the most common mode of failures. Other modes of failure include excessive elastic deflection or buckling. The actual failure mechanism may be quite complicated each failure theory is only an attempt to explain the failure mechanism for a given class of materials. In each case a safety factor is employed to eliminate failure. 

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... 

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. 

This analysis is similar to a conventional static analysis with the exception of non-hiv ar member properties and pressure-time loadings. Member adequacy is judged by maximum deflection and support rotation rather than the member stress criteria used in static design. 

The shaft flexibility factor is directly related to the static deflection of a simply supported shaft, and is therefore a good indicator of the runout attainable during manufacture and the quality of balance that can be achieved and maintained. 

For bending experiments either 3 or 4 point bending may be used. For static or creep tests the load is usually applied as a weight on a hanger and the deflection measured using an... 

Static Objects deflecting compass needles bending metal keys making stopped watches run. 

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