Method Of Complex Amplitudes Research Articles

Response analysis of undamped primary system subjected to base excitation with a dynamic vibration absorber integrated with a piezoelectric stack energy harvester

Dynamic vibration absorber (DVA) integrated with a piezoelectric stack energy harvesting subjected to base excitation is introduced in this paper. The system of dynamic vibration absorber and piezoelectric stack energy harvesting system (DVA-PSEH) has two functions, the first is to reduce vibrations for the primary system, and the second is to convert a part of the vibrational energy into electricity through the piezoelectric effect. The mechanical and electrical responses of the electromechanical system are determined by the complex amplitude method, then the numerical simulations are carried out to investigate the characteristics of DVA-PSEH.

Эффективный метод построения амплитудно-частотных характеристик оболочки

Timoshenko type equations are used, taking into account the transverse shift. The shell has the properties of constructive anisotropy. Forced oscillations in the frequency range, including the first significant low-frequency resonances, are considered. The internal scattering of vibrational energy is taken into account by the method of complex amplitudes. The influence of a number of parameters on the amplitude-frequency characteristics (frequency response) of input compliance is investigated. A semi-analytical method of constructing a solution is used. In the case of a cylindrical shell freely supported at the ends, Fourier series are used in two coordinates. The problem of forced oscillations is solved by decomposing the amplitudes of displacements according to their own forms of oscillations. At the same time, the separation of equations for determining coefficients by harmonic numbers is provided. The algorithm on this basis allows you to quickly build the amplitudefrequency characteristics necessary for analysis.

Application of resonance functions in estimating the parameters of interwell zones

It is shown that the use of force resonance leads to the effect of “shaking” the formation, followed by breaking up the film oil and involving it in the further filtration process. For the first time in oilfield geophysics, the concept of passive noise-metering method is justified for monitoring oil and gas deposit development by measuring the quality factor of the contours in the point areas of formation development channels in interwell zones. It is established that determining the depth of modulation for the reactive substitution parameter of the linear FDC chain is crucial not only for determining the parametric excitation in FDC attenuation systems, but also without attenuation in the metrological support for the analysis of petrophysical properties of rock samples from the wells. It is shown that based on the method of complex amplitudes (for formation pressure current, differential flow rates, impedance), different families of resonance curves can be plotted: displacement amplitudes (for differential flow rates on the piezocapacity of the studied formation section), velocities (amplitudes of formation pressure current) and accelerations (amplitudes of differential flow rates on the linear piezoinductivity of the FDC section). The use of predicted permeability and porosity properties of the reservoir with its continuous regulation leads to increased accuracy of isolation in each subsequent sub-cycle of new segment formation in the FDC trajectories, which contributes to a more complete development of productive hydrocarbon deposits and increases the reliability of prediction for development indicators.

Generalization of the Fourier Problem on Fluctuations in the Temperature of the Earth’s Crust

The problem of asymptotic fluctuations of temperature and moisture content in a half-space is solved by the method of complex amplitudes. The material filling the half-space consists of a solid base (capillary-porous body) and water. The well-known Fourier solution for temperature fluctuations in half-space in the absence of moisture and under the boundary conditions of heat exchange of the first kind is generalized to the case of a wet material under the boundary conditions of Newton for temperature and Dalton for moisture content. The results of the work can be used in geocryology to model seasonal fluctuations in the thermophysical characteristics of frozen rocks and soils.

Multi-parametric Dynamic Analysis of a Rolling Bearings System

A method for calculating amplitudes and constructing frequency characteristics of forced and self-excited vibrations of a rotor-fluid-foundation system on rolling bearings with a non-linear characteristic based on the method of complex amplitudes and harmonic balance has been developed. Non-linear equations of motion of the rotor-fluid-foundation system are derived, and analytical methods of their solution are presented. Frequencies of fundamental and ultra-harmonic resonances are determined. The intervals between self-oscillation frequencies are estimated. The dependence of amplitudes on the amount of fluid in the rotor cavity, the mass of the foundation, linear imbalance, the value of the stiffness coefficient, and the damping coefficient is shown.

Generalization of the Fourier problem of temperature waves in half-space

The problem of asymptotic fluctuations of temperature and moisture content in a half-space whose boundary is blown by an air flow with a temperature varying according to the harmonic law is solved by the method of complex amplitudes. The material filling the half-space consists of a solid base (capillary-porous body) and water. The well-known Fourier solution for temperature fluctuations in half-space in the absence of moisture and under the boundary conditions of heat exchange ofthefirst kind is generalized to the case of a wet material under the boundary conditions of Newton for temperature and Dalton for moisture content. The results of the work can be used in geocryology to model seasonal changes in the thermophysical state offrozen rocks and soils, in the theory of building structures to study the thermal regime of indoor premises with fluctuations in ambient temperature, in the theory of drying by electromagnetic radiation to study the processes of heat and mass transfer inoscillating modes.

