Uniform beam

Example The equation for the unsteady transverse motion of a uniform beam clamped at the ends is... 

Dreisewerd, K. Schiirenberg, M. Karas, M. Hillenkamp, F. Influence of the Laser Intensity and Spot Size on the Desorption of Molecules and Ions in MALDI With a Uniform Beam Profile. Int. J. Mass Spectrom. Ion Proc. 1995, 747, 127-148. 

Irradiation area and Uniformity Beam defocusing and a scatterer... 

The choice of the method depends on the type of process. With electron beams the critical process parameters are beam energy, beam current, scanning factors and uniformity, beam pulse characteristics, and the configuration of the product being processed. 

TC Huang. The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions. J Appl Mech 28 579, 1961. 

Focusing mirror system Two bent metal mirrors that deflect the X-ray beam and produce a small intense beam with a narrow angular divergence, uniform beam profile and a low background intensity. They are useful for experiments involving crystals with large unit cells. 

Dreisewerd, K.L. et al., Influence of the laser intensity and spot size on the desorption of molecules and ions in matrix-assisted laser desorption/ionization with a uniform beam profile, Ini. J. Mass Spectrom., 141, 127, 1995. 

The calculation is for a uniform beam incident on isolated atoms in a channel (Fig. 8.7). Since we are only interested in scattering angles greater than the critical angle (y/c 1°), the impact parameter is relatively small (rt 10 2 A) thus we use the unscreened Coulomb potential. In this calculation the dechanneling is a result of binary scattering by isolated displaced atoms in an otherwise perfect crystal. 

The second case corresponds to the release of the quantity of heat 2pCTo jtKyi per unit area over the plane z = 0 at time f = 0. This could be a decent approximation to the case of laser heating of a semi-infinite metal irradiated by a short pulse [defined in terms of the relative values of beam radius and (/ctp) / ] in a uniform beam where we wish to know a temperature on the beam axis. The quantity of heat per unit area would be the laser intensity I times the pulse duration Tp times the fraction absorbed or... 

In this case the energy absorbed per unit area (assuming a uniform beam) is /o ip and it is used to heat a layer (/cip) 1 thick. Thus... 

The output beam has the form of an annulus with a zero-intensity central region produced by the part of the beam that is blocked by the extraction mirror. Such an output beam, when passed through a conventional telescope designed to accommodate an unobscured beam, has an annular intensity distribution which departs from the ideal uniform intensity (such would give the minimum far-field beam width). In high-power lasers, it is frequently found that the annular beam departs so little in beam quality from the uniform beam that other factors, such as gain medium homogeneity, are more important than uniform intensity. 

Note that the first mode of this beam with nonuniform mass is only slightly different from that for a uniform beam the second mode differs more between the two beams. 

Another possible deflection mechanism is the occurrence of whirling. Whirling occurs when a shaft reaches a critical speed and becomes dynamically unstable with large lateral amplitudes. This phenomenon is due to the resonance frequency when the rotational speed corresponds to the natural frequencies of lateral vibration of the shaft. For uniform beams vibrating in flexure, the natural frequencies can be expressed as ... 

Recent years have seen great advances in nonlinear analysis of frame structures. These advances were led by the development and implementation of force-based elements (Spacone et al. 1996), which are superior to classical displacement-based elements in tracing material nonlinearities such as those encountered in reinforced concrete beams and columns. In the classical displacement-based frame element, the cubic and linear Hermitian polynomials used to interpolate the transverse and axial displacement fields, respectively, are only approximations of the actual displacement fields in the presence of non-uniform beam cross-section and/or nonhnear material behaviour. On the other hand, force-based frame element formulations stem from equilibrium between section and nodal forces, which can be enforced exactly in the case of a frame element. The exact flexibiUty matrix can be computed for an arbitrary (geometric) variation of the cross-section and for any section/material constitutive law. Thus, force-based elements enable, at no significant additional computational costs, a drastic reduction in the number of elements required for a given level of accuracy in the simulated response of a EE model of a frame structure. 

F6 - Flexure—uniform beam bending moment, 6 in. span... 

Young s modulus may be measured by a beam-bending technique with a universal mechanical testing machine. For a three-point centrally loaded uniform beam, the elastic deflection 8 is related to the load F and the beam geometry through the relation... 

In order to reduce the large number of parameters, we take into account a few hypotheses about the shape of the links. Thus, if the links are modeled as homogeneous and uniform beams of constant and symmetric cross section, the integral on link i becomes a product of an integral on the section and of an integral along the length of link i. 

Haunches can be modeled by means of uniform beam section over the entire length of the haunch, usually the one at haunch mid-length. This provides a satisfactory representation of increased girder stiffness in the area of the haunch and enables safe prediction of strength for the design phase. 

The mode shapes shown in O Fig. 30.6 are for a uniform beam. A lap joint has a thicker portion in the middle part of the beam so it is necessary to use more complex mode shapes than the ones shown. For this reason, the following analysis is restricted to mode 1, and even this has to be simplified. It will therefore be assumed that there is a constant bending moment, M, carried over the overlap portion, and that this bending decreases linearly from the edge of the lap to the free end of the beam. 

A source of finite cross-section which radiates along its axial direction only produces a collimated beam, as shown in Fig. 4-3 (b). Each differential element dA of the source area emits light in the direction = 0 of Fig. 4-2. For a uniform beam, the intensity of Eq. (4-1) is constant Iq over the beam cross-section and approximates the output from a laser. 

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