Mathematical Model of Multi-Frequency Piezoresonance Oscillation System

Alexander A. Zelensky; Sergey K. Pidchenko; Alla A. Taranchuk

doi:doi:10.11648/j.com.20130101.11

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Mathematical Model of Multi-Frequency Piezoresonance Oscillation System

Alexander A. Zelensky, Sergey K. Pidchenko, Alla A. Taranchuk

Published in Communications (Volume 1, Issue 1)

Received: 24 December 2012 Accepted: Published: 10 January 2013

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Abstract

The paper represents the basic model of multi-frequency piezoresonance oscillation system (MPOS) – the piezoresonance devices (PRD) core, which enables to study the processes of establishing multi-frequency oscillation mode and its stability. The basic structure of multi-channel multi-frequency PRD core, which is based on principles of filter schemes, is proposed, and the main designations are entered. The peculiarities of truncated differential equations for amplitude, phase and auto-bias voltage of MPOS for the quantity of simultaneously generated frequencies are examined. On the example of three-frequency mode of oscillation under polynomial approximation of transferable characteristics of active elements the characteristic cases of establishing oscillations in MPOS are represented. The area of a steady three-frequency oscillating behavior is defined and the assessment of time of establishment of oscillations and value of group runout of frequencies is made. Received results enable to form a new approach to construction of piezoresonance devices with controlled dynamics, which are represented in the form of adaptive controlled systems with predictive standard model and develop on its basis the new class of invariant to destabilizing disturbing PRD factors. On the basis of such approach there is the principle of using natural redundancy in multi-frequency basis of PRD core – multi-frequency oscillation system, which enables not only to synthesize the system with current identification of disturbing factors on basis of instruments of invariance theory, but also do the adaptation of PRD in accordance with their influences.

Published in	Communications (Volume 1, Issue 1)
DOI	10.11648/j.com.20130101.11
Page(s)	1-8
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Stabilization of Oscillations, Multi-Frequency Quartz Oscillatory System, Invariant Piezoresonance System

References

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APA Style

Alexander A. Zelensky, Sergey K. Pidchenko, Alla A. Taranchuk. (2013). Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications, 1(1), 1-8. https://doi.org/10.11648/j.com.20130101.11

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ACS Style

Alexander A. Zelensky; Sergey K. Pidchenko; Alla A. Taranchuk. Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications. 2013, 1(1), 1-8. doi: 10.11648/j.com.20130101.11

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AMA Style

Alexander A. Zelensky, Sergey K. Pidchenko, Alla A. Taranchuk. Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications. 2013;1(1):1-8. doi: 10.11648/j.com.20130101.11

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@article{10.11648/j.com.20130101.11,
  author = {Alexander A. Zelensky and Sergey K. Pidchenko and Alla A. Taranchuk},
  title = {Mathematical Model of Multi-Frequency Piezoresonance Oscillation System},
  journal = {Communications},
  volume = {1},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.com.20130101.11},
  url = {https://doi.org/10.11648/j.com.20130101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.com.20130101.11},
  abstract = {The paper represents the basic model of multi-frequency piezoresonance oscillation system (MPOS) – the piezoresonance devices (PRD) core, which enables to study the processes of establishing multi-frequency oscillation mode and its stability. The basic structure of multi-channel multi-frequency PRD core, which is based on principles of filter schemes, is proposed, and the main designations are entered. The peculiarities of truncated differential equations for amplitude, phase and auto-bias voltage of MPOS for the quantity of simultaneously generated frequencies   are examined. On the example of three-frequency mode of oscillation under polynomial approximation of transferable characteristics of active elements the characteristic cases of establishing oscillations in MPOS are represented. The area of a steady three-frequency oscillating behavior is defined and the assessment of time of establishment of oscillations and value of group runout of frequencies is made. Received results enable to form a new approach to construction of piezoresonance devices  with controlled dynamics, which are represented in the form of adaptive controlled systems with predictive standard model and develop on its basis the new class of invariant to destabilizing disturbing PRD factors. On the basis of such approach there is the principle of using natural redundancy in multi-frequency basis of PRD core – multi-frequency oscillation system, which enables not only to synthesize the system with current identification of disturbing factors on basis of instruments of invariance theory, but also do the adaptation of PRD in accordance with their influences.},
 year = {2013}
}

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TY  - JOUR
T1  - Mathematical Model of Multi-Frequency Piezoresonance Oscillation System
AU  - Alexander A. Zelensky
AU  - Sergey K. Pidchenko
AU  - Alla A. Taranchuk
Y1  - 2013/01/10
PY  - 2013
N1  - https://doi.org/10.11648/j.com.20130101.11
DO  - 10.11648/j.com.20130101.11
T2  - Communications
JF  - Communications
JO  - Communications
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2328-5923
UR  - https://doi.org/10.11648/j.com.20130101.11
AB  - The paper represents the basic model of multi-frequency piezoresonance oscillation system (MPOS) – the piezoresonance devices (PRD) core, which enables to study the processes of establishing multi-frequency oscillation mode and its stability. The basic structure of multi-channel multi-frequency PRD core, which is based on principles of filter schemes, is proposed, and the main designations are entered. The peculiarities of truncated differential equations for amplitude, phase and auto-bias voltage of MPOS for the quantity of simultaneously generated frequencies   are examined. On the example of three-frequency mode of oscillation under polynomial approximation of transferable characteristics of active elements the characteristic cases of establishing oscillations in MPOS are represented. The area of a steady three-frequency oscillating behavior is defined and the assessment of time of establishment of oscillations and value of group runout of frequencies is made. Received results enable to form a new approach to construction of piezoresonance devices  with controlled dynamics, which are represented in the form of adaptive controlled systems with predictive standard model and develop on its basis the new class of invariant to destabilizing disturbing PRD factors. On the basis of such approach there is the principle of using natural redundancy in multi-frequency basis of PRD core – multi-frequency oscillation system, which enables not only to synthesize the system with current identification of disturbing factors on basis of instruments of invariance theory, but also do the adaptation of PRD in accordance with their influences.
VL  - 1
IS  - 1
ER  -

