Yuceer M.,Turksat AS |
Lukin I.P.,Zuev Institute of Atmospheric Optics
Applied Physics B: Lasers and Optics | Year: 2010
Scintillations of Laguerre-Gaussian (LG) beams for weak atmospheric turbulence conditions are derived for on-axis receiver positions by using Huygens-Fresnel (HF) method in semi-analytic fashion. Numerical evaluations indicate that at the fully coherent limit, higher values of radial mode numbers will give rise to more scintillations, at medium and low partial coherence levels, particularly at longer propagation distances, scintillations will fall against rises in radial mode numbers. At small source sizes, the scintillations of LG beams having full coherence will initially rise, reaching saturation at large source sizes. For LG beams with low partial coherence levels, a steady fall toward the larger source sizes is observed. Partially coherent beams of medium levels generally exhibit a rising trend toward the large source sizes, also changing the respective positions of the related curves. Beams of low coherence levels will be less affected by the variations in the refractive index structure constant. © 2010 Springer-Verlag.
Sahin M.,Turksat AS
Journal of Engineering Mechanics | Year: 2014
The governing dynamic equilibrium equation of N-story periodic shear structure with arbitrary top-story mass, arbitrary base-story stiffness, and that is subjected to base excitation is given in the form of a constant coefficient second-order finite-difference equation. The first integration of the governing difference equation for the eigenanalysis results in the Volterra difference equation of convolution type and yields the first boundary condition. The z-transform method is applied to the equation to obtain the general solution for displacement mode shapes. Applying the second boundary condition to the general solution results in the characteristic equation in which the frequencies are obtained by solving it. The general form of the characteristic equation for eigenfrequencies is presented, and analytical solutions for some special cases are derived. Displacement and drift mode shape functions are obtained. All the modal parameters, including modal mass, excitation factor, participation factor, and effective modal mass, are derived using the sum and the sum of the square modal displacements and are presented as closed-form solutions. © 2014 American Society of Civil Engineers.