Stationary and Transient Resonant Response of a Spring Pendulum

Awrejcewicz, Jan; Starosta, R.; Sypniewska–Kamińska, Grażyna

doi:10.1016/j.piutam.2016.03.026

Cited by 21 publications

(13 citation statements)

References 4 publications

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“…An approximate mathematical model of a spring pendulum is formed to analyse the steady-state and transient motion of the system by varying the parameters. All analytical and numerical results were found to be in agreement [5]. A harmonically excited damped spring pendulum system with an attached rigid body is investigated utilizing the multiple scales technique that helped obtain asymptotic solutions to the governing equations of motion up to a good approximation.…”

Section: Introductionmentioning

confidence: 68%

Action of pendulum in transient fluid flow

Tipāns

Vība

Vutukuru

et al. 2021

20th International Scientific Conference Engineering for Rural Development Proceedings

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The work is dedicated to the authors' latest research on the interaction of moving inflexible objects when subjected to non-constant velocity fluid flow (air, water) without the use of work-intensive space-time programming methods. In the first part of the study, the differential equation of the plane pendulum motion is derived using the novel approach of fluid-rigid body interaction phenomenon, in this equation, the moment caused by the fluid interaction is simplified by ignoring the flow viscosity. This makes it possible to obtain the usual second-order differential equation of pendulum motion, which contains components of relative velocity in a simplified way, instead of the partial differential equations in a continuous mathematical space. The application of the obtained equation is further used in solving specific tasks of engineering importance. The first task analyzes the pendulum swing motion in a still airflow. Here, the equation described above is numerically integrated and the results are compared with an experiment in a natural environment. The comparison resulted in a drag interaction factor that was further used in other more complex cases. The second task analyzes the pendulum motion when fluid flow velocities are a decreasing function of time in a harmonic behavior. In addition, in this case, the possibilities of applying the developed theory to other forms of flow rate change, such as pulse or poly harmonic forms, are considered. In the third task, the synthesis of motion control in a mechatronic system was performed. In this case, the possibility of regulating the additional resistance torque arising from the rotary damping generator is considered. The work is illustrated with graphical results. The outcomes obtained in the work can be used in the analysis of the interaction of existing moving objects with the fluid flow, as well as in the synthesis of new technological processes, for example, for obtaining energy from vibrating objects immersed in fluid flow.

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Section: Introductionmentioning

confidence: 68%

Action of pendulum in transient fluid flow

Tipāns

Vība

Vutukuru

et al. 2021

20th International Scientific Conference Engineering for Rural Development Proceedings

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“…On the other side, dynamical pendulum models with 2 or 3 DOF have been studied in many research works such as (Awrejcewicz et al, 2016;Starosta et al, 2011;Starosta et al, 2012;Amer et al, 2016;Nayfeh, 2004;Awrejcewicz et al, 2013;Amer et al, 2018;Amer et al, 2019;El-Sabaa et al, 2020). The plane motion of nonlinear spring pendulum with 2DOF is investigated in (Awrejcewicz et al, 2016) for a fixed supported point under the influence of two external forces in the direction of a spring arm and its perpendicular direction.…”

Section: Introductionmentioning

confidence: 99%

On the motion of a triple pendulum system under the influence of excitation force and torque

Amer

Galal

Abolila

2021

KJS publishes peer-review articles in Mathematics, Computer Sci

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In this article, a nonlinear dynamical system with three degrees of freedom (DOF) consisting of multiple pendulums (MP) is investigated. The motion of this system is restricted to be in a vertical plane, in which its pivot point moves in a circular path with constant angular velocity, under the action of an external harmonic force and a moment acting perpendicular to the direction of the last arm of MP and at the suspension point respectively. Multiple scales technique (MST) among other perturbation methods is used to obtain the approximate solutions of the equations of motion up to the third approximation because it is authorizing to execute a specific analysis of the system behaviour and to realize the solvability conditions given the resonance cases. The stability of the considered dynamical model utilizing the nonlinear stability analysis approach is examined. The solutions diagrams and resonance curves are drawn to illustrate the extent of the effect of various parameters on the solutions. The importance of this work is due to its uses in human or robotic walking analysis.

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“…Furthermore, they designed a controller free of singular points by proposing a new Lyapunov function which shapes a part of the total mechanical energy including the kinetic energy of rotation and the potential energy of VLP, and showed their method can stabilize the motion of VLP to a desired swing motion with given desired energy and length of the pendulum by numerical simulations. In [22][23][24][25][26], the motion of the spring pendulum is analyzed as a VLP, and the dynamic response of a harmonically and kinematically excited spring pendulum is studied. In those studies, the transient and steady-state response of resonant/non-resonant states are investigated using the multiple scale method.…”

Section: Introductionmentioning

confidence: 99%

Amplitude and rotational speed control of variable length pendulum by periodic input

Kajiwara

Aoyagi

2021

Meccanica

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In this paper, a control law to stabilize the amplitude or rotational speed of a variable length pendulum to a desired value by periodically changing the position of the center of gravity is proposed. First, the motion of the pendulum oscillating around a lower equilibrium point is analyzed using the averaging method, and a first-order differential equation for the amplitude of the pendulum is derived. Subsequently, using the derived equation of motion, a control law is designed to control the amplitude of the pendulum to the desired value. Similarly, the motion of a pendulum rotating continuously around the rotation axis is analyzed, the first-order differential equation for the angular velocity of the pendulum is derived, and then a control law of the rotational speed is designed. The derived nonlinear feedback control law consists of the amplitude, angle, and angular velocity of the pendulum in the case of amplitude control, and in the case of rotational speed control, the rotational velocity and angular acceleration of the pendulum. Finally, by using the proposed control method, it is shown that the amplitude and rotational speed of the pendulum can be controlled to the desired values.

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Stationary and Transient Resonant Response of a Spring Pendulum

Cited by 21 publications

References 4 publications

Action of pendulum in transient fluid flow

Action of pendulum in transient fluid flow

On the motion of a triple pendulum system under the influence of excitation force and torque

Amplitude and rotational speed control of variable length pendulum by periodic input

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