Development of the analytical method of the general mathieu equation solution

Purpose This paper aims to develop resonant vibratory gyroscopes for high sensitive detection. The dynamic characteristics of resonant vibratory gyroscopes are investigated. Design/methodology/approach Firstly, the working principle and the dynamic output characteristics of the resonant vibratory gyroscope could be described by the damped Mathieu equation. Moreover, an approximate analytical method based on the small parameter perturbation has been used for the purpose of investigating the approximate solution of the damped Mathieu equation. Finally, to verify the feasibility of the approximate analytical method of the damped Mathieu equation, dynamic output characteristics’ experiments of the resonant vibratory gyroscope are built. Findings The theoretical analysis and numerical simulations show that the approximate solution of the damped Mathieu equation is close to the dynamic output characteristics of the resonant vibratory gyroscope. On the other hand, it is concluded from the tested result that there exists a correlation between the theoretical curve and the experimental data processing result, meaning the damped dynamics analytical method is effective in building resonant vibratory gyroscopes. Originality/value This paper seeks to establish a foundation for optimizing and testing the performance of the resonant vibratory gyroscope. To this end, the approximate analytical method of the damped Mathieu equation was discussed. The result of this research has proved that the dynamic characteristics based on the damped Mathieu equation is an effective approach and is instructional in the practical resonant sensor design.

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Design of a beam of variable cross-section on the elastic base by the quasi-analytical method considering boundary conditions

Innovative Materials and Technologies in Metallurgy and Mechanical Engineering ◽

10.15588/1607-6885-2021-2-12 ◽

2021 ◽

pp. 73-76

Author(s):

Р. Shtanko ◽

S. Ryagin ◽

І. Geletiy ◽

А. Kononenko

Keyword(s):

Differential Equation ◽

Boundary Conditions ◽

Nonlinear Differential Equation ◽

Cross Section ◽

Analytical Method ◽

Variable Cross Section ◽

Elastic Base ◽

Variable Cross ◽

Equation Solution ◽

Linear Algebraic Equations

Purpose. Improvement of the quasi-analytical method of nonlinear differential equation solution and its approbation with reference to beams of variable cross-section on the elastic base with two base factors. Research methods. Boundary conditions in the form of required number of correspondently transformed equations are added to the system of the linear algebraic equations which results from substitution of approximating function with constant factors (for example – power function) in the nonlinear differential equation and fixation of a set of variable values. The total number of the equations have to correspond to quantity of constant factors if the further solution will be carried out by an analytical method. Results. Deflection diagram of a trapezoid concrete beam with rectangular cross-section of variable height on the elastic base with two base factors has been calculated during approbation. Average solution error was equal to 0.06%. Distributions of the bending moments and normal stresses along the beam have been researched. Scientific novelty. The authors did not meet in literature such method of nonlinear differential equation solution. Practical value. The quasi-analytical method with realised consideration of boundary conditions that has been offered can be used for solution of differential equations of any order with various types of nonlinearity, including calculations of beams of variable cross-section on the elastic base.

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Densitometric Identification of Primitive Erythroblasts After Reaction With Diaminobenzidine

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100072083 ◽

1973 ◽

Vol 31 ◽

pp. 328-329

Author(s):

John A. Trotter

Keyword(s):

Red Blood Cells ◽

Analytical Method ◽

Blood Cells ◽

Guinea Pigs ◽

Specific Protein ◽

Visual Examination ◽

Hemoglobin Synthesis ◽

Peroxidatic Activity ◽

Small Density

Hemoglobin is the specific protein of red blood cells. Those cells in which hemoglobin synthesis is initiated are the earliest cells that can presently be considered to be committed to erythropoiesis. In order to identify such early cells electron microscopically, we have made use of the peroxidatic activity of hemoglobin by reacting the marrow of erythropoietically stimulated guinea pigs with diaminobenzidine (DAB). The reaction product appeared as a diffuse and amorphous electron opacity throughout the cytoplasm of reactive cells. The detection of small density increases of such a diffuse nature required an analytical method more sensitive and reliable than the visual examination of micrographs. A procedure was therefore devised for the evaluation of micrographs (negatives) with a densitometer (Weston Photographic Analyzer).

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Bulk standards for low-temperature biological x-ray microanalysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100111525 ◽

1984 ◽

Vol 42 ◽

pp. 282-283

Author(s):

P. Echlin ◽

M. McKoon ◽

E.S. Taylor ◽

C.E. Thomas ◽

K.L. Maloney ◽

...

Keyword(s):

Phase Separation ◽

Low Temperature ◽

Analytical Method ◽

Salt Solutions ◽

Absolute Concentration ◽

Cooling Process ◽

X Ray ◽

The Absolute ◽

Analytical Procedures ◽

Electrical Conductors

Although sections of frozen salt solutions have been used as standards for x-ray microanalysis, such solutions are less useful when analysed in the bulk form. They are poor thermal and electrical conductors and severe phase separation occurs during the cooling process. Following a suggestion by Whitecross et al we have made up a series of salt solutions containing a small amount of graphite to improve the sample conductivity. In addition, we have incorporated a polymer to ensure the formation of microcrystalline ice and a consequent homogenity of salt dispersion within the frozen matrix. The mixtures have been used to standardize the analytical procedures applied to frozen hydrated bulk specimens based on the peak/background analytical method and to measure the absolute concentration of elements in developing roots.

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The synephrine content of Shiikuwasha (Citrus depressa HAYATA) fruit: Analytical method and change during fruit growth

Planta Medica ◽

10.1055/s-0028-1084638 ◽

2008 ◽

Vol 74 (09) ◽

Author(s):

K Miyagi ◽

T Fujise ◽

N Koga ◽

K Wada ◽

M Yano ◽

...

Keyword(s):

Analytical Method ◽

Fruit Growth ◽

Citrus Depressa

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Guidelines for Analytical Method Selection & Appropriate Use when Determining Chemical Constituents in Dietary Supplements

Planta Medica ◽

10.1055/s-2008-1075164 ◽

2008 ◽

Vol 74 (03) ◽

Author(s):

PN Brown ◽

JM Betz

Keyword(s):

Dietary Supplements ◽

Analytical Method ◽

Chemical Constituents ◽

Appropriate Use ◽

Method Selection

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A novel analytical calculation of magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping

International Journal of Applied Electromagnetics and Mechanics ◽

10.3233/jae-201505 ◽

2020 ◽

pp. 1-15

Author(s):

Jianqi Li ◽

Yu Zhou ◽

Jianying Li

Keyword(s):

Magnetic Field ◽

Conformal Mapping ◽

Permanent Magnet ◽

Flux Density ◽

Analytical Method ◽

Electromotive Force ◽

Analytical Calculation ◽

Air Gap ◽

Permanent Magnet Machines ◽

Peak Value

This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.

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