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Author Information

Alexander A. Zelensky

N.E. Zhukovsky National Aerospace University ?KhAI?, Kharkov, Ukraine
Sergey K. Pidchenko

Khmelnitskiy National University, Khmelnitskiy, Ukraine
Alla A. Taranchuk

Khmelnitskiy National University, Khmelnitskiy, Ukraine

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APA Style

Alexander A. Zelensky, Sergey K. Pidchenko, Alla A. Taranchuk. (2013). Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications, 1(1), 1-8. https://doi.org/10.11648/j.com.20130101.11

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ACS Style

Alexander A. Zelensky; Sergey K. Pidchenko; Alla A. Taranchuk. Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications. 2013, 1(1), 1-8. doi: 10.11648/j.com.20130101.11

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AMA Style

Alexander A. Zelensky, Sergey K. Pidchenko, Alla A. Taranchuk. Mathematical Model of Multi-Frequency Piezoresonance Oscillation System. Communications. 2013;1(1):1-8. doi: 10.11648/j.com.20130101.11

Copy | Download

@article{10.11648/j.com.20130101.11,
  author = {Alexander A. Zelensky and Sergey K. Pidchenko and Alla A. Taranchuk},
  title = {Mathematical Model of Multi-Frequency Piezoresonance Oscillation System},
  journal = {Communications},
  volume = {1},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.com.20130101.11},
  url = {https://doi.org/10.11648/j.com.20130101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.com.20130101.11},
  abstract = {The paper represents the basic model of multi-frequency piezoresonance oscillation system (MPOS) – the piezoresonance devices (PRD) core, which enables to study the processes of establishing multi-frequency oscillation mode and its stability. The basic structure of multi-channel multi-frequency PRD core, which is based on principles of filter schemes, is proposed, and the main designations are entered. The peculiarities of truncated differential equations for amplitude, phase and auto-bias voltage of MPOS for the quantity of simultaneously generated frequencies   are examined. On the example of three-frequency mode of oscillation under polynomial approximation of transferable characteristics of active elements the characteristic cases of establishing oscillations in MPOS are represented. The area of a steady three-frequency oscillating behavior is defined and the assessment of time of establishment of oscillations and value of group runout of frequencies is made. Received results enable to form a new approach to construction of piezoresonance devices  with controlled dynamics, which are represented in the form of adaptive controlled systems with predictive standard model and develop on its basis the new class of invariant to destabilizing disturbing PRD factors. On the basis of such approach there is the principle of using natural redundancy in multi-frequency basis of PRD core – multi-frequency oscillation system, which enables not only to synthesize the system with current identification of disturbing factors on basis of instruments of invariance theory, but also do the adaptation of PRD in accordance with their influences.},
 year = {2013}
}

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TY  - JOUR
T1  - Mathematical Model of Multi-Frequency Piezoresonance Oscillation System
AU  - Alexander A. Zelensky
AU  - Sergey K. Pidchenko
AU  - Alla A. Taranchuk
Y1  - 2013/01/10
PY  - 2013
N1  - https://doi.org/10.11648/j.com.20130101.11
DO  - 10.11648/j.com.20130101.11
T2  - Communications
JF  - Communications
JO  - Communications
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2328-5923
UR  - https://doi.org/10.11648/j.com.20130101.11
AB  - The paper represents the basic model of multi-frequency piezoresonance oscillation system (MPOS) – the piezoresonance devices (PRD) core, which enables to study the processes of establishing multi-frequency oscillation mode and its stability. The basic structure of multi-channel multi-frequency PRD core, which is based on principles of filter schemes, is proposed, and the main designations are entered. The peculiarities of truncated differential equations for amplitude, phase and auto-bias voltage of MPOS for the quantity of simultaneously generated frequencies   are examined. On the example of three-frequency mode of oscillation under polynomial approximation of transferable characteristics of active elements the characteristic cases of establishing oscillations in MPOS are represented. The area of a steady three-frequency oscillating behavior is defined and the assessment of time of establishment of oscillations and value of group runout of frequencies is made. Received results enable to form a new approach to construction of piezoresonance devices  with controlled dynamics, which are represented in the form of adaptive controlled systems with predictive standard model and develop on its basis the new class of invariant to destabilizing disturbing PRD factors. On the basis of such approach there is the principle of using natural redundancy in multi-frequency basis of PRD core – multi-frequency oscillation system, which enables not only to synthesize the system with current identification of disturbing factors on basis of instruments of invariance theory, but also do the adaptation of PRD in accordance with their influences.
VL  - 1
IS  - 1
ER  -

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