Finite thickness

About: Finite thickness is a research topic. Over the lifetime, 1245 publications have been published within this topic receiving 19481 citations.

Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates

Abstract: Based on Mindlin's plate theory and the plane wave expansion method, a formulation is proposed to study the propagation of Lamb waves in two-dimensional phononic-crystal plates. The method is applied to calculate the frequency band structure of a square array of crystalline gold cylinders in an epoxy matrix with a finite thickness. It is found that complete frequency band gaps for Lamb waves between different pass bands are opened up by tuning thickness of the phononic-crystal plate. The influence of plate thickness on the width of complete frequency band gap is calculated and discussed as well; the existence of frequency stop bands is sensitive to the variation of the thickness of the plate. Finally, we note that the proposed method provides a concise and efficient way in analyzing the frequency band structures of phononic-crystal plates in lower bands.

Lamb waves in binary locally resonant phononic plates with two-dimensional lattices

Abstract: The authors study the propagation of Lamb waves in two-dimensional locally resonant phononic-crystal plates, composed of periodic soft rubber fillers in epoxy host with a finite thickness. Our calculations are based on the efficient plane wave expansion formulation which utilized Mindlin’s plate theory. Calculated results show that the low-frequency gaps of Lamb waves are opened up by the localized resonance mechanism. The resonant frequencies of flexure-dominated plate modes are significantly dependent not only on the radius of circular rubber fillers but also on the plate thickness. The properties of localized resonance are qualitatively analogous to the vibration of a circular thin plate.

The Effect of Thermoelastic Stresses on Injection Well Fracturing

Abstract: This work considers thermoelastic stresses which would result from cooled regions of fixed thickness and of elliptical cross section. The stresses for an infinitely thick reservoir have been deduced from information available in public literature. A numeric method has been developed to calculate thermoelastic stresses induced within elliptically shaped regions of finite thickness. Results of these 2 approaches were combined, and empirical equations were developed to give an approximate but convenient, explicit method for estimating induced stresses. An example problem is given which shows how this theory can be applied to calculate the fracture lengths, bottom-hole pressures, and elliptical shapes of the flood front as the injection process progresses. (20 refs.)

Propagation modes on a dielectric coated wire

Abstract: The theory of propagation modes on a dielectric coated wire, sometimes referred to as the Harms-Goubau line, has been extended to wires coated with a finite thickness of a dielectric coating. Conditions for existence of some modes have been derived. General relations between higher order modes, requirements for trapped surface waves, and limits on the phase velocities of respective modes have been established.

Elastic state and thermodynamical properties of inhomogeneous epitaxial layers: Application to immiscible III‐V alloys

Abstract: The elastic strain and stress fields and the elastic energy of the system composed of a crystalline epitaxial layer of finite thickness coherently grown on a bulk substrate are calculated, when the intrinsic stress‐free lattice parameter of the layer is modulated along directions parallel to the substrate surface. When the modulation has components with spatial periods of the same order as the thickness of the layer, the elastic energy is considerably reduced with respect to the same modulation occurring in a bulk sample. There exists an optimal period of elementary sinusoidal modulation, proportional to the layer thickness. Consequently, for immiscible alloys where changes of composition induce changes of intrinsic lattice parameter, the critical temperature (below which they become thermodynamically unstable with respect to composition modulations) is much higher (and the domain of instability larger) if the material is in the epitaxial layer form than in the bulk form. This extends Cahn’s theory of spinodal decomposition to epitaxial layers. It is also pointed out that if a modulation has started to occur in a growing layer, the elastic deformation induced near the free surface should have important consequences on the subsequent growth of this layer. These results are applied to III‐V semiconductors immiscible alloys, such as In x Ga1−x As y P1−y , where such composition modulations are known to exist. New values of the critical temperatures for these alloys are calculated and compared with lower former estimates. The mode of development of these modulations is discussed in light of previous experimental results and these new calculations.