Mathematical models of resonance and antiresonance processes

2021 ◽  
pp. 17-27
Author(s):  
V. D. Pavlov ◽  
Keyword(s):  
Current Source ◽  
Voltage Source ◽  
Complex Method ◽  
Connecting Rod ◽  
Parallel Connection ◽  
Near Resonance ◽  
Serial Connection ◽  
Mechanical Analogue ◽  
In Series ◽  
Pneumatic Cylinders

The use of the symbolic (complex) method has significantly simplified the study of resonance and near-resonance phenomena, in particular, it has made it possible to deeply unify and formalize the consideration of various mechanical systems. The cumbersome and time-consuming operations associated with composing and solving differential equations have been replaced by simple algebraic transformations. The method is based on the mechanical analogue of Ohm’s law in a complex representation and the concept of mechanical reactance, resistance, impedance, susseptance, conductance and admittance. Resonances and antiresonances of forces and velocities are determined. Resonances occur when the elements are connected in parallel with a force source, or when the elements are connected in series with a velocity source. Antiresonances occur when a parallel connection and a speed source are combined, or a serial connection and a force source are combined. These concepts are a generalization to mechanics of the concepts of «voltage source» and «current source» from theoretical electrical engineering. The closest to the source of speed in its properties is a crank-rocker (connecting rod) mechanism with a massive flywheel. The source of force corresponds more to the rod of the significantly smaller of the two connected pneumatic cylinders.

Anti-Resonance — Velocity Resonance

2019 ◽  
Vol 20 (6) ◽  
pp. 362-366
Author(s):  
I. P. Popov
Keyword(s):  
Mechanical System ◽  
Elastic Element ◽  
Electrical Engineering ◽  
Current Source ◽  
Mechanical Power ◽  
Voltage Source ◽  
Mechanical Resonance ◽  
Parallel Connection ◽  
In Series ◽  
Inert Body

The task of the study is to establish the nature of mechanical resonance, namely, it is a resonance of forces or speeds. Two definitions are introduced. Definition 1. Resonance of forces is a resonance arising at a frequency ω = (k/m)0,5 in a mechanical system including an inert body and an elastic element, at which the reactive forces developed by them are maximal and opposite. Definition 2. The velocity resonance is a resonance arising at a frequency ω = (k/m)0,5 in a mechanical system, including an inert body and an elastic element, at which the speeds developed by them are maximum and opposite. The equation of forced mechanical oscillations corresponds to a parallel connection scheme, in which the inert body and changes in the dimensions of the elastic element and damper have a uniform speed, and their reactive forces are added. The sum of the reactive forces of the consumers of mechanical power is equal to the force developed by the source of mechanical power, which, like a voltage source in electrical engineering, can be called a source of power. Theorem 1 holds. If the condition ω = (k/m)0,5 is satisfied in a mechanical system consisting of parallel-connected inert bodies, an elastic element and a damper, a resonance of forces occurs. The inert body, the elastic element and the damper can be connected not only in parallel but also in series. With a series connection, a single force is applied to the elements of the system, and the velocities of the inert body and the changes in the dimensions of the elastic element and damper are added. The sum of the speeds of consumers of mechanical power is equal to the speed developed by the source of mechanical power, which, like a current source in electrical engineering, can be called a source of speed. Theorem 2 is valid. Under the condition ω = (k/m)0,5 in a mechanical system consisting of a series-connected inert body, an elastic element and a damper, a velocity resonance occurs. The mechanical resonance described in the courses of theoretical mechanics is the resonance of forces. It corresponds to a parallel connection of an inert body, an elastic element and a damper. When these elements are connected in series, a velocity resonance occurs.

Design and Simulation of LED Drive Power Supply Based on ARM

2012 ◽  
Vol 588-589 ◽  
pp. 936-939
Author(s):  
Hong Li Cheng ◽  
Xiao Dan Ren ◽  
Shuai Sun
Keyword(s):  
Power Supply ◽  
High Efficiency ◽  
Current Source ◽  
Constant Current ◽  
Voltage Source ◽  
Drive Power ◽  
Small Current ◽  
Constant Current Source ◽  
Pid Algorithm ◽  
In Series

This paper introduces a kind of numerical controlled LED drive power supply based on ARM7. User can set the number and brightness of the LEDs to be lit by the remote control. Switching voltage source and the linear constant current source are connected in series, this circuit structure can ensure high efficiency and small current ripple. ARM7 completes the data collection, fuzzy PID algorithm processing, and real-time output adjustment. This paper explains the working principle of the system in detail and then simulates it in the simulink. The results show that it can satisfy the users' diverse requirements well and give full play to the convenience and controllability of the digital controller.

scholarly journals Modeling Battery Connections in the Electronic Lab

2021 ◽  
Vol 64 (5) ◽  
pp. 381-392
Author(s):  
K. V. Dobrego ◽  
Y. V. Bladyko
Keyword(s):  
Time Intervals ◽  
Parallel Connection ◽  
Charge Voltage ◽  
Timing Diagrams ◽  
Cyclic Operation ◽  
Serial Connection ◽  
Wide Range ◽  
In Series ◽  
Battery Degradation ◽  
Parallel Series

