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Oscillators: Phenomenological mappings and analogies: Second part: Structural analogy and chains

Oscillateurs: Correspondance phénoménologiques et analogies: Deuxieme partie: Analogie structurale et les chaînes

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2015
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Authors
Hedrih-Stevanović, Katica
Ivanović-Šašić, Ana
Simonović, Julijana
Kolar-Anić, Ljiljana
Čupić, Željko
Article (Published version)
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Abstract
New analytical and numerical results of dynamics for both linear and nonlinear system with two degrees of freedom are presented. For the mechanical chain system with two degrees of freedom, oscillations are investigated analytically and numerically with corresponding comparison between free and forced oscillatory dynamics of linear and nonlinear system. Using the Mihailo Petrović's theory of elements of mathematical phenomenology, the phenomenological mappings in vibrations, signals, resonances and dynamical absorptions in models with two degrees of freedom-abstractions of different real system dynamics are identified, as well as in eigen time functions of multi-deformable coupled body system dynamics, and presented. Mathematical description of a chain mechanical system with two mass particles coupled by linear and nonlinear elastic springs and with two degree of freedom is given. By the analysis of corresponding solutions for free and forced vibrations, series of related two-frequency... regimes and resonant states, as well as dynamical absorption states, are identified. Phenomenological mappings are used to explain dynamics in two deformable body (beams, plates or membranes) systems. In short, new analytical and numerical results of linear and non-linear dynamics of a system with two-degrees of freedom in analogy with eigen time functions oscillations of transversal vibrations of two body system dynamics are presented. Structural analogies are identified between eigen time functions of different multi-coupled deformable body transversal vibrations (plates, beams, belts or membranes). Mathematical phenomenology elements and phenomenological mappings are applied in the scientific results integration. Mathematical analogy and phenomenological mappings of linear and nonlinear singular phenomena in discrete and multi-body system vibrations (torsional system, multi-pendulum system, coupled electrical circuit and multi-deformable-body oscillations-beams, plates, membranes) are performed. Structural analogy is used to explain phenomenological mappings between displacements of the mass particles in discrete system and eigen time functions in one eigen amplitude mode of dynamics in two coupled deformable body (beams, plates or membranes) systems.

Predstavljeni su novi analitički i numerički rezultati o dinamici linearnih i nelinearnih sistema sa sva stepena slobode kretanja. Za mehaničke sisteme sa dva stepena slobode kretanja izučavane su, analitički i numerički sa odgovarajućim poređenjima svojstava između sopstvenih i prinudnih režima, oscilatorne linearne i nelinearne dinamike u njima. Koristeći teoriju Mihaila Petrovića - Elementi matematičke fenomenologije i Fenomenološko preslikavanje, u oscilacijama, signalima, fenomenima rezonancija i dinamičkoj apsorpciji u modelima sa dva stepena slobode dinamika apstrakcija različitih modela realnih sistema identifikovane su matematička i kvailitativne analogije sa sopstvenim vremenskim funkcijama transverzalnih oscilacija sistema više spregnutih deformabilnih tela (ploča, greda, traka ili membrana) i predstavljene. Matematički opis jednog mehaničkog lanca sa dvema matrijalnim tačkama spregnutim linearno elastičnom ili nelinearno elastičnim oprugama i sa dva stepena slobode kretanja... je prikazan zajedno sa odgovarajućom analizom kinetičkih parametara u analogiji sa sistemom dvaju spregnutih tela diskretno-kontinualnim spojem. Analizom odgovarajućih rešenja za sopstvene i prinudne dvofrekventne režime oscilacija i rezonantnih stanja, kao i stanja dinamičke apsorpcije došlo se do novih saznanja o interakciji modova u nelinearnoj dinamici. Korišćenjem matematičke analogije i fenomenološkog preslikavanja svojstvenih fenomena izučavanog mehaničkog sistema, pokazano je da se ta saznanja mogu koristiti za saznanja o fenomenima i svojstvima dinamika drugih apstrakcija realnih sistema modelima sistema sa dva stepena slobode oscilovanja (npr. dvojnog klatna, ili modela torzijskih oscilacija vratila sa dva diska, ili dvojnog električnog kola, kao i transverzalnih oscilacija spregnutih dveju greda, ili ploča ili membrana). Fenomenološko preslikavanje je korišćeno za objašnjavanje dinamike sopstvenih vremenskih funkcija u sistemu spregnutih jednakih deformabilnih tela (greda, ploča, ili membrana). I u najkraćem, analitički i numerički rezultati linearnih i nelinearnih dinamika sistema sa dva stepena slobode su prikazani kao univerzalni, koji se mogu preneti i na razlićite druge sisteme analogijama i preslikavanjima linearnih i nelinearnih fenomena.

Keywords:
nonlinear dynamics / oscillations / free oscillations / forced oscillations / discrete system / continuous system / oscillator / nelinearna dinamika / oscilacije / sopstvene oscilacije / prinudne oscilacije / diskretni sistem / kontinualni sistem / oscilator
Source:
Scientific Technical Review, 2015, 65, 4, 37-45
Publisher:
  • Belgrade, Serbia : Military Technical Institute
Projects:
  • Dynamics of hybrid systems with complex structures. Mechanics of materials. (RS-174001)

DOI: 10.5937/STR1504037S

ISSN: 1820-0206

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URI
http://cer.ihtm.bg.ac.rs/handle/123456789/1767
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  • Radovi istraživača / Researchers' publications
Institution
IHTM

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