Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length.Based on Rayleigh’s quotient,an iterative strategy is developed to find the approximated torsional stiffness coefficients,which allows the reconciliation between the theoretical model results and the experimental ones,obtained through impact tests.The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh’s quotient but also on the mode shapes,considering the shape functions defined in branches.Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

TRANSVERSELY ISOIROPIC BEAM UNDER INITIAL STRESS

Starling from Novozhilov's nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.These equations are applied to investigate the vibration and buckling characteristics of a transversely isotropic beam under uniform initial axial force and bending moment.

Creation of Super Long Transversely Polarized Optical Needle Using Azimuthally Polarized Multi Gaussian Beam

The intensity distribution in the focal region of a high-NA lens for the incident azimuthally polarized multi Gaussian beam transmitted through a multi belt spiral phase hologram is studied on the basis of the vector diffraction theory. Here we report a new method used to generate a needle of transversely polarized light beam with sub diffraction beam size of 0.366A that propagates without divergence over a long distance of about 22A in free space. We also expect that such a light needle of transversely polarized beam may find its applications in utilizing optical materials or instruments responsive to the transversal field only.

Design study of an improved laser wire system for electron beam measurement

The laser wire （LW） method has been demonstrated to be an effective non-interceptive technique for measuring transverse profile and emittance of electron beams in colliders, storage rings and dumping rings. In this paper, we present an improved design of high repetition LW system for high average power free electron lasers （HAP FELs） and energy recovery linacs （ERLs）. This improved LW utilizes the excess power of the photocathode drive laser, thus making itself much cheaper and simpler. The system main parameters are optimized with numerical calculations and Monte Carlo simulations, indicating that resolutions would be better than 100 ~m and scanning time less than 1 minute. Status of the experiment preparation is also presented.

Generating a uniform transverse distributed electron beam along a beam line

It has been reported that transverse distribution shaping can help to further enhance the energy extraction efficiency in a terawatt, tapered X-ray free-electron laser. Thus, methods of creating and keeping an almost uniform transverse distributed（UTD） beam within undulators are required. This study shows that a UTD electron beam can be generated within evenly distributed drift sections where undulators can be placed, by means of octupoles and particular optics. A specific design is presented, and numerical simulations are performed to verify the proposed method.