On a toroidal pendulum

We consider the problem of motion of a heavy particle on the surface of a torus with horizontal axis of rotation.     

Measurement of soil reaction forces on a single movable lug

In order to clarify characteristics of a new mechanism called a movable lug, a model of a single movable lug equipped with an L-shaped force transducer has been developed. The soil reaction forces (normal and tangential) on a flat single movable lug, a curved single movable lug and a fixed lug were measured on wet sandy loam soil in the laboratory soil bin test. These measured forces then were converted to lug pull and lift forces. The pull and lift forces obtained by the flat movable lug with 45° lug inclination angle and the curved movable lug were higher than those of the fixed lug. It was observed that the lift force of the fixed lug achieved its peak and dropped earlier than those of the movable lugs. However, the peaks of pull and lift forces of the flat and curved movable lugs were almost the same. The flat movable lug with 45° lug inclination angle generated a slightly higher peak of pull force than those with 30° and 60° lug inclination angles. However, the higher lug inclination angle produced, the lower peak of lift force. It was observed that the pull and lift forces increased as the sinkage increased. In contrast to the flat movable lug with 45° lug inclination angle, the curved movable lug produced greater lift force especially at high sinkage. The increase in lug slip from 5% to 25 and 50% caused an increase in the peaks of pull and lift forces. The soil moisture content affected the lug forces significantly.     

A thermohaline-diffusion tank with a movable plate

An easy-to-use type double-diffusion tank equipped with a horizontally movable plate has been developed for observing thermohaline flow patterns. The design of the tank is described, and some of the salt-finger patterns formed in the tank are presented.     

Effects of springs on a pendulum electromechanical energy harvester

This paper studies a model of energy harvester that consists of an electromechanical pendulum system subjected to nonlinear springs. The output power is analyzed in terms of the intrinsic parameters of the device leading to optimal parameters for energy harvesting. It is found that in an appropriate range of the springs constant, the power attains higher values as compared to the case without springs. The dynamical behavior of the device shows transition to chaos.     

On oscillations of a frictional pendulum

Conditions are established under which a standard limit cycle occurs in the system under consideration, or the trajectory closes under the influence of a stagnation domain. It is pointed out that when the solution falls into the stagnation domain it makes no sense to use the asymptotic method because of a large error __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 104–112, February 2006.     

Damping in a parametric pendulum with a view on energy harvesting

The present article addresses the quantification of damping in a parametric pendulum, with a view on further applications in the design of energy harvesting devices. Detailed new experimental data is obtained for such purpose, and a novel mathematical model is presented. Linear and quadratic viscous damping and also dry friction are taken into account. To introduce the dry friction component, the pendulum axis is mounted on ball bearings. This is considered as a very realistic situation of a harvester. Damping parameters are determined by minimizing the difference between numerical and experimental time histories. It is shown that the damping model here presented is more adequate to replicate experiments than commonly used linear models, which consider only a linear viscous damping term characterized by means of free decay tests. It is also pointed that linear models are not adequate for refined studies, since they can lead to erroneous predictions of rotation zones, and consequently to wrong considerations in the design of pendulum harvesters.     

Cycloidal pendulum with a rolling cylinder

Free vibrations of a heavy homogeneous cylinder rolling in a cylindrical cavity whose directing curve is a brachistochrone are considered. The equation of motion of the cylinder is derived and the circular frequency of free vibrations of the cylinder center of mass is determined. An analogy between the cycloidal pendulum with a rolling cylinder and the classical cycloidal pendulum in the form of a material point is obtained.     

The characteristics of soil reaction forces on a single movable lug

In order to understand clearly the characteristics of the soil reaction forces on a single movable lug, the resultant of measured soil reaction forces was determined and presented along with its position on the lug plate. The resultant of soil reaction forces acting on the movable lug increased gradually and reached the maximum value when the lug was on about its lowest position in the soil, then it decreased without offering any downward resistance to the lug till the lug left the soil. The maximum resultant force of the movable lug was higher than that of a fixed lug. The point of action of the resultant force on the movable lug shifted in a similar way in all test cases, that is, it moves to the center of the lug from the outer tip until it reaches the position where it becomes the maximum, then it moves to the outer tip till the lug leaves the soil. The inclination angle of the resultant force increased with the decrease of lug inclination angle. The bigger lug sinkage of the movable lug produced bigger soil reaction forces and shifted the point of action of the resultant force from the tip part to the central part of the lug. However, there was no significant effect of the lug sinkage on the direction of the resultant force. The increase in lug slippage from 25% to 50% brought bigger soil reaction forces on the movable lug, but did not influence the direction and point of action of the resultant force.     

Experimental analysis of soil reaction on a lug of a movable lug wheel

A movable lug wheel was tested in a soil bin test apparatus to determine its traction performance and to measure the soil reaction forces on its lugs. Similar tests were also conducted using a fixed lug wheel. The effects of the lug motion pattern, lug spacing and horizontal load on pull and lift forces were studied. From the experiments it is confirmed that the movable action of the lug plate could generate superior pull and lift forces in comparison with the fixed lug wheel. Among the test wheels, lug motion pattern-2 generated the highest pull and lift forces. Within the range of the test conditions, there was no significant difference in pull and lift forces of the lug plate between the test lug wheels with 12 lugs and 15 lugs at the same level of horizontal and vertical loads. The increase of horizontal load up to 200 N generally increased the pull force and generated smaller rolling resistance before the lug left the soil, but did not increase the lift force significantly. The patterns of pull force, lift force and drawbar pull generated under a constant slip were slightly different from those under a constant horizontal load. Finally, the results were also elucidated by their actual lug trajectories in soil.     

Time-optimal swing-up feedback control of a pendulum

Time-optimal feedback control is obtained that brings a pendulum to the upper unstable equilibrium position. The solution is based on the maximum principle and involves analytical investigations combined with numerical computations. As a result, the switching and dispersal curves that bound the domains in the phase plane corresponding to different values of the optimal bang-bang control are constructed for various values of the maximal admissible control torque.     

Chaos in a pendulum with feedback control

We study chaotic dynamics of a pendulum subjected to linear feedback control with periodic desired motions. The pendulum is assumed to be driven by a servo-motor with small inductance, so that the feedback control system reduces to a periodic perturbation of a planar Hamiltonian system. This Hamiltonian system can possess multiple saddle points with non-transverse homoclinic and/or heteroclinic orbits. Using Melnikov's method, we obtain criteria for the existence of chaos in the pendulum motion. The computation of the Melnikov functions is performed by a numerical method. Several numerical examples are given and the theoretical predictions are compared with numerical simulation results for the behavior of invariant manifolds.     

Rotating a pendulum with an electromechanical excitation

The objective of this paper is showing investigation of pendulum rotations via vertical, non-linear electromechanical excitation generated using a RLC-circuit-powered solenoid, which is originally built for an electro-vibro-impact mechanism. Various non-linear phenomena of pendulum dynamics, namely period-1 rotation, period-1 oscillation and period-2 oscillation, have been observed experimentally from the proposed apparatus. A mathematical model has been developed for the experimental rig and the system parameters have also been identified for the mathematical model. Finally, numerical results have been generated using the developed mathematical model and identified parameters, and their correlations with experimental observations have been discussed.     

Parametric resonances in a base-excited double pendulum

Two parametrically-induced phenomena are addressed in the context of a double pendulum subject to a vertical base excitation. First, the parametric resonances that cause the stable downward vertical equilibrium to bifurcate into large-amplitude periodic solutions are investigated extensively. Then the stabilization of the unstable upward equilibrium states through the parametric action of the high-frequency base motion is documented in the experiments and in the simulations. It is shown that there is a region in the plane of the excitation frequency and amplitude where all four unstable equilibrium states can be stabilized simultaneously in the double pendulum. The parametric resonances of the two modes of the base-excited double pendulum are studied both theoretically and experimentally. The transition curves (i.e., boundaries of the dynamic instability regions) are constructed asymptotically via the method of multiple scales including higher-order effects. The bifurcations characterizing the transitions from the trivial equilibrium to the periodic solutions are computed by either continuation methods and or by time integration and compared with the theoretical and experimental results.     

一种新的"弹簧振子-单摆"耦合摆研究

介绍了一种新发现的"弹簧振子-单摆"耦合摆,采用拉格朗日方程推导出了耦合摆的运动微分方程.进一步根据耦合摆的实际参数,利用Matlab软件进行了数值计算,发现耦合摆的弹簧振子振幅与单摆的摆幅此消彼长,系统的能量在两者之间不断交换,呈周期性变化,与实际符合很好.通过作出耦合摆的轨迹图,发现与实际一致.最后,分析了耦合摆实现的条件.     

Wave action on a movable plate immersed into a fluid. Physical and numerical experiments

The effect of the motion of a rigid inclined plate immersed into a fluid counter incident waves is studied both experimentally and numerically. In the wave water channel experiments the velocity of a trolley with a plate running freely on rails is determined as a function of the wave parameters, the immersion depth, the angle of inclination, and the plate dimensions. The interaction between the traveling waves and the plate having a single translational degree of freedom along the horizontal axis is numerically calculated in the time-dependent, two-dimensional formulation. The dependence of the upwave motion effect on the parameters varied in the full-scale experiment is analyzed. In the numerical experiment a regime of the downwave plate motion at a constant high velocity is found to exist. The channel bottom effect is estimated and the behavior of the plate with a flap is studied.