Self-Modulation of Quasi-Harmonic Bending Waves in Rods

Kazhaev, V. V.; Semerikova, N. P.

doi:10.18411/vntr2019-142-2

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“…This result follows from Fig. 3, which is a graphical representation of the solution to the equation system (16).…”

Section: Discussion Of the Influence Of Kinematic And Physicalmechani...supporting

confidence: 52%

“…However, in engineering and design calculations, even for such fluctuations, it is impossible to neglect such a kinematic quantity as the longitudinal speed of movement. The result is explained by the form of the right-hand part (16).…”

Section: Discussion Of the Influence Of Kinematic And Physicalmechani...mentioning

confidence: 97%

“…2. With increasing speed, the frequency of longitudinal oscillations of the beam falls according to the parabolic law because in formula (16) there is a square of the velocity value. Therefore, the impact of speed will be significant at high speeds (already at a speed of 20 m/s -the frequency of oscillations decreases by 7 %).…”

Section: Discussion Of the Influence Of Kinematic And Physicalmechani...mentioning

confidence: 99%

“…Variational methods are also used. In particular, the Ostrohrad-Hamilton principle is used to solve the equations of longitudinal, torsional, and transverse vibrations of the rod [16]. By establishing the equivalence of solving boundary problems to solving problems about the extremum of the functionality, this principle opens up the possibility for application to vibration calculations of some special methods of variational calculus.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…Our review of literary sources [12][13][14][15][16][17][18] reveals that such an important issue as the influence of the speed of movement of elements of mechanisms on the oscillations of one-dimensional nonlinear elastic systems was not considered in detail. The main reason for this in the analytical study of dynamic processes was the lack of a mathematical apparatus for solving appropriate nonlinear differential equations that describe the laws of motion of those systems.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Advancing asymptotic approaches to studying the longitudinal and torsional oscillations of a moving beam

Slipchuk

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Vovk

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EEJET

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This paper analyzes the influence of kinetic and physical-mechanical parameters of systems on the characteristics of dynamic processes in moving one-dimensional nonlinear-elastic systems. Improved convenient calculation formulas have been derived that describe the laws of changing the amplitude-frequency characteristics of systems for both a non-resonant case and a resonant one. An important issue of studying the influence of the speed of movement of elements of mechanisms on the oscillations of one-dimensional nonlinear-elastic systems has not been considered in detail until now in the scientific literature. This issue relates to the vibrations of shafts in gears, pipe strings when drilling oil and gas wells, the oscillations of turbine blades and rotating turbine discs, the longitudinal vibrations of the beam as an element of structures. The main reason for this in the analytical study of dynamic processes were the shortcomings of the mathematical apparatus for solving the corresponding nonlinear differential equations that describe the laws of motion of those systems. It was found that in the case of longitudinal oscillations in the moving beam with an increase in the longitudinal speed of the medium to 10 m/s, the amplitude of the oscillation also increases by 13.5 %. However, when the longitudinal velocity of the beam is 5 m/s, the amplitude will increase by only 3 %. It is established that with the growth of the amplitude, the frequency of longitudinal oscillations decreases sharply, and if the system moves at a higher speed, for example, 20 m/s, it reduces the frequency of oscillation by about 13 %. The results reported here make it possible to assess the effect of kinetic and physical-mechanical parameters on the frequency and amplitude of oscillations. The research that involved the asymptotic method makes it possible to predict resonant phenomena and obtain engineering solutions to improve the efficiency of technological equipment.

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“…This result follows from Fig. 3, which is a graphical representation of the solution to the equation system (16).…”

Section: Discussion Of the Influence Of Kinematic And Physicalmechani...supporting

confidence: 52%

Section: Discussion Of the Influence Of Kinematic And Physicalmechani...mentioning

confidence: 97%

Section: Discussion Of the Influence Of Kinematic And Physicalmechani...mentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

See 3 more Smart Citations

Advancing asymptotic approaches to studying the longitudinal and torsional oscillations of a moving beam

Slipchuk

Пукач

Vovk

et al. 2022

EEJET

View full text Add to dashboard Cite

show abstract

Self-Modulation of Quasi-Harmonic Bending Waves in Rods

Abstract: The features of propagation of quasi-harmonic waves in nonlinear elastic Euler-Bernoulli and Timoshenko rods are studied. It is shown that bending waves in Euler-Bernoulli rod are stable by means of self-modulation, while in Timoshenko rod there exist domains of modulation instability.

Cited by 1 publication

References 0 publications

Advancing asymptotic approaches to studying the longitudinal and torsional oscillations of a moving beam

Advancing asymptotic approaches to studying the longitudinal and torsional oscillations of a moving beam

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