Plane wave diffraction by circular transmission grating; finite-difference approach

Transmission gratings with circular elemental cross section are analyzed for diffraction of plane electromagnetic waves incident at oblique angles of incidence. The new solution method which is based on the finite-difference scheme is simple in nature and involves no unchecked approximation. Numerical results are obtained for various gratings at arbitrary angles of incidence. These results favorably compare with a number of similar data available in the literature. They further reveal some of the important properties of the transmission gratings. The proposed solution technique is also applicable to problems involving finite conductivity, and, therefore, should be of considerable interest to engineers and physicists.     

Damage Identification of a Composite Beam Using Finite Element Model Updating

Abstract:   The damage identification study presented in this article leveraged a full-scale sub-component experiment conducted in the Charles Lee Powell Structural Research Laboratories at the University of California, San Diego. As a payload project attached to a quasi-static test of a full-scale composite beam, a high-quality set of low-amplitude vibration response data was acquired from the beam at various damage levels. The Eigensystem Realization Algorithm was applied to identify the modal parameters (natural frequencies, damping ratios, displacement and macro-strain mode shapes) of the composite beam based on its impulse responses recorded in its undamaged and various damaged states using accelerometers and long-gage fiber Bragg grating strain sensors. These identified modal parameters are then used to identify the damage in the beam through a finite element model updating procedure. The identified damage is consistent with the observed damage in the composite beam.     

Plane wave diffraction by dielectric gratings finite-differenceformulation

Plane-wave diffraction by dielectric gratings of arbitrary profile (groove shape and size) is analyzed using an analytical-numerical technique. The solution method is simple, general, and numerically efficient. It involves expansion in a Fourier series of the periodic permittivity function in the inhomogeneous grating region and application of the finite differences to solve numerically the inhomogeneous vector wave equation in the region. The obliquely incident radiation is of linear polarization with either of its fields parallel to the rulings. Numerical results are presented for several gratings to demonstrate the convergence, accuracy, and reliability of the method. These also show the effect of the grating profile on its diffraction characteristics     

Close-contact melting as a subtractive machining process

This study assesses the feasibility of close-contact melting for machining low melt point materials. The primary results of interest are the width and uniformity of the cut and the resistance force at the contact surface. The theoretical gap size and resistance force is derived around a cylindrical heating element with given material properties, temperatures, heating element dimensions, and cutting speed. A differential equation for the gap size is developed and solved numerically. An approximate closed form solution is found for molten wax velocity in the gap. The momentum equation is then solved to find the pressure and shear stress distributions in the gap. Resistance force against the cylinder is derived. The theory is derived for the width and uniformity of the cut and how it may be controlled with a computer numerically controlled (CNC) machine. A series of experiments that were performed to verify the theory.