On the vibrational analysis for the motion of a harmonically damped rigid body pendulum

Amer, T. S.; Bek, M. A.; Abouhmr, M. K.

doi:10.1007/s11071-017-4027-7

Cited by 55 publications

(35 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A generalization of this work is found in [16], where the authors studied a damped spring motion that follows an elliptic route. An extension of this research was found in [17,18], when the suspension point was travelling in the same direction, with a constant angular velocity of a linear spring and nonlinear one, respectively. The case of the attached tuned absorber with the spring was investigated in [19].…”

Section: Introductionmentioning

confidence: 65%

Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance

et al. 2021

Self Cite

View full text Add to dashboard Cite

This work looks at the nonlinear dynamical motion of an unstretched two degrees of freedom double pendulum in which its pivot point follows an elliptic route with steady angular velocity. These pendulums have different lengths and are attached with different masses. Lagrange’s equations are employed to derive the governing kinematic system of motion. The multiple scales technique is utilized to find the desired approximate solutions up to the third order of approximation. Resonance cases have been classified, and modulation equations are formulated. Solvability requirements for the steady-state solutions are specified. The obtained solutions and resonance curves are represented graphically. The nonlinear stability approach is used to check the impact of the various parameters on the dynamical motion. The comparison between the attained analytic solutions and the numerical ones reveals a high degree of consistency between them and reflects an excellent accuracy of the used approach. The importance of the mentioned model points to its applications in a wide range of fields such as ships motion, swaying buildings, transportation devices and rotor dynamics.

show abstract

Section: Introductionmentioning

confidence: 65%

Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…The motion takes a slow spin rotation about the symmetric z-axis of the disc. The equations of motion and their first integrals are derived and reduced to two quasilinear differential equations of the second order and one first integral [16][17][18][19]. The periodic solutions for this problem are constructed applying the periodicity conditions and assuming a large parameter [20] proportional to 1/r 0 .…”

Section: Discussionmentioning

confidence: 99%

Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point

Ismail

2020

International Journal of Aerospace Engineering

View full text Add to dashboard Cite

In this paper, the motion of a disk about a fixed point under the influence of a Newtonian force field and gravity one is considered. We modify the large parameter technique which is achieved by giving the body a sufficiently small angular velocity component r0 about the fixed z-axis of the disk. The periodic solutions of motion are obtained in the neighborhood r0 tends to 0. This case of study is excluded from the previous works because of the appearance of a singular point in the denominator of the obtained solutions. Euler-Poison equations of motion are obtained with their first integrals. These equations are reduced to a quasilinear autonomous system of two degrees of freedom and one first integral. The periodic solutions for this system are obtained under the new initial conditions. Computerizing the obtained periodic solutions through a numerical technique for validation of results is done. Two types of analytical and numerical solutions in the new domain of the angular velocity are obtained. Geometric interpretations of motion are presented to show the orientation of the body at any instant of time t.

show abstract

“…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. The accuracy of the multiple scales method was found to be good, and the time response of the solution is compared with the numerical results of the governing equations [6]. Fluid -structure interaction model by the dynamic mesh method using Fluent for a 2D mechanical heart valve simulation for a cardiac cycle was successfully validated by comparing the computer simulation results to experiments that are obtained from in vitro studies with the help of a CCD camera [7].…”

Section: Introductionmentioning

confidence: 99%

Action of pendulum in transient fluid flow

Tipāns

Vība

Vutukuru

et al. 2021

20th International Scientific Conference Engineering for Rural Development Proceedings

View full text Add to dashboard Cite

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.

show abstract

On the vibrational analysis for the motion of a harmonically damped rigid body pendulum

Cited by 55 publications

References 20 publications

Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance

Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance

Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point

Action of pendulum in transient fluid flow

Contact Info

Product

Resources

About