Controlling nonstationary vibrations of a plate by means of additional loads

Yanyutin, E. G.; Voropay, Alexey

doi:10.1016/j.ijsolstr.2004.04.022

Cited by 3 publications

(1 citation statement)

References 5 publications

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“…In [16], Tikhonov's regularization method was used to determine the dynamic load in a mechanical system with four degrees of freedom. The problem to control nonstationary vibrations of a rectangular plate by introducing an additional (controlling) load is considered in [17]. The problem is solved using the no classical theory of plates and Tikhonov's regularization method.…”

Section: Analysis Of Publicationsmentioning

confidence: 99%

Two inverse non-stationary problems of axially symmetric deformation of a finite-length elastic cylindrical shell

Batygin¹,

Ragulin

Sharapata

2022

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Among the many problems of the solid mechanics, there is a whole class of problems that are related to inverse problems. In turn, among the inverse problems, many problems are ill-posed. Obtaining an exact analytical solution of such problems is related to certain mathematical difficulties and requires using special methods. Goal. The goal of the study is to obtain analytical solutions for inverse problems of the identification of non-stationary load and the control of non-stationary vibrations of a cylindrical shell with asymmetric boundary conditions. Methodology. In this investigation, a refined theory of medium-thickness shells was used. Fourier series expansion, the theory of integral equations and the Laplace transform were used to obtain the solution of the direct problem. Tikhonov’s regularization method was used to solve inverse problems. Results. As a result of the investigation, the solutions of two inverse problems of the solid mechanics were obtained. The first task is to identify a fixed and moving concentrated axisymmetric non-stationary force acting on a cylindrical shell, based on the displacement values at any point of the shell; identification of two fixed concentrated forces. The second task is to control vibrations at any point of the cylindrical shell by introducing an auxiliary concentrated force. Numerical results obtained demonstrate the fulfillment of the control criterion as a result of the action of the given and auxiliary force. Originality. Analytical solutions of the inverse problems of the solid mechanics for a cylindrical shell of medium thickness with asymmetric boundary support conditions are obtained. Practical value. The technique received allows effective identification of an unknown non-stationary load. It’s important for the rational design of reliable cylindrical shell structures. Its use also makes possible to create a theoretical basis to control the deflected mode parameters of cylindrical shell structural elements

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Section: Analysis Of Publicationsmentioning

confidence: 99%

Two inverse non-stationary problems of axially symmetric deformation of a finite-length elastic cylindrical shell

Batygin¹,

Ragulin

Sharapata

2022

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Features of a High-Stiffness Tire Interaction with a Bearing Surface During the Starting Period of Motion

Karpenko,

Voropay,

Czerepicki

et al. 2024

JES

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The article emphasizes the importance and necessity of studying the behavior of automobile tires during operation in the starting mode, from the beginning of driving on “cold” tires to stabilizing its temperature and internal pressure. During this period, the main performance characteristics of the tire can change in a relatively wide range. Therefore, the main focus was on the initial period of driving as the most dangerous from the point of view of predicting the behavior of automobile tires. This article presents the results of analyzing a car tire’s condition and behavior during the starting movement. Features of the main parameter for assessing the stiffness characteristics of the tires were investigated. The research was conducted under conditions of low ambient temperatures during the operation of automobile tires. A numerical-analytical approach was used to estimate the stiffness parameters. Simultaneously, the initial data required for a correct analysis were obtained from the experimental results in actual road conditions. The obtained results allow for providing recommendations on the peculiarities of the automobile tires’ operation under adverse conditions, such as low ambient temperatures.

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Oscillations of a Pulse Loaded Oscillator With a Square Resistance in the Composition of the Dissipative Force

Olshanskiy¹,

Slipchenko²,

Твердохліб³

et al. 2021

Vibrations in Engineering and Technology

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The unsteady oscillations of a dissipative oscillator caused by an instantaneous impulse of the force are described. The case is considered when the dissipative force consists of quadratic viscous resistance and dry friction, and the theoretical results are generalized to the case of the sum of three forces. The third is the force of positional friction. Formulas for calculating the ranges of oscillations have been constructed In this case, the Lambert function of negative and positive arguments is used. It is a tabulated special function. Its value can also be calculated using its known approximations in elementary functions. It is shown that, due to the action of the dissipative force, the process of post-pulse oscillations consists of a finite number of cycles and is limited in time. This is due to the presence of dry friction among the resistance components. Examples of calculations that illustrate the possibilities of the stated theory are given. In order to check the reliability of the derived calculation formulas, numerical computer integration of the differential equation of motion was also carried out. The convergence of the numerical results obtained by two different methods is shown. Thus, it has been confirmed that with the help of analytical solutions it is possible to find the extreme displacements of the oscillator without numerically solving its nonlinear differential equation of motion. Using Lambert function and the first integral of the equation of motion made it possible to derive precise calculation formulas for determining the range of oscillations caused by the pulsed load of the oscillator. The derived formulas are suitable for calculating the value of the instantaneous impulse applied to the oscillator, which refers to the inverse problems of mechanics. Thus, by measuring the maximum displacement of the oscillator, it is possible to identify the initial velocity or instantaneous impulse applied to the oscillator. The performed numerical computer integration of the output differential equation confirmed the adequacy of the obtained analytical solutions, which concern not only direct, but also inverse problems of dynamics.

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Controlling nonstationary vibrations of a plate by means of additional loads

Cited by 3 publications

References 5 publications

Two inverse non-stationary problems of axially symmetric deformation of a finite-length elastic cylindrical shell

Two inverse non-stationary problems of axially symmetric deformation of a finite-length elastic cylindrical shell

Features of a High-Stiffness Tire Interaction with a Bearing Surface During the Starting Period of Motion

Oscillations of a Pulse Loaded Oscillator With a Square Resistance in the Composition of the Dissipative Force

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