Exact Characteristic Equations Research Articles

Numerical analysis of mode structures and attenuations in dielectric-coated circular hollow waveguides for the infrared

The changes of the mode structures and attenuation constants in dielectric-coated circular metallic hollow waveguides are numerically investigated by solving the exact characteristic equations. It is shown that the mode structures in the small-core waveguides change drastically with the thickness of the coated-dielectric.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Exact solutions for the non-conservative elastic stability of non-uniform columns

The exact characteristic equations for the non-conservative elastic stability of general elastic restrained non-uniform columns governed by a fourth order ordinary differential equation with arbitrarily varying polynomial coefficients are derived. The results are compared with those in the existing literature. In addition, the influence of the boundary conditions, taper ratio and variation of linearly distributed tangential forces on the non-conservative elastic stability of two kinds of tapered columns subjected to linearly distributed tangential forces is investigated. It is shown that the parameter e of the linearly distributed tangential forces g(X) = g 0(1−eX/l) has great influence on the instability mechanism for the clamped-clamped columns.

Modes and attenuation constants in circular hollow waveguides with small core diameters for the infrared

The mode structures and attenuation constants in circular hollow waveguides are evaluated numerically based on the exact characteristic equations. Mode properties, which are strongly dependent on waveguide materials, and attenuation constants are discussed when the core diameter becomes small. Special modes are also analyzed in oversized metallic waveguides which approach very familiar modes in perfectly conducting cylindrical waveguides when the core diameter becomes small.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

First higher-mode cutoff in two-layer elliptical fibre waveguides

The first higher-mode cutoff parameter of an elliptical optical fibre waveguide is computed from the exact characteristic equations. Discrepancies with previously published results are attributed to limitations of the approximation used in that work.

Natural frequencies of rectangular orthotropic plates with a pair of parallel edges simply supported

Solutions of the exact characteristic equations for the title problem derived earlier by an extension of Bolotin's asymptotic method are considered. These solutions, which correspond to flexural modes with frequency factor, R, greater than unity, are expressed in convenient forms for all combinations of clamped, simply supported and free conditions at the remaining pair of parallel edges. As in the case of uniform beams, the eigenvalues in the CC case are found to be equal to those of elastic modes in the FF case provided that the Kirchoff's shear condition at a free edge is replaced by the condition ∂M n ∂n = 0 . The flexural modes with frequency factor less than unity are also investigated in detail by introducing a suitable modification in the procedure. When Poisson's ratios are not zero, it is shown that the frequency factor corresponding to the first symmetric mode in the free-free case is less than unity for all values of side ratio and rigidity ratios. In the case of one edge clamped and the other free it is found that modes with frequency factor less than unity exist for certain dimensions of the plate—a fact hitherto unrecognized in the literature.

The free vibration of rectangular plates

This work attempts to present comprehensive and accurate analytical results for the free vibration of rectangular plates. Twenty-one cases exist which involve the possible combinations of clamped, simply-supported, and free edge conditions. Exact characteristic equations are given for the six cases having two opposite sides simply-supported. The existence of solutions to the various characteristic equations is carefully delineated. The Ritz method is employed with 36 terms containing the products of beam functions to analyze the remaining 15 cases. Accurate frequency parameters are presented for a range of aspect ratios (a/b = 0·4, 2/3, 1·0, 1·5, and 2·5) for each case. For the last 15 cases, comparisons are made with Warburton's useful, approximate formulas. The effects of changing Poisson's ratio are studied.

Propagation characteristics of the TM 01 surface-wave mode in dielectric-lined coaxial cables

Accurate calculations of the propagation coefficients of the TM01 surface-wave mode in coaxial cables with dielectric linings on the inner, outer or both conductors were carried out using a perturbation method, and were checked by solving the exact characteristic equations. The calculations show that the perturbation method yields very accurate results, and that the attenuation coefficients cannot be reduced below that of the quasi-TEM mode in the unlined cable.

Approximate theories of the propagation of elastic waves in bounded solids

Except for certain limiting cases, the propagation of elastic waves in bounded solids is a dispersive phenomenon. In linear solids which are free from losses, dispersion is associated with the geometry of the solid. It is usually a function of the ratio of a lateral dimension of the solid to the wavelength. In practice, the equations of motion and the equations representing the boundary conditions are so complex that only in a very few cases have the exact characteristic equations been obtained.