Multi-parametric Dynamic Analysis of a Rolling Bearings System

A method for calculating amplitudes and constructing frequency characteristics of forced and self-excited vibrations of a rotor-fluid-foundation system on rolling bearings with a non-linear characteristic based on the method of complex amplitudes and harmonic balance has been developed. Non-linear equations of motion of the rotor-fluid-foundation system are derived, and analytical methods of their solution are presented. Frequencies of fundamental and ultra-harmonic resonances are determined. The intervals between self-oscillation frequencies are estimated. The dependence of amplitudes on the amount of fluid in the rotor cavity, the mass of the foundation, linear imbalance, the value of the stiffness coefficient, and the damping coefficient is shown.

Homotopy Perturbation Analysis in an energy transit problem closed to a Stretching Surface

Present study explored the influence of stretching constraint in addition with inclusion of energy.An analytical solution for the system of non-linear equations of motion is worked out by adopting HomotopyPerturbation method (HPM). Physical and graphical reflections various parameters are demonstrated in thepresent problem. Utility of this model has been perceived in diverse industrial and chemical processes.2010 AMS subject classification: 76W05

Nonlinear vibration absorbers for ropeway roller batteries control

This work investigates a nonlinear passive control strategy designed to reduce the peak accelerations in ropeway roller batteries systems by deploying an array of nonlinearly visco-elastic vibration absorbers. The control effectiveness is compared with that of an equivalent array made of linearly visco-elastic absorbers. A nonlinear parametric model describing the interactions between the different parts of this mechanical multibody system previously developed by the present authors is here extended to include the passive vibration control system aimed to mitigate the acceleration peaks induced by the vehicles transit at different operational speeds. To this aim, a set of linearly visco-elastic vibration absorbers is first optimized through the Differential Evolution (DE) algorithm seeking to minimize the area below the frequency-response curves of the linear equations of motion. Then, a new group of nonlinearly visco-elastic absorbers, that can be largely tuned (i.e., they can exhibit either softening or hardening behaviors), is proposed to mitigate the accelerations induced in the roller by the vehicle transit. These nonlinearly visco-elastic absorbers are optimized by means of the DE algorithm and comparisons with the control achieved by the linear absorbers are carried out to show the higher performance of the proposed nonlinear device. A possible design of the nonlinearly visco-elastic absorber, based on the hysteresis of a wire rope assembly undergoing flexural cycles, is also proposed and discussed.

The strange instability of the equatorial Kelvin wave

<p>The Kelvin wave is perhaps the most important of the equatorially trapped waves in the terrestrial atmosphere and ocean, and plays a role in various phenomena such as tropical convection and El Nino. Theoretically, it can be understood from the linear dynamics of a stratified fluid on an equatorial β-plane, which, with simple assumptions about the disturbance structure, leads to wavelike solutions propagating along the equator, with exponential decay in latitude. However, when the simplest possible background flow is added (with uniform latitudinal shear), the Kelvin wave (but not the other equatorial waves) becomes unstable. This happens in an extremely unusual way: there is instability for arbitrarily small nondimensional shear <em>λ</em>, and the growth rate is proportional to exp(-1/λ^2) as λ → 0. This in contrast to most hydrodynamic instabilities, in which the growth rate typically scales as a positive power of λ-λ<sub>c</sub> as the control parameter λ passes through a critical value λ<sub>c</sub>.</p><p>This Kelvin wave instability has been established numerically by Natarov and Boyd, who also speculated as to the underlying mathematical cause by analysing a quantum harmonic oscillator perturbed by a potential with a remote pole. Here we show how the growth rate and full spatial structure of the Kelvin wave instability may be derived using matched asymptotic expansions applied to the (linear) equations of motion. This involves an adventure with confluent hypergeometric functions in the exponentially-decaying tails of the Kelvin waves, and a trick to reveal the exponentially small growth rate from a formulation that only uses regular perturbation expansions. Numerical verification of the analysis is also interesting and challenging, since special high-precision solutions of the governing ordinary differential equations are required even when the nondimensional shear is not that small (circa 0.5). </p>

Dynamics and rigidity of a manipulator with three DOFs

The problem of dynamic elastic four-link initial kinematic chain (IKC) of the load-bearing manipulator, which is the basis for various modifications are considered. Using the Lagrange operator for this system, equations of motion in matrix form are obtained. To determine the potential energy of an elastic four-link IKC manipulator, we use the formula for the elastic potential energy of a rectilinear homogeneous rod of length l. The cross-section of the rod is considered annular or circular. Solving the system of linear equations of motion on a computer using the ADAMS program, the results of the movement of links and cargo were obtained. Kinematics and dynamics are presented for a generic 3 DOFs Initial Kinematic Chain; with anthropometric data and the dynamics equations, simulations were performed to understand its behavior.

Dynamic analysis of vibration-driven systems moving based on frictional locomotion principles

In this article, we investigate the dynamic analysis of vibration-driven systems moving based on frictional locomotion principles. Symmetrically actuating particles with longitudinal harmonic forces or with longitudinal vibration of the base does not lead to the net motion, unless the generated slip varies during back and forth motion. Harmonically varying the normal contact force and employing asymmetric friction coefficients are two approaches for obtaining frictional locomotion principles. In order to study the simultaneous effect of these required conditions of generating net displacement, a mathematical model is developed, and the resulting non-linear equations of motion are analytically solved. We have shown that the proposed model can be simply generalized to many other frictional, vibration-induced principles, such as the friction drive and the directional friction concepts. The obtained results are in good agreement with those achieved from numerical integration and experiments, reported in the literature. The presented theoretical findