Characteristic Exponents of Mathieu Functions

Tamir, T.

doi:10.2307/2003814

Cited by 3 publications

(1 citation statement)

References 3 publications

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“…Integer and noninteger Mathieu's functions have been computed using formulas in [23] and [24]; the first four pairs of integer-order Mathieu's functions and are shown in Fig. 4 in terms of and respectively, where and correspond to the case when the periodic function in (4) contains only one cosine term [as in (3)].…”

Section: B Analytic Solution Of the Descriptive Equationsmentioning

confidence: 99%

Controlling the Bandlimits of TE-Surface Wave Propagation Along a Modulated Microstrip-Line-Based High Impedance Surface

Matekovits

Colome

Orefice

2008

IEEE Trans. Antennas Propagat.

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A hybrid numerical-analytical method for the characterization of the propagation of the transverse-electric surface waves along a high impedance surface (HIS) is presented. The HIS is obtained by a 2-D periodic repetition of a rectangular unit cell on a Cartesian grid. The unit cell consists of a microstrip line with variable width immersed in a grounded multilayer dielectric substrate. Inside the unit cell, the effective value of the dielectric is sinusoidally modulated along the direction of the microstrip line, and the dimension of the unit cell is equal to the period of the modulation. On the basis of the modulation parameters, limits of the stop/pass bands are determined analytically employing Mathieu's functions. The synthesis of the shape of the microstrip line that guarantees the desired modulation requires the numerical determination of the phase velocity-line width relationship which is not known in closed form for the considered unbounded open structure. The limits of the pass/stop bands determined analytically are in very good agreement with those found numerically and measured values for different modulation parameters. Index Terms-Electromagnetic band gap (EBG), high impedance surface (HIS), microstrip, surface impedance synthesis.

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Section: B Analytic Solution Of the Descriptive Equationsmentioning

confidence: 99%

Controlling the Bandlimits of TE-Surface Wave Propagation Along a Modulated Microstrip-Line-Based High Impedance Surface

Matekovits

Colome

Orefice

2008

IEEE Trans. Antennas Propagat.

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Relationship between a Damped Discrete Hill's Equation and an associated Undamped Discrete Hill's Equation

Venegas

Collado

2019

2019 16th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)

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Refined Dynamic Stability Theory of Laminated Isotropic Circular Plates

Krizhevsky

Stavsky

1998

Journal of Applied Mechanics

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Hamilton’s variational principle is used for the derivation of transversally isotropic laminated circular plates motion. Nonlinear strain-displacements relations are considered. Linearized dynamic stability equations are obtained for circular plates subjected to the same uniformly distributed periodic radial loads. The effects of transverse shear and rotational inertia are included. The exact solutions of vibrations and buckling problems are given initially in the terms of Bessel, power, and trigonometric functions. The vibrational modal functions are used then as a basis in the Galerkin method that reduced the study of dynamic stability to investigation of bounds of instability of Mathieu’s equations. Analytic expressions for the bounds of both principal and combination-type instability regions are obtained using the methods of Bolotin and Tamir. A new effect—sensitivity of certain instability regions to slight imperfections in the symmetry of lamination—is found out and discussed here.

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Characteristic Exponents of Mathieu Functions

Cited by 3 publications

References 3 publications

Controlling the Bandlimits of TE-Surface Wave Propagation Along a Modulated Microstrip-Line-Based High Impedance Surface

Controlling the Bandlimits of TE-Surface Wave Propagation Along a Modulated Microstrip-Line-Based High Impedance Surface

Relationship between a Damped Discrete Hill's Equation and an associated Undamped Discrete Hill's Equation

Refined Dynamic Stability Theory of Laminated Isotropic Circular Plates

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