Bifurcation analysis of a double pendulum with internal resonance

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Periodic solution and chaotic behavior of a class of nonautonomic pendulum systems with large damping

In this paper the existence and uniqueness of the periodic solution is studied for a class of second order nonautonomic pendulum aystems x + ax + ψ(t)sinx=F(t) anil the parameter regions tor which the system in chaos is myestigated when ψ(t)=1-ελcosωt, F(t)=β +εμ(cosωt-ωsinωt) and the tamping coefficient a>0 is large. The result obtained generalize the corresponding conclusions of papers [1-8].     

Stability of the stationary motion of a spherical pendulum interacting with a string

The equation of motion of a spherical pendulum suspended at some point of a horizontal string is derived using a hybrid model of this mechanical system. The conditions for the asymptotic stability of the stationary motion of the spherical pendulum interacting with the elastic string are established     

Experimental studies of the postbuckling behavior of complete spherical shells

In experiments performed on elastic, complete spherical shells of large radius-to-thickness ratio, pressure and volume-displacement instrumentation and photography were used to study postbuckling behavior. Photographs of a number of the distinct modes observed are presented.     

On damping properties of a frictionless physical pendulum with a moving mass

The damping effects are generated in a frictionless oscillating physical pendulum by a continuous motion of an auxiliary mass. The main parameters affecting the damping properties of the pendulum-mass system are identified. In particular, the effective damping ratio for a cycle is introduced and derived in a closed form from the energy considerations and then independently from Mathieu's equation. It is shown that a continuous damping can be achieved if the mass motion is synchronized with the pendulum rotation. Otherwise the system becomes prone to ‘beating’ phenomenon. The results presented may be useful for design of active control strategy of autonomous systems with negligible passive damping.     

Dynamics of the shift in resonance frequency in a triple pendulum

We propose a general model for pendular systems with an arbitrary number of links arranged sequentially. The form of this model is easily adaptable to different settings and operating conditions. The main subject of analysis is a system obtained as a specific case taken from the general analysis, a three-links pendulum with damping subject to periodic perturbation. We performed a theoretical analysis of the frequency response and compared it with results from temporal integration. Moreover, a law was obtained explaining the behavior of the shift of the resonant frequencies due to a change in a parameter.     

Estimation of parameters of various damping models in planar motion of a pendulum

Meccanica - In this work, planar free vibrations of a single physical pendulum are investigated both experimentally and numerically. The laboratory experiments are performed with pendula of...     

Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Nonlinear Dynamics - This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the...     

Ultimate deformation behavior of a laminated spherical shell

Summary A solution method is developed for a laminated spherical shell, subject to uniform normal tractions or constant radial displacements on the boundary. Displacements and stresses in the shell can be obtained from the solution formulas, which are as simple as those for homogeneous spherical shells. These formulas are accurate when the thicknesses of the constituent spherical layers are small in comparison with the radii of the shell, and become exact in case these thicknesses tend to zero under a fixed overall shell thickness. The solution is obtained mainly by exactly treating the product of an infinitely large number of matrices which link the displacements and stresses in different constituent spherical layers. A continuous analysis and a number of numerical results are provided to validate this development. Received 4 December 1996; accepted for publication 12 September 1997     

Periodic, quasiperiodic and chaotic behavior of a driven Froude pendulum

An investigation of the dynamic behavior of a driven Froude pendulum is carried out. Numerical solutions of a highly non-linear Froude pendulum are developed by making use of the piecewise-constant procedure. Periodic, quasiperiodic and chaotic motions of the pendulum are distinguished by making use of the criterion of periodicity ratio and are graphically demonstrated for varying system parameters and different initial conditions. Periodic and quasiperiodic routes to chaos are analyzed on the basis of period–quasiperiodic–chaotic diagrams.     

Motion of a spherical particle under the influence of osmotic forces

One of the basic mechanisms through which biological cells preserve the consistency of their structure is the regulation of material exchange between cell and surrounding medium. The regulation is performed by a thin semipermeable membrane surrounding the cell; it passes some materials freely, while allowing only slight transmission of others, or completely blocking passage. Water shows the maximum penetrating power. If there exists on both sides of the membrane an aqueous solution of some material which does not penetrate the membrane, then under the influence of osmotic pressure water flows into that region where the material concentration is higher, as long as the difference in hydrostatic pressure does not suppress the motion [1, 2]. The viscous flow which develops may lead to displacement of a particle.     

捷联惯组减振系统角振动、线振动共振频率理论分析

当前实际工程中,角振动试验技术和设备尚不成熟。以指导捷联惯组减振系统设计过程为目的,结合捷联惯性组合减振系统对角共振频率的特殊要求,对线振动、角振动共振频率的关系进行了分析与讨论。建立了捷联惯性组合减振系统的动力学模型,得到了捷联惯组减振系统数学模型,利用刚体动力学方法分析捷联惯组的转动惯量和回转半径,得出理想情况下捷联惯性组合减振系统线共振、角共振频率存在一定的比例关系,并与减振器安装中心到转动中心线的平均距离和惯组回转半径有关的结论。最后讨论了改变减振系统刚度和减振器布置方式两种改变共振频率的方法,并对两种方法进行了比较。     

Stochastic resonance in a harmonic oscillator with damping trichotomous noise

In this paper, the phenomenon of stochastic resonance (SR) in a prototype fluctuating damping harmonic oscillator with trichotomous Markovian noise is investigated. The exact expression of output amplitude gain has been calculated using the well-known Shapiro–Loginov formula. The phenomenon of SR has been found in a broad sense—that is, the non-monotonic behavior of output amplitude gain as a function of noise parameters. Then the influences of noise amplitude, noise switching rate, and noise flatness on the output amplitude gain have also been discussed. Finally, the reverse resonance phenomenon has been presented.