Qualitative Methods for the Investigation of a Mathematical Model of Nonlinear Vibrations of a Conveyer Belt

A mathematical model is developed for the nonlinear vibrations of automatic reed valves in high-speed refrigeration compressors. Specifically considered are a general class of values which wrap about curved backer plates. Two simple experiments are described which allow the nonlinearities of the valve system to be defined by a single nonlinear second order differential equation. Valve oscillation frequencies inside an operating compressor are predicted through a linearization of the valve equation. Comparisons with experiment are included.

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Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

Symmetry ◽

10.3390/sym13020255 ◽

2021 ◽

Vol 13 (2) ◽

pp. 255

Author(s):

N. A. Saeed ◽

Emad Mahrous Awwad ◽

Talaat Abdelhamid ◽

Mohammed A. El-Meligy ◽

Mohamed Sharaf

Keyword(s):

Mathematical Model ◽

Natural Frequency ◽

Nonlinear Vibrations ◽

Excitation Frequency ◽

External Excitation ◽

Main System ◽

Positive Position Feedback ◽

Position Feedback ◽

Excitation Force ◽

External Excitation Frequency

The nonlinear vibration control of a nonlinear dynamical system modeled as the well-known Duffing oscillators is investigated within this article. The conventional Positive Position Feedback (PPF) controller is proposed to mitigate the considered system nonlinear vibrations. The whole system mathematical model is analyzed by applying the multiple time scales perturbation method. The slow-flow modulation equations that govern the oscillation amplitudes of both the main system and controller are derived. The stability analysis is investigated based on Lyapunov’s first method. The effects of the different control parameters on both the main system and controller are explored. The obtained analytical and numerical results illustrated that the PPF controller can eliminate the main system nonlinear vibrations once the controller natural frequency is tuned to be the same value as the external excitation frequency, otherwise, the controller adds excessive vibrational energy to the main system rather than suppressing it. In addition, the PPF controller can destabilize the main system motion when excited by strong excitation force. Therefore, a modified version of the PPF controller named the Adaptive Positive Position Feedback (APPF) controller is proposed to overcome the main drawbacks of the conventional PPF controller. The idea is to track the external excitation frequency using an adaptive frequency measurement technique to update continuously the PPF controller natural frequency to become the same value of the excitation frequency. Based on this strategy, the system mathematical model is analyzed again by making the controller’s natural frequency equal to the external excitation frequency. The obtained analytical and numerical simulations showed that the adaptive positive position feedback controller can suppress the main system nonlinear vibration close to zero regardless of the excitation force amplitude and excitation frequency.

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On an Non-Ideal Global and Local Energy Transfer, Using an Electro-Magneto and Magneto-Rheological Dampers

Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C ◽

10.1115/detc2009-86556 ◽

2009 ◽

Author(s):

Jose´ Manoel Balthazar ◽

Jorge L. F. Palacios

Keyword(s):

Mathematical Model ◽

Steady State ◽

Nonlinear Vibrations ◽

Resonance Condition ◽

Mr Damper ◽

Local Energy ◽

Sommerfeld Effect ◽

Large Amplitude Vibrations ◽

Magneto Rheological ◽

Global And Local

In this paper, we investigated the nonlinear vibrations of a Non-ideal (NIS) electromechanical absorber (NEVA), taking into account a modified mathematical model of (MR) Damper. We observed the presence of the Sommerfeld effect (it is the steady state frequencies of the DC motor, which it will usually increasing as more power (Voltage) is given to it, in a step-by-step fashion. When a resonance condition it is reached, the better part of this energy it is consumed to generate large amplitude vibrations of the foundation, without sensible change of the motor frequency). The obtained results, by using numerical and analytical simulations, were discussed, in details.

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MSEICR Fractional Order Mathematical Model of The Spread Hepatitis B

Jurnal Matematika Statistika dan Komputasi ◽

10.20956/jmsk.v17i2.10994 ◽

2020 ◽

Vol 17 (2) ◽

pp. 314-324

Author(s):

Suriani Suriani ◽

Syamsuddin Toaha ◽

Kasbawati Kasbawati

Keyword(s):

Mathematical Model ◽

Hepatitis B ◽

Qualitative Methods ◽

Numerical Simulations ◽

Equilibrium Point ◽

Fractional Order ◽

Jacobian Matrix ◽

Equilibrium Points ◽

Endemic Equilibrium ◽

Fractional Orders

This research aims to develop the MSEICR model by reviewing fractional orders on the spread of Hepatitis B by administering vaccinations and treatment, and analyzing fractional effects by numerical simulations of the MSEICR mathematical model using the method Grunwald Letnikov. Researchers use qualitative methods to achieve the object of research. The steps are to determine the MSEICR model by reviewing the fractional order, looking for endemic equilibrium points for each non-endemic and endemic equilibrium point, determining the equality of characteristics and eigenvalues of the Jacobian matrix. Next, look for values (Basic Reproductive Numbers), analyze stability around non-endemic and endemic equilibrium points and complete numerical simulations. From the simulation provided, it is known that by giving a fractional alpha value of and , the greater the value of the fractional order parameters used, the movement of the solution graphs is getting closer to the equilibrium point. If given and still endemic, whereas if and the value is increased to non-endemic, then the number of hepatitis B sufferers will disappear.

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Qualitative methods in nursing planning and structure of teaching units in nursing

Pflege ◽

10.1024/1012-5302.12.1.52 ◽

1999 ◽

Vol 12 (1) ◽

pp. 52-57

Author(s):

Tilmann Netz

Keyword(s):

Qualitative Methods

Um die direkte Pflege weiter zu professionalisieren, ist es notwendig, neue Lehrmethoden für Aus- und Fortbildung zu entwickeln. Werden qualitative Verfahren bei der Planung und Gestaltung von Lehreinheiten im Fachbereich Pflege favorisiert, so werden auch subjektive Theorien transparent, die das Pflegegeschehen unterschwellig beeinflussen. Ziel handlungsorientierter Unterrichtseinheiten im Fachbereich Pflege ist, diese gezielt im Sinne des neuen Pflegeparadigmas zu beeinflussen.

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