Truncation Ratio Research Articles

Propagation characteristics of a diffracted M2 beam.

The propagation characteristics of a beam diffracted by a circular aperture are investigated. The beam-quality factor M2 defined by an 86.5% power-content radius is given theoretically and experimentally as a function of the truncation ratio. It is found that the theoretical limit of M2 is 2.37 times as great as that of an incident beam as the truncation ratio approaches 0. For a weakly diffracted beam a simple formula giving M2 is derived. Although M2 does not increase much with diffraction, the influence of diffraction should be taken into account in beam brightness.

Gaussian beam transfer through hard-aperture optics

We consider Gaussian beam diffraction by hard circular and rectangular-slit apertures. Both numerical results and accurate elementary analytic approximations are derived for the fraction of transmitted power (or energy) contained within the main central lobe of the far-field (or focal-plane) irradiation distribution as a function of the truncation ratio.

Parametric Analysis of Truncated Gaussian Beams

The Fresnel diffraction field of a truncated gaussian beam diffracted by a circular aperture is investigated. A new parametrization is introduced which allows the changes of the truncated beam in comparison to the untruncated one to be determined with the aid of three dimensionless parameters: the beam truncation ratio, the defocusing and the normalized radial distance. The limitations of the method are discussed.

A singular hybrid finite element analysis of boundary-layer stresses in composite laminates

A singular hybrid finite element method for studying boundary-layer stresses in composite laminates is presented. The laminate elasticity basis and the fundamental solution structure for the boundary-layer field are briefly reviewed first. Formulation of a singular composite-edge element is based on the recently developed boundary-layer theory and the variational principle of a modified hybrid functional. The singular hybrid element is used conveniently in conjunction with displacement-based conventional elements. Numerical solutions for the well-known Pipes-Pagano problem are presented for illustration. Comparisons of the present solution with the laminate elasticity solution and conventional finite element results are made to demonstrate the accuracy and efficiency of the present approach. Influences of eigenfunction truncation, size and aspect ratio of the singular hybrid element as well as mesh configuration are studied.

Theoretical analysis of the performance of a conical solar concentrator

This paper describes a study of the conical solar energy concentrator with tubular axial absorber. The concentrated power is evaluated, in a dimensionless form, as a function of the mirror surface quality and the absorber-to-aperture diameter ratio. The irradiated length of the absorber is determined and the axial concentration distribution along its surface is expressed mathematically. An integrated, or average, concentration ratio is used to measure the concentrating power of the reflector-absorber assembly. In addition to the mirror reflectivity, the performance is shown to be influenced by three parameters—the apex angle, the diameter ratio and the truncation ratio. The effects of these parameters on the concentrated power, the concentration profile and the reflector-surface area are investigated.

Shear vibration of vertically inhomogeneous earth dams

AbstractClosed‐form solution to the problem of free vibrations of vertically inhomogeneous earth dams, modelled as truncated‐wedge‐shaped shear beams, has been obtained by implementing an inverse procedure in which the determination of the function descrbing the inhomogeneity constitutes part of the problem. The resulting cube‐root variation of the shear‐wave velocity with distance from the crest compares very favourably with measurements in two Japanese dams. The results of the method are presented in theform of natural periods, modal shapes and average seismic coefficients for a number of truncation ratios. Compared with an ‘equivalent’ homogeneous dam, the inhomogeneous experiences sharper amplification of modal displacements and greater averge seismic, coefficients near the crest and has natural periods which are closer to each other. This behaviour is in better agreement with the observed response of a 37m‐high dam during five earthquake motions.