Analysis of the quasiperiodic response of a generalized van der Pol nonlinear system in the resonance zone

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68378297%3A_____%2F18%3A00477536" target="_blank" >RIV/68378297:_____/18:00477536 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.compstruc.2017.07.021" target="_blank" >https://doi.org/10.1016/j.compstruc.2017.07.021</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.compstruc.2017.07.021" target="_blank" >10.1016/j.compstruc.2017.07.021</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Analysis of the quasiperiodic response of a generalized van der Pol nonlinear system in the resonance zone

Popis výsledku v původním jazyce

The paper addresses the description of the complex behavior of simple nonlinear systems that are excited in the neighborhood of the resonance frequency. Depending on the detuning of the excitation frequency, resonant response can vary from purely stationary to various cases of quasiperiodic or chaotic response. This type of response is characterized by regular or irregular changes of the amplitude, which, in the quasiperiodic case, represents the beating effect. The beating frequency then changes from zero in resonance to a positive value outside the resonance zone. The ratio of the energy content of quasiperiodic and stationary components decreases in the same time. Starting at a certain detuning, the quasiperiodic component fully vanishes and the stationary component absorbs the whole response energy. The motivation of this study originates from the aeroelasticity of large bridges, the tuned mass damper application, and other domains of civil engineering, where beating effects have been observed in the past. Such effects are very dangerous, hence, robust theoretical background for the design of adequate countermeasures should be developed. Nevertheless, investigations of the internal structure of a quasiperiod and its dependence on the difference between excitation frequency and eigenfrequency were conducted on a heuristic basis and an objective theoretical background is still missing. A qualitative analysis of nonlinear systems using combinations of harmonic balance, small-parameter methods, and perturbation techniques is presented in the paper. Parametric evaluations are presented along with a discussion concerning the applicability of the presented approach.

Název v anglickém jazyce

Analysis of the quasiperiodic response of a generalized van der Pol nonlinear system in the resonance zone

Popis výsledku anglicky

The paper addresses the description of the complex behavior of simple nonlinear systems that are excited in the neighborhood of the resonance frequency. Depending on the detuning of the excitation frequency, resonant response can vary from purely stationary to various cases of quasiperiodic or chaotic response. This type of response is characterized by regular or irregular changes of the amplitude, which, in the quasiperiodic case, represents the beating effect. The beating frequency then changes from zero in resonance to a positive value outside the resonance zone. The ratio of the energy content of quasiperiodic and stationary components decreases in the same time. Starting at a certain detuning, the quasiperiodic component fully vanishes and the stationary component absorbs the whole response energy. The motivation of this study originates from the aeroelasticity of large bridges, the tuned mass damper application, and other domains of civil engineering, where beating effects have been observed in the past. Such effects are very dangerous, hence, robust theoretical background for the design of adequate countermeasures should be developed. Nevertheless, investigations of the internal structure of a quasiperiod and its dependence on the difference between excitation frequency and eigenfrequency were conducted on a heuristic basis and an objective theoretical background is still missing. A qualitative analysis of nonlinear systems using combinations of harmonic balance, small-parameter methods, and perturbation techniques is presented in the paper. Parametric evaluations are presented along with a discussion concerning the applicability of the presented approach.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20101 - Civil engineering

Projekt

<a href="/cs/project/GA15-01035S" target="_blank" >GA15-01035S: Dynamická stabilita a post-kritické procesy v nekonzervativních a neholonomních stochastických soustavách s interakcemi</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computers and Structures

ISSN

0045-7949

e-ISSN

—

Svazek periodika

207

Číslo periodika v rámci svazku

September

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

16

Strana od-do

59-74

Kód UT WoS článku

000447109600006

EID výsledku v databázi Scopus

2-s2.0-85027224241