The paper deals with the modeling of the processes of charge-discharge of battery assemblies taking into account their degradation. The results of simulating the cyclic operation of battery assemblies in the Electronics Workbench electronic laboratory are presented, possible schemes of inclusion are given, and options for re-switching batteries during operation are considered as well as connecting additional elements to extend the life of the connection. The simulation took into account the presence of one defective battery in the assembly. The operation of the assembly with a defective battery and a reference battery was compared. As a result of the analysis of parallel-serial and serial-parallel battery connections, the first one is considered preferable. For an assembly with a parallel-serial connection, the time parameters of operation remained almost unchanged, but the differences in the voltages of the defective and other batteries changed more than twice as compared with a serial-parallel connection. The changes in charge, voltage and current of assemblies with a degraded battery and a reference battery are analyzed. Timing diagrams are shown for batteries connected in parallel and in series with defective batteries. Power losses in a defective battery are reduced by choosing a parallel-series assembly, while switching a connection from a serial-parallel connection to a parallel-series one does not lead to compensation for the degradation of battery parameters. Changing the switching time intervals in a wide range does not contribute to increasing the capacity of a defective battery. Degradation of battery parameters leads to sharper surges in voltage, charge and current. The additional power recharge of the defective battery maintains the performance of the entire assembly. Recharge can be performed by connecting in parallel a defective additional battery or a capacitor, which is equivalent to replacing a degraded battery with a new one.

KANTHAL 70

Alloy Digest ◽  
1981 ◽  
Vol 30 (9) ◽  
Keyword(s):  
Operating Temperature ◽  
Heat Treating ◽  
Positive Temperature Coefficient ◽  
Pure Nickel ◽  
Voltage Source ◽  
Voltage Regulator ◽  
Positive Temperature ◽  
Automotive Applications ◽  
Resistance Thermometers ◽  
In Series

Abstract KANTHAL 70 alloy was designed to provide a high positive temperature coefficient to electrical resistance comparable with that of pure nickel; however, it has much higher electrical resistivity than pure nickel. This makes it useful as a voltage regulator when placed in series with another electrical device across a fluctuating voltage source. Kanthal 70 has a maximum recommended operating temperature of 600 C and is used widely in resistance thermometers and in various appliance and automotive applications. This datasheet provides information on composition, physical properties, and tensile properties. It also includes information on corrosion resistance as well as forming, heat treating, and joining. Filing Code: Ni-270. Producer or source: The Kanthal Corporation.

scholarly journals Flyback Converter for Solid-State Lighting Applications with Partial Energy Processing

Electronics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 60
Author(s):  
Mario Ponce-Silva ◽  
Daniel Salazar-Pérez ◽  
Oscar Miguel Rodríguez-Benítez ◽  
Luis Gerardo Vela-Valdés ◽  
Abraham Claudio-Sánchez ◽  
...  
Keyword(s):  
Solid State ◽  
Power Supply ◽  
Design Methodology ◽  
Low Frequency ◽  
Solid State Lighting ◽  
Voltage Source ◽  
Flyback Converter ◽  
Partial Energy ◽  
In Series ◽  
Energy Processing

The main contribution of this paper is to show a new AC/DC converter based on the rearrangement of the flyback converter. The proposed circuit only manages part of the energy and the rest is delivered directly from the source to the load. Therefore, with the new topology, the efficiency is increased, and the stress of the components is reduced. The rearrangement consist of the secondary of the flyback is placed in parallel with the load, and this arrangement is connected in series with the primary side and the rectified voltage source. The re-arranged flyback is only a reductive topology and with no magnetic isolation. It was studied as a power supply for LEDs. A low frequency averaged analysis (LFAA) was used to determine the behavior of the proposed circuit and an equivalent circuit much easier to analyze was obtained. To validate the theoretical analysis, a design methodology was developed for the re-arranged flyback converter. The designed circuit was implemented in a 10 W prototype. Experimental results showed that the converter has a THDi = 21.7% and a PF = 0.9686.

scholarly journals Contribution of Voltage Support Function to Virtual Inertia Control Performance of Inverter-Based Resource in Frequency Stability

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4220
Author(s):  
Dai Orihara ◽  
Hiroshi Kikusato ◽  
Jun Hashimoto ◽  
Kenji Otani ◽  
Takahiro Takamatsu ◽  
...  
Keyword(s):  
Reactive Power ◽  
Control Function ◽  
Current Source ◽  
Voltage Control ◽  
Frequency Stability ◽  
Voltage Regulation ◽  
System Stability ◽  
Voltage Source ◽  
Apparent Difference ◽  
Virtual Inertia

Inertia reduction due to inverter-based resource (IBR) penetration deteriorates power system stability, which can be addressed using virtual inertia (VI) control. There are two types of implementation methods for VI control: grid-following (GFL) and grid-forming (GFM). There is an apparent difference among them for the voltage regulation capability, because the GFM controls IBR to act as a voltage source and GFL controls it to act as a current source. The difference affects the performance of the VI control function, because stable voltage conditions help the inertial response to contribute to system stability. However, GFL can provide the voltage control function with reactive power controllability, and it can be activated simultaneously with the VI control function. This study analyzes the performance of GFL-type VI control with a voltage control function for frequency stability improvement. The results show that the voltage control function decreases the voltage variation caused by the fault, improving the responsivity of the VI function. In addition, it is found that the voltage control is effective in suppressing the power swing among synchronous generators. The clarification of the contribution of the voltage control function to the performance of the VI control is novelty of this paper.

scholarly journals Design and Analysis of a Novel Piezoceramic Stack-based Smart Aggregate

Sensors ◽  
2020 ◽  
Vol 20 (22) ◽  
pp. 6438
Author(s):  
Guangtao Lu ◽  
Xin Zhu ◽  
Tao Wang ◽  
Zhiqiang Hao ◽  
Bohai Tan
Keyword(s):  
Resonance Frequency ◽  
Electromechanical Coupling ◽  
Structural Parameters ◽  
Electromechanical Coupling Factor ◽  
Coupling Factor ◽  
Stress Waves ◽  
Parallel Connection ◽  
Smart Aggregate ◽  
In Series ◽  
Piezoelectric Wafers

A novel piezoceramic stack-based smart aggregate (PiSSA) with piezoceramic wafers in series or parallel connection is developed to increase the efficiency and output performance over the conventional smart aggregate with only one piezoelectric patch. Due to the improvement, PiSSA is suitable for situations where the stress waves easily attenuate. In PiSSA, the piezoelectric wafers are electrically connected in series or parallel, and three types of piezoelectric wafers with different electrode patterns are designed for easy connection. Based on the theory of piezo-elasticity, a simplified one-dimensional model is derived to study the electromechanical, transmitting and sensing performance of PiSSAs with the wafers in series and parallel connection, and the model was verified by experiments. The theoretical results reveal that the first resonance frequency of PiSSAs in series and parallel decreases as the number or thickness of the PZT wafers increases, and the first electromechanical coupling factor increases firstly and then decrease gradually as the number or thickness increases. The results also show that both the first resonance frequency and the first electromechanical coupling factor of PiSSA in series and parallel change no more than 0.87% as the Young’s modulus of the epoxy increases from 0.5 to 1.5 times 3.2 GPa, which is helpful for the fabrication of PiSSAs. In addition, the displacement output of PiSSAs in parallel is about 2.18–22.49 times that in series at 1–50 kHz, while the voltage output of PiSSAs in parallel is much less than that in parallel, which indicates that PiSSA in parallel is much more suitable for working as an actuator to excite stress waves and PiSSA in series is suitable for working as a sensor to detect the waves. All the results demonstrate that the connecting type, number and thickness of the PZT wafers should be carefully selected to increase the efficiency and output of PiSSA actuators and sensors. This study contributes to providing a method to investigate the characteristics and optimize the structural parameters of the proposed PiSSAs.

scholarly journals Bandwidth and Common Mode Optimization for Current and Voltage Sources in Bioimpedance Spectroscopy

2021 ◽  
Vol 12 (1) ◽  
pp. 135-146
Author(s):  
Tobias Menden ◽  
Jascha Matuszczyk ◽  
Steffen Leonhardt ◽  
Marian Walter
Keyword(s):  
Patient Safety ◽  
Current Source ◽  
The Body ◽  
Voltage Source ◽  
Bioimpedance Spectroscopy ◽  
Laboratory Measurements ◽  
Output Impedance ◽  
Frequency Range ◽  
Common Mode ◽  
High Bandwidth

Abstract Bioimpedance measurements use current or voltage sources to inject an excitation signal into the body. These sources require a high bandwidth, typically from 1 kHz to 1 MHz. Besides a low common mode, current limitation is necessary for patient safety. In this paper, we compare a symmetric enhanced Howland current source (EHCS) and a symmetric voltage source (VS) based on a non-inverting amplifier between 1 kHz and 1 MHz. A common mode reduction circuit has been implemented in both sources. The bandwidth of each source was optimized in simulations and achieved a stable output impedance over the whole frequency range. In laboratory measurements, the output impedance of the EHCS had its -3 dB point at 400 kHz. In contrast, the VS reached the +3 dB point at 600 kHz. On average over the observed frequency range, the active common mode compensation achieved a common mode rejection of -57.7 dB and -71.8 dB for the EHCS and VS, respectively. Our modifications to classical EHCS and VS circuits achieved a low common mode signal between 1 kHz and 1 MHz without the addition of complex circuitry, like general impedance converters. As a conclusion we found VSs to be superior to EHCSs for bioimpedance spectroscopy due to the higher bandwidth performance. However, this only applies if the injected current of the VS can be measured.

Sign in / Sign up

Export Citation Format

Share Document