In this article, the bending and free vibration analysis of functionally graded (FG) nanocomposites Timoshenko beam model reinforced by single-walled boron nitride nanotube (SWBNNT) using micro-mechanical approach embedded in an elastic medium is studied. The modified coupled stress (MCST) and nonlocal elasticity theories are developed to take into account the size-dependent effect. The mechani...

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FO...

An elementary theory for beam waveguides based upon geometrical optics as well as upon the HUYGENS undulatory theory is developed. A homogeneous FREDHOLM integral equation of the first kind is derived. It connects the field distribution as observed on a mathematical surface behind the n-th lens with the given initial distribution. If the spacing between the lenses is chosen such that the beam w...

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equati...

We outline a theory for the calculation of the beam quality factor of an aberrated laser beam. We provide closed-form equations that show that the beam quality factor of an aberrated Gaussian beam depends on all primary aberrations except tilt, defocus, and x-astigmatism. The model is verified experimentally by implementing aberrations as digital holograms in the laboratory.

The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback is studied. Firstly, two auxiliary operators are introduced, and the Riesz basis property of their eigenvector systems is proved. This property is used to show that the generalized eigenvector system of a Timoshenko beam with some linear boundary feedback forms a Riesz basis in the corresp...

Fiber-reinforced composites, due to their high specific strength, and stiffness, which can be tailored depending on the design requirement, are fast replacing the traditional metallic structures in the weight sensitive aerospace and aircraft industries. An analysis Timoshenko beam theory for complex composite beams is presented. Composite materials have considerable potential for wide use in ai...

A theory of parametric amplification in a filamentary electron beam by transverse fields is developed in coupled mode form. Space charge effects are neglected. In addition to beam modes at the signal frequency, beam modes at frequencies wn=w+wv, n=O, ±1, ±2· ··,where wp is the pump frequency, are coupled together. A discussion of the general form of the equations is given and reveals the circum...

Fast realistic rendering of objects in scattering media is still a challenging topic in computer graphics. In presence of participating media, a light beam is repeatedly scattered by media particles, changing direction and getting spread out. Explicitly evaluating this beam distribution would enable efficient simulation of multiple scattering events without involving costly stochastic methods. ...

In the present study, free vibration behaviors of of carbon nanotube (CNT) and boron nitride nanotube (BNNT) have been investigated via Eringen’s nonlocal continuum theory. Size effect has been considered via nonlocal continuum theory. Nanotubes have become popular in the world of science thanks to their characteristic properties. In this study, free vibrations of Boron Nitride Nanotube (BNNT) ...