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1
Content available remote Resonance phenomena in micro/nanoelectromechanical systems
Foryś A., Foryś A. S.
Czasopismo Techniczne. Nauki Podstawowe
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2013
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R. 110, z. 1-NP
3--10
EN
In the paper, some aspects of nonlinearity of micro/nanoelectromechanical systems (MEMS/ NEMS) are presented. Because of great values of strains of micro/nanobeams the nonlinear description is necessary. Particularly, the nonlinear inertia term is added to equation relating to motion of the beam. Numerical calculations of resonance curves and instability regions are given. Results are presented on graphs.
PL
W artykule przedstawiono pewne aspekty nieliniowości w mikro/nanoukładach elektromechanicznych (MEMS/NEMS). Ze względu na duże odkształcenia mikro/nanobelek nieliniowy opis jest konieczny. W szczególności do równania ruchu belki wprowadzono wyraz opisujący nieliniową bezwładność. Podano wyniki obliczeń numerycznych dla krzywych rezonansowych oraz obszarów niestateczności. Rezultaty przedstawiono na wykresach.
2
Content available remote Analiza układów nanomechanicznych w stanach rezonansowych ze względu na stateczność
Foryś A., Foryś A.
Czasopismo Techniczne. Nauki Podstawowe
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2011
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R. 108, z. 1-NP
95-102
PL
Nanoukłady elektromechaniczne (NEMS) znajdują zastosowanie w różnego rodzaju detektorach i czujnikach. Często wykorzystuje się przejście tych układów od drgań stabilnych do niestabilnych. Tematem pracy jest analiza stabilności dwu nieliniowych nanoukładów elektromechanicznych. Obszary niestateczności są przedstawione na wykresach.
EN
Nano-electro-mechanical systems (NEMS) are applicable to various detectors and sensors. Transition between stable and unstable vibrations of these systems is frequently used. Analysis of stability of two nonlinear nanosystems is the subject of the paper. Instability regions are presented on graphs.
3
Content available remote Three-parameter optimization of an axially loaded beam on a foundation
Foryś A. S., Foryś A.
Engineering Transactions
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2007
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Vol. 55, iss. 2
101-113
EN
A beam of circular cross-section, made of viscoelastic material of Kelvin-Voigt type, is considered. The beam is symmetric with respect to its center, the length and volume of the beam are fixed and its ends are simply supported. The radius of the cross-section is a cubic function of co-ordinate. The beam interacts with a foundation of Winkler, Pasternak or Hetknyi a, type and is axially loaded by a non-conservative force P(t) = PO + PI cos vt. Only the first instability region is taken into account. The shape of the beam is optimal if the critical value of P1 is maximal. A few numerical examples are presented on graphs.
4
Content available remote Analysis and optimization of a nonlinear, continuous, autoparametric system
Foryś A., Foryś A. S.
Engineering Transactions
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2002
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Vol.50, iss.4
233-249
EN
In the present paper a transversely vibrating autoparametric system consisting of three non-prismatic rods is presented. The considerations refer especially to stability of the semi-trivial solution. Proper selection of the values of parameters may lead to considerable reduction of the autoparametric resonance effects or may shift the autoparametric resonance to another frequency region.
5
Content available remote Objective functions in monocriterial and multicriterial optimizations problems against a loss of dynamic stability
Foryś A., Snamina J.
Engineering Transactions
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2000
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Vol. 48, iss. 1
73-94
EN
The paper concerns the specification and comparison of numerical examples of optimization of beams in the state periodic parametric resonance with respect to different measures of the phenomena considered, i.e., with respects to different optimization criteria - some objective functions in monocriterion and multicriterial optimization. A formulation of monocriterion and multicriterial optimization problems. for mechanical elements, subjected to paramatricallyexciting force periodic in time, is given. In multicriterial optimization the scalar objective functions characterizing the parametric resonance are introduced. The paper deals with the problems of finding the control function - function of the shape (the area of cross-section of the beam) which maximizes or minimizes the objective functions under the constraint of constant volume. In some cases the optimization problems under conditions of parametric resonance reduce to the optimization problems with respect to natural frequency. The examples of parametric optimization against loss of stability are solved and analysed.
6
Content available remote Charitonov theorem and stability of paramatrically excited systems
Foryś A., Kowynia J.
Engineering Transactions
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2000
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Vol. 48, iss. 2
99-118
EN
The present paper concerns the application of the Charitonov theorem to an analysis of stability of parametrically excited mechanical or physical systems with intervally changing parameters of systems. In such systems the problems of stable solutions of the equation of motion also arise. In some methods the stability analysis of the parametrically excited systems with intervally changing parameters transformes into the analysis of stability of some n-th degree interval polynomials. On the basis of ChT we can check that the solution is stable in the whole interval of changing parameters, without constructing of the boundary of instability regions. Examples of application of the ChT to the analysis of stability of some special systems in steady states of the periodic parametric resonance are considered.
7
Optimization problem against a loss of dynamic stability of macroscopic particles in a "Paul trap"
Foryś A.
Journal of Technical Physics
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1999
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Vol. 40, no 2
235-246
EN
The Mathieu-Hill differential equation is often encountered in engineering and physical problems (1-6). The stability of periodic response of vibrating non-linear systems can be also examined by means of the variational Mathieu-Hill equation. Therefore the problems of optimization of parametrically excited systems described by Mathieu-Hill equation against a loss of stability are important. In this paper an optimization problem for particles in traps, subjected to a parametric excitation in electrical field, periodic in time, is considered. Objective functions characterizing the parametric resonance are introduced. The paper deals with the problem of finding the control parameters, the parameters of particle and surroundings, which maximize one of the objective functions under some constraint.
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