Chaotic dynamics of flexible beams with piezoelectric and temperature phenomena

Кrysko, V.А.; Awrejcewicz, Jan; Кутепов, И. Е.; Загниборода, Н. А.; Папкова, И. В.; Serebryakov, A.V.; Krysko, Anton V.

doi:10.1016/j.physleta.2013.06.040

Cited by 35 publications

(7 citation statements)

References 21 publications

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“…In the papers [21][22][23][24][25][26][27] we proved that this method was sufficient and efficient. Since the governing equations of the curvilinear beam differ from those of the flexible straight linear beam only due to the terms related to …”

Section: Beam Modelmentioning

confidence: 99%

“…The general numerical approach used in this work, as employed to structural members, has already been presented in our earlier papers [21][22][23][24][25][26][27]. This type of the studied problem has been analyzed briefly in reference [25].…”

Section: Introductionmentioning

confidence: 99%

“…This type of the studied problem has been analyzed briefly in reference [25]. However, the mentioned short report concerned a straight beam.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chaotic vibrations of flexible curvilinear beams in temperature and electric fields

Awrejcewicz

Кrysko

Кутепов

et al. 2015

International Journal of Non-Linear Mechanics

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Section: Beam Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chaotic vibrations of flexible curvilinear beams in temperature and electric fields

Awrejcewicz

Кrysko

Кутепов

et al. 2015

International Journal of Non-Linear Mechanics

Self Cite

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“…Nonlinear vibrations of continuous systems were investigated in works [11,12]. In reference [13] the influence of different kinds of the temperature field on the vibration regimes of a one-layer beam was analyzed. It was shown that though a temperature field had a marginal influence on the vibration amplitude, it changed the character of exhibited vibrations.…”

Section: On a Contact Problem Of Two-layer Beams 469mentioning

confidence: 99%

On a Contact Problem of Two-Layer Beams Coupled by Boundary Conditions in a Temperature Field

Krysko

Awrejcewicz

Кутепов

et al. 2015

Journal of Thermal Stresses

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We consider a mathematical model of two-layer beams coupled by boundary conditions in a stationary temperature field taking into account geometric nonlinearity. The stationary temperature field is defined by a 2D heat transfer equation with boundary conditions of the first kind. The geometric nonlinearity is introduced via von Kármán's relations for both beams. Equations of beam deflection are derived due to theEuler-Bernoulli hypothesis. The contact interaction is described using Winkler's model. Scenarios of a transition from regular to chaotic regimes are studied. Phase synchronization of beam vibrations versus both character and intensity of the applied temperature field is investigated.

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“…This type of non-linear damage is exemplified by breathing cracks [ 12 , 13 , 14 ] and material stratification [ 15 , 16 ]. Wavelet-based time-frequency methods are representative techniques for characterizing structural progressive degradation or deterioration, the first type of non-linear damage, with its ability to detect the relationship between frequencies and its time dependence, and has a certain noise robustness [ 17 , 18 , 19 , 20 , 21 , 22 ]. Nevertheless, the method suitable for characterizing the second type of non-linear damage, particularly the breathing crack, is pretty absent while desirable.…”

Section: Introductionmentioning

confidence: 99%

Use of Bispectrum Analysis to Inspect the Non-Linear Dynamic Characteristics of Beam-Type Structures Containing a Breathing Crack

Cui

Ge³

et al. 2021

Sensors

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A breathing crack is a typical form of structural damage attributed to long-term dynamic loads acting on engineering structures. Traditional linear damage identification methods suffer from the loss of valuable information when structural responses are essentially non-linear. To deal with this issue, bispectrum analysis is employed to study the non-linear dynamic characteristics of a beam structure containing a breathing crack, from the perspective of numerical simulation and experimental validation. A finite element model of a cantilever beam is built with contact elements to simulate a breathing crack. The effects of crack depth and location, excitation frequency and magnitude, and measurement noise on the non-linear behavior of the beam are studied systematically. The result demonstrates that bispectral analysis can effectively identify non-linear damage in different states with strong noise immunity. Compared with existing methods, the bispectral non-linear analysis can efficiently extract non-linear features of a breathing crack, and it can overcome the limitations of existing linear damage detection methods used for non-linear damage detection. This study’s outcome provides a theoretical basis and a paradigm for damage identification in cracked structures.

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Chaotic dynamics of flexible beams with piezoelectric and temperature phenomena

Cited by 35 publications

References 21 publications

Chaotic vibrations of flexible curvilinear beams in temperature and electric fields

Chaotic vibrations of flexible curvilinear beams in temperature and electric fields

On a Contact Problem of Two-Layer Beams Coupled by Boundary Conditions in a Temperature Field

Use of Bispectrum Analysis to Inspect the Non-Linear Dynamic Characteristics of Beam-Type Structures Containing a Breathing Crack

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