On oscillations of an oscillator with cubic-nonlinear stiffness

Olshanskiy, V. P.; Burlaka, Vladimir; Slipchenko, Maksym; Malec, O. M.

doi:10.20998/2078-9130.2017.39.115767

Cited by 3 publications

(5 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3) The initial value of the amplitude for a system of differential equations (24) in both of the above cases should be close to k a  . 4) The boundary value problems considered in this paper also describe the relative torsional oscillations of a flexible body under the action of a system of impulse moments, provided that the portable angular velocity of rotation of the body is a constant value.…”

Section: B the Methods Of Research Of Nonlinear Resonant Torsional Os...mentioning

confidence: 96%

“…Since the resonance phenomenon occurs when the amplitude of oscillations approaches the value k a  during the numerical simulation of the obtained system of differential equations (24), the following approaches are considered: for the resonance case, the value   Notes:…”

Section: B the Methods Of Research Of Nonlinear Resonant Torsional Os...mentioning

confidence: 99%

“…A significant development was found when the set of single-frequency solutions could be built for undisturbed analogs of the interconnected systems with the help of trigonometric and periodic Ateb-functions [24][25][26][27][28][29].…”

Section: Review Of Related Workmentioning

confidence: 99%

“… are the known constants. From the properties of periodic Ateb-functions [24][25][26][27][28][29], the independence of the phases of natural and forced (pulse) oscillations, it follows that the integrals in the right parts of the dependences ( 26) are zero because…”

Section: Resonance Relative Torsional Oscillations Of the Nonlinear F...mentioning

confidence: 99%

See 3 more Smart Citations

Impulse Moments Influence on Single-Frequency Torsional Oscillations of Nonlinear Flexible Bodies

et al. 2022

View full text Add to dashboard Cite

A method of analytical study of the influence of impulse moments on nonlinear torsional oscillations of a homogeneous constant cross-section of a body under classical boundary conditions of the first, second, and third types have been developed. When the flexible material properties meet the body close to the power law of flexibility, mathematical models of the process have been obtained. They are the boundary value problems for an equation of hyperbolic type with a small parameter at the discrete righthand side. The latter expresses the effect of pulse momentum on the oscillatory process. Under the effect of periodic pulse momentum on a flexible body, resonant and non-resonant processes are possible, and resonant processes occur when the amplitude of natural oscillations approaches a fixed value. The peculiarities of resonant oscillations are established. Relative torsional oscillations of a nonlinear flexible body that rotates around the axis with a constant portable angular velocity are considered, taking into account the periodic action of pulse momentum acting in a fixed cross-section. It is shown that: the amplitude of passing through the main resonance is more significant for larger values of the nonlinearity parameter; the case of the action of pulse momentum closer to the middle of the body. If the initial perturbation amplitude is less than the amplitude at which the resonance occurs in the presence of only internal forces of viscous friction, the external periodic impulse moments of resonance processes have occurred. The reliability of the calculation formulas is confirmed by the fact that in the extreme case known from the literature, resources are obtained related to the dynamics of the respective objects under the continuous action of autonomous perturbation.

show abstract

Section: B the Methods Of Research Of Nonlinear Resonant Torsional Os...mentioning

confidence: 96%

Section: B the Methods Of Research Of Nonlinear Resonant Torsional Os...mentioning

confidence: 99%

Section: Review Of Related Workmentioning

confidence: 99%

Section: Resonance Relative Torsional Oscillations Of the Nonlinear F...mentioning

confidence: 99%

See 2 more Smart Citations

Impulse Moments Influence on Single-Frequency Torsional Oscillations of Nonlinear Flexible Bodies

et al. 2022

View full text Add to dashboard Cite

show abstract

“…The most effective methods of investigating oscillating processes in nonlinear systems with concentrated masses and distributed parameters are those based on introductory provisions of perturbation methods [2,8], combined with the principle of simultaneity of oscillations. A significant development was found when the set of single-frequency solutions can be built for undisturbed analogs of interconnected systems with the help of trigonometric and periodic Abet functions [9,10]. The latter describes the dynamics of a wide range of systems with power nonlinearity [10,11,12] and has several features that are not typical for a linear system.…”

Section: Introductionmentioning

confidence: 99%

Influence of Impulse Moments On Single-Frequency Torsional Oscillations of Nonlinearly Elastic Bodies

Сокіл

Andrukhiv

Федушко

et al. 2021

Preprint

View full text Add to dashboard Cite

Analytical study of the impulse moment influences on the nonlinear torsional oscillations in the homogeneous constant cross-section of a body under classical boundary conditions of the first, second, and third types has been developed. For the case when the elastic material properties meet the body close to the power law of elasticity, mathematical models of the process are obtained. They are the boundary value problems for an equation of hyperbolic type with a small parameter at the discrete right-hand side. The latter expresses the effect of pulse momentum on the oscillatory process. The peculiarities of resonant oscillations are established. Relative torsional oscillations of a nonlinear elastic body that rotates around the axis with a constant portable angular velocity are considered, taking into account the periodic action of pulse momentum acting in a fixed cross-section. The reliability of the obtained calculation formulas is confirmed.

show abstract

Methodology of Force Parameters Justification of the Controlled Steering Wheel Suspension

Sokil¹,

Lyashuk²,

Сокіл³

et al. 2022

Communications

View full text Add to dashboard Cite

The methodology for selecting the main force parameters of nonlinear nonconservative suspension for the main performance characteristics of wheeled vehicles has been developed based on the longitudinal-angular oscillations. The following has been established: a) change limits of static deformation of the elastic suspension system and its other parameters at which the basic operational characteristics for various ranges of amplitude change are satisfied; b) the amplitude of the initial perturbation of oscillations depending on the shape of the inequality and its entry speed; c) the influence of the main characteristics of damping devices on the amplitudefrequency characteristics. The results of this work can be a basis for the choice of such parameters of the considered controlled suspension, which ensure the stability of the vehicle along the curved sections of the road, its controllability, etc.

show abstract

On oscillations of an oscillator with cubic-nonlinear stiffness

Cited by 3 publications

References 0 publications

Impulse Moments Influence on Single-Frequency Torsional Oscillations of Nonlinear Flexible Bodies

Impulse Moments Influence on Single-Frequency Torsional Oscillations of Nonlinear Flexible Bodies

Influence of Impulse Moments On Single-Frequency Torsional Oscillations of Nonlinearly Elastic Bodies

Methodology of Force Parameters Justification of the Controlled Steering Wheel Suspension

Contact Info

Product

Resources

About