Deflection analysis

M.J. Turner, R.W. Clough, H.C. Martin, and LJ. Topp. Stiffness and deflection analysis of complex structures. Journal of the Aeronautical Sciences, 23(9) 805, 1956. 

For the reactions K + HBr and K + DBr, the KBr recoil energy distribution has been determined in a crossed-molecular beam experiment using a mechanical velocity selector. No difference was found in the form of the translational energy distributions for the two reactions for which a value of 0.30 may be derived. Although all the angular momentum appears in the product rotation, the moments of inertia for the alkali halides are large, which implies that the mean product rotational energy is quite small ( 0.21, 0.21 and 0.09 for K, Rb, Cs + HBr, respectively [3] these values are derived from the rotational temperatures obtained by electric deflection analysis). 

These experiments show conclusively that the available energy is released almost entirely as internal excitation of the products. The observation that the diatomic product can subsequently excite M atoms electronically demands a degree of excitation which precludes the formation of 2P1/2 halogen atoms, which requires 21.7 kcal/mole (0.94 eV) for I and 10.5 kcal/mole (0.46 eV) for Br. Where electric deflection analysis has been performed [34-36], the averaged rotational energy yield, is about 5 kcal/mole (0.22 eV),... 

Gillen et al. [67] estimated the distribution of c.m. recoil energies from the velocity analysis. No significant differences were observed in scattering from K + HBr and from K + DBr, and E mp was approximately 1.5 kcal/mole (0.06 eV). Electric deflection analysis [34, 35] on MBr from K (and Cs) + HBr indicates that (IFr ot) = 1.5 kcal/mole (0.06 eV) and confirms that the rotational momentum of KBr is approximately equal to the orbital momentum of the reactive collisions [see equation (43)]. These measurements suggest that a considerable fraction of the small amount of energy available in this reaction enters the KBr vibration. 

Figure 5. Deflection analysis of a cantilever beam to estimate bending effect.

Fig. 17. Electric deflection analysis of the M/z = 63.5 peak in the iodine mass spectrum.

Similar arguments apply to the results (see Fig. 18) of the electric deflection analysis of the M/z = 254 ion beam. Both l2 and the formed as a result of the repulsive electron detachment from in the first field-free region (that is, I(R) ) will be transmitted by the magnetic sector. Kinetic energy analysis of this ion beam requires 2U(. to bring the I(R) species to Faraday cup 2 and to detect the l2 ion. Any formed by dissociation of I2 in the second field-free region, I(D), will be detected at Faraday cup 2 by application oiUJl to the electric deflection plates. 

Schnitzer and Anbar s experiments are rather similar to those of Baumann, Heinicke, Kaiser and Bethge Both employed plasma ion sources that employed by Schnitzer and Anbar was a hollow cathode duoplasmatron. Also, both used einzel lenses and momentum/charge analysis. But the different lifetimes of the doubly-charged negative ions studied dictated somewhat different analyses. Baumann, et al. used an electric deflection analysis after the magnetic sector, as already seen, whereas Schnitzer and Anbar employed a Wien velocity filter and einzel lens voltage variation prior to the magnetic sector. 

T. Horibe, Boundary Strip Method for Large Deflection Analysis of Elastic Rectangular Plates, Transaaion of the Japan Society of Mechanical Engineers, 56(532) (1990) 140 (Japanese). 

The coefficients a, Px and Py in Equations (4.46)—(4.48) are based on small deflection analysis and are valid for a maximum deflection less than or equal to half the plate thickness. For deflections greater than half the plate thickness a non-linear analysis which takes account of the plate membrane action is required. 

The pressures which are generated within the lubricant film have sufficient magnitude to deform the bounding surfaces elastically, since the area over which significant elastic deformation occurs Is small compared to the physical dimensions of the surfaces that form the contact, It Is reasonable to conduct the deflection analysis by modeling the surfaces as homogenous elastic half-spaces At any point within the contact, the total normal elastic deflection of both surfaces [24] is given by... 

An exact comparison of the present results with those from zhu Dong and Wen Shi-zhu [25] cannot be made, since some differences exist between the mathematical descriptions of the problem and in the methods by which they were solved (The work by [25] was probably not formulated with a conservative fluid flow solution, used a higher order deflection analysis, neglected conduction of heat In the x-direction within the solids, but Included heat convection within the fluid). 

Fig. 5.31. The variation of membrane tension in the film versus pressure applied within the bulge region. The solid curve represents the result of large deflection analysis given in (5.79), and the discrete points follow from a finite element simulation of the bulge. Both of these results approach the high-pressure asymptote represented by membrane theory, shown as the dashed line, but only very gradually.

Assumptions A uniform cylindrical peg has been selected. It is assumed that the peg itself is rigid and undergoes negligible elastic deformation during the insertion process. This assumption will be established to be valid during the finite element study to be reported separately. It is further stipulated that coefficient of friction (/x) between the gripper jaws and the peg is the same at each point of contact. The insertion is attempted when the axes of the peg and hole are parallel/co-axial. A double v-block jaw configuration has been selected after considerable deflection analysis of other forms. 

Deflection Analysis for Design of Gripper Jaws The forces on each jaw are the reaction in the normal direction and friction in the tangential direction to the surface, as shown in Figure 5. The stress distribution due to the reactive force R in yz plane is the sum of the stress due to bending moment of Ry and the compressive stress due to The compressive stress distribution over the cross sectional area is given by ... 

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