Dynamic Vibration Extinguished on a Viscously Elastic Base

The aim of the work is to develop algorithms and a set of programs for studying the dynamic characteristics of viscoelastic thin plates on a deformable base on which it is installed with several dynamic dampers. The theory of thin plates is used to obtain the equation of motion for the plate. The relationship between the efforts and the stirred plate obeys in the hereditary Boltzmann Voltaire integral. With this, a system of integro-differential equations is obtained which is solved by the method of complex amplitudes. As a result, a transcendental algebraic equation was obtained to determine the resonance frequencies, which is solved numerically by the Muller method. To determine the displacement of the point of the plate with periodic oscillations of the base of the plate, a linear inhomogeneous algebraic equation was obtained, which is solved by the Gauss method. The amplitude - frequency response of the midpoint of the plate is constructed with and without regard to the viscosity of the deformed element. The dependence of the stiffness of a deformed element on the frequency of external action is obtained to ensure optimal damping of vibrational vibrations of the plate.

Nonlinear distortion of angle modulation signal in output power amplifiers

The output power amplifier is operated in nonlinear mode to increase its efficiency, at which the signal is distorted more. The goal is to analyze effects of nonlinearity on the modulating signal of angle-modulated signal distortions for single-ended and push-pull output power amplifiers with memory and without it. The amplifier characteristic ic(vBE) is preset by the cubic polynomial. The output voltage of memoryless amplifier uout(t) is found by Ohm's law. And in case with amplifier with memory, the output voltage uout(t) is found by Complex amplitude method with a Fourier series of function ic(t). The output voltage uout(t) is represented as the narrowband process with envelope of the waveform U1(t) and initial phase Ф1(t) to determine the angular modulation law Ф1(t) at the amplifier output. The function U1(t) is defined as combination of in-phase А(t) and quadrature В(t) components. The distortion estimate based on Total Harmonic Distortion (THD). The measurement of THD is defined as the ratio of the RMS amplitude of a set of higher harmonic frequencies to the RMS amplitude of the first harmonic. The spectrum of function Ф1(t) is represented a Fourier series. In single-ended memoryless amplifier and non-cutoff mode, the THD decreases as m increases and THD of modulating signal is {37.6; 18.8; 6.3%} at m {0.5; 1; 3}. In cutoff mode, the smallest THD is {15.18; 5.13%} at m {1; 3} as θ = 140o. In push-pull memoryless amplifier and θ = 90o, the THD is {22.2; 11.1; 3.7%} at m {0.5; 1; 3} which is 1.7 times less than in a single-ended amplifier without cutoff. This is due to compensation even-order harmonic of amplified signal at the output of a pushpull amplifier. In this case of memoryless amplifier, the transistor load is a parallel RLC circuit. The distortion decreases under m increases at first (up m is 1.5), but then rapidly increases (from m is 1.7). This is due to increase of the parasitic harmonics level caused by the nonlinearity of the phase-frequency characteristic of RLC circuit. The calculations show that THD of modulating signal is 3.35, 9.02 and 22.88 % at Q = 10 and m {0.5; 1; 3}, respectively. In cutoff mode, the smallest THD is at θ = 90o and it does not depend on θ at large values of m. In push-pull amplifier with memory, the THD is 2.8, 2.5 and 3.0 times less than for a singleended amplifier without cutoff at Q {2.5; 5; 10}, respectively. The results of this paper can be used for the design of signal processing systems.

Analysis of the electrodynamic model of a biologically active point of animal skin

Flat-layered dielectric structure was considered as an electrodynamic model of bioactive point (BAP). This structure is formed by three flat dielectric layers and eventual cylinder filled by a dielectric (by the albumen of collagen). The upper layer designs burly cages, middle layer is blood and lymphatic vessels and an understratum is formed by nervous fibres that conduct and pass management signals from BAP to the central nervous system.Such electrodynamic structure is the dielectric resonator (eventual cylinder) located in a dielectric environment.We will examine affecting of informative electromagnetic radiation on bioactive point, the wave-length of which considerably excels geometrical sizes bioactive point. This fact allows averaging of material parameters on a coordinate . Therefore, it was assumed further, that material parameters (dielectric constant) of flat layered structure (model of bioactive point) does not depend on a coordinate , i.e. the electromagnetic field is axisymmetric.Such electromagnetic field can be excited by the circular electric current located at some distance from the external surface of bioactive point. It was supposed that this current excited harmonic oscillation with circular frequency and modulated on amplitude with frequency of modulation .The problem of the interaction of radio-pulse waves with a biologically active point is an unsteady diffraction problem. Using the complex amplitude method, this problem was reduced to the diffraction problem for electromagnetic fields that depend exponentially on time.By virtue of the principle of superposition, the solution to the original problem can be obtained as a superposition of the solutions of three problems using the complex amplitude method.Such electrodynamic structure allows defining the necessary parameters of the informative electromagnetic field for treatment of dyspepsia of newborn calves.

Existence et stabilité de solutions périodiques pour des équations différentielles quasi-linéaires d'ordre n

We study the existence and stability of periodic solutions of quasi-linear n-th order differential equations by a method closely related to that of Cesari-Hale. When the method is applied to quasi-linear n-th order equations not in matrix form it is possible to use certain classical methods in the theory of linear differential equations, particularly the method of complex amplitudes (or the method of impedances) and the development into Fourier series.