Юрий Михлин - Academia.edu (original) (raw)
Юрий Михлин
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Transient in a system containing a linear oscillator, linearly coupled to an essentially nonlinea... more Transient in a system containing a linear oscillator, linearly coupled to an essentially nonlinear attachment with a comparatively small mass, is considered. A damping is taken into account. The multiple scales method is used to construct a rocess of transient in the system under consideration. A transfer of energy from the initially perturbed linear subsystem to the nonlinear absorber can be observed. A similar construction is made to describe the transient in a system which contains a linear oscillator and a vibro-impact attachment with a comparatively small mass. A transient in such system under the external periodical excitation was considered too. Numerical simulation confirms an efficiency of the analytical construction in both systems
Transient in a non-ideal system with limited excitation, where an interaction of engine and linea... more Transient in a non-ideal system with limited excitation, where an interaction of engine and linear elastic subsystem takes place, is considered. The transient in described by the multiple scales method. Possibility of transfer to stationary regimes, including a resonance regime, is considered. Numerical simulation confirms an efficiency of the obtained analytical solutions
Themethod of nonlinear normal modes is used to study nonlinear dynamics of mechanical system with... more Themethod of nonlinear normal modes is used to study nonlinear dynamics of mechanical system with snap-through truss. Mathieu's equation is derived to study the motions stability. The domain of instability of nonlinear normal mode is obtaine
Розглянуто стаціонарні режими у неідеальній системі, в якій відбувається взаємодія між джерелом е... more Розглянуто стаціонарні режими у неідеальній системі, в якій відбувається взаємодія між джерелом енергії (двигуном) та лінійною пружною підсистемою, досліджено стійкість цих режимів. Чисельно-аналітичними методами досліджується ефект Зоммерфельда. Аналізується вплив нелінійного гасителя на динамічну поведінку системи.Stationary regimes in a non-ideal system, where an interaction of source of enetgy (the engine) and linear elastic subsystem takes place, is considered, and the regimes stability is investigated. The Zommerfeld effect is studied by numerical-analytical methods. The influence of nonlinear absorber to the system dynamical behavior is analyzed
В статье рассмотрены вопросы построения оптимальных диаграмм скорости движения шахтных подъемных ... more В статье рассмотрены вопросы построения оптимальных диаграмм скорости движения шахтных подъемных установок. На основе принципа оптимального управления Понтрягина решается задача минимизации расхода энергии. Кроме того, сделан расчет оптимальных по быстродействию диаграмм скорости движения подъемных установок с учетом ограничения ускорения и рывка, что обеспечивает уменьшение колебаний подъемного сосуда при движении.Problems of construction of optimal speed diagrams construction for the hoisting plant motion are considered. A problem of minimization of the motion energy on the basis of the Pontriagin principle is solved. Besides, it is realized a determination of optimal by speed diagrams of the hoisting plants taking into account a limitation by acceleration and jerk to reduce the skip vertical oscillations
Free damped oscillations in the automobile with a nonlinear response of the suspension are consid... more Free damped oscillations in the automobile with a nonlinear response of the suspension are considered. The 7-DOF nonlinear model is considered. As a result, nonlinear vibration modes and the corresponding skeleton curves are obtained. The transient is described in this system. The obtained results are compared with solutions of the corresponding linearized syste
Transient in a system containing a linear oscillator, linearly coupled to an essentially nonlinea... more Transient in a system containing a linear oscillator, linearly coupled to an essentially nonlinear attachment with a comparatively small mass, is considered. A damping is taken into account. The multiple scales method is used to construct a rocess of transient in the system under consideration. A transfer of energy from the initially perturbed linear subsystem to the nonlinear absorber can be observed. A similar construction is made to describe the transient in a system which contains a linear oscillator and a vibro-impact attachment with a comparatively small mass. A transient in such system under the external periodical excitation was considered too. Numerical simulation confirms an efficiency of the analytical construction in both systems
Transient in a non-ideal system with limited excitation, where an interaction of engine and linea... more Transient in a non-ideal system with limited excitation, where an interaction of engine and linear elastic subsystem takes place, is considered. The transient in described by the multiple scales method. Possibility of transfer to stationary regimes, including a resonance regime, is considered. Numerical simulation confirms an efficiency of the obtained analytical solutions
Themethod of nonlinear normal modes is used to study nonlinear dynamics of mechanical system with... more Themethod of nonlinear normal modes is used to study nonlinear dynamics of mechanical system with snap-through truss. Mathieu's equation is derived to study the motions stability. The domain of instability of nonlinear normal mode is obtaine
Розглянуто стаціонарні режими у неідеальній системі, в якій відбувається взаємодія між джерелом е... more Розглянуто стаціонарні режими у неідеальній системі, в якій відбувається взаємодія між джерелом енергії (двигуном) та лінійною пружною підсистемою, досліджено стійкість цих режимів. Чисельно-аналітичними методами досліджується ефект Зоммерфельда. Аналізується вплив нелінійного гасителя на динамічну поведінку системи.Stationary regimes in a non-ideal system, where an interaction of source of enetgy (the engine) and linear elastic subsystem takes place, is considered, and the regimes stability is investigated. The Zommerfeld effect is studied by numerical-analytical methods. The influence of nonlinear absorber to the system dynamical behavior is analyzed
В статье рассмотрены вопросы построения оптимальных диаграмм скорости движения шахтных подъемных ... more В статье рассмотрены вопросы построения оптимальных диаграмм скорости движения шахтных подъемных установок. На основе принципа оптимального управления Понтрягина решается задача минимизации расхода энергии. Кроме того, сделан расчет оптимальных по быстродействию диаграмм скорости движения подъемных установок с учетом ограничения ускорения и рывка, что обеспечивает уменьшение колебаний подъемного сосуда при движении.Problems of construction of optimal speed diagrams construction for the hoisting plant motion are considered. A problem of minimization of the motion energy on the basis of the Pontriagin principle is solved. Besides, it is realized a determination of optimal by speed diagrams of the hoisting plants taking into account a limitation by acceleration and jerk to reduce the skip vertical oscillations
Free damped oscillations in the automobile with a nonlinear response of the suspension are consid... more Free damped oscillations in the automobile with a nonlinear response of the suspension are considered. The 7-DOF nonlinear model is considered. As a result, nonlinear vibration modes and the corresponding skeleton curves are obtained. The transient is described in this system. The obtained results are compared with solutions of the corresponding linearized syste