Determination of the first natural frequency of an elastic rod of a discrete-continuous vibratory system

Lanets, Oleksii; Kachur, Oleksandr; Korendiy, Vitaliy; Dmyterko, Petro; Нікіпчук, С. В.; Derevenko, Iryna

doi:10.21595/vp.2021.21981

Cited by 2 publications

(1 citation statement)

References 9 publications

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“…У такому випадку, використовуючи (20), (31) та (32), ми можемо скласти систему рівнянь: Враховуючи сказане вище, вирішено відмовитись від одномасової конструкції і використати двомасову, котра складніша, проте може забезпечити значно вищі амплітуди коливань, а отже, і швидкість транспортування та знижене споживання потужності завдяки використанню резонансних режимів [9][10][11][12][13][14][15][16][17][18][19][20]. , що призводитиме до значних втрат магнітного потоку.…”

Section: відносно максимальної амплітуди коливань він становитимеunclassified

Adjustment of analytical examples for installation of inertical and fastest parameters of bilateral resonance vibrating machines

Lanets¹,

Derevenko²,

Novytskyi³

et al. 2022

ISTCIPA

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Goal. It consists in substantiating the rational design of the vibroconveyor as a component of the vibroconveyor line of length , which will provide the necessary technological parameters for the transportation of artificial cargoes. The difficulty of this task is that the speed of transporting goods by mass should be at least . Topicality. The need for these studies is due to the fact that the vibration machine interacts with the parameters of the oscillation system, the main of which are inertial, rigid and power. If they are correctly calculated and implemented in the design of a vibration machine, it will be robust. Failure to consider one type of parameters causes an error in the calculation. Method. The refinement of analytical expressions is carried out using the classical approaches for linear vibrational systems with harmonic perturbation. For this the physical model of the two-mass resonance oscillation system is considered and its mathematical model is developed as a system of linear differential equations. On the basis of this the solution is formed (the values of the amplitudes of oscillations). Unknown parameters remain rigid, provided that the inertia is constructed. Therefore, using the determinants of the matrix of coefficients for unknowns, the necessary mathematical operations are performed that satisfy the imposed conditions for the establishment of rigid parameters. Results. In the paper a series of analytical expressions are obtained that examine the mutual influence of rigid parameters in the system. A comparison of the obtained results according to the specified expressions with classical analytical expressions is made. It is established that the values according to the proposed expressions do not differ significantly from the classical approaches, and therefore, in the case of in-energy calculations, it is sufficient to use existing expressions. The proposed expressions are more precise and therefore recommended for scientific research. Scientific novelty. For the first time, we succeeded in synthesizing analytical expressions for the establishment of inertia-rigid parameters that allow more accurate calculation of two-mass resonance oscillation systems. It is established that for the correct choice of resonant alignments in the system, the mutual influence of rigid parameters in the system is not significant, and therefore it is scientifically grounded to use classical approaches. Practical significance. Established analytical expressions can be widely used in the design of vibration process equipment. The transparency of the output and the relative simplicity of the proposed analytical expressions allows for their widespread use in practice.

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Section: відносно максимальної амплітуди коливань він становитимеunclassified

Adjustment of analytical examples for installation of inertical and fastest parameters of bilateral resonance vibrating machines

Lanets¹,

Derevenko²,

Novytskyi³

et al. 2022

ISTCIPA

Self Cite

View full text Add to dashboard Cite

show abstract

Mathematical modelling of forced oscillations of continuous members of resonance vibratory system

Kachur¹,

Lanets²,

Korendiy³

et al. 2021

Vib. proced.

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The article considers the possibilities of developing the combined discrete-continuous vibratory systems, in which the disturbing member is designed in the form of the uniform elastic rod with distributed inertia and stiffness parameters. The forced oscillations of the continuous member of the three-mass vibratory system are analyzed. Based on the Krylov-Duncan functions (circular and hyperbolic functions), the system of equations describing the motion of the continuous rod is derived. The novelty of the present paper consists in deriving the mathematical model of the discrete-continuous vibratory system, in which the model of the discrete subsystem is combined with the model of the continuous subsystem by applying the reactions in the supports holding the uniform elastic rods. The inertia-stiffness parameters of the vibratory system are determined and the analytical dependencies for calculating the reactions in supports are derived. The frequency-response curves of the considered discrete-continuous vibratory system are constructed. The deflection (bending) diagram of the continuous members is plotted for the case of forced oscillations of the combined discrete-continuous vibratory system.

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Determination of the first natural frequency of an elastic rod of a discrete-continuous vibratory system

Cited by 2 publications

References 9 publications

Adjustment of analytical examples for installation of inertical and fastest parameters of bilateral resonance vibrating machines

Adjustment of analytical examples for installation of inertical and fastest parameters of bilateral resonance vibrating machines

Mathematical modelling of forced oscillations of continuous members of resonance vibratory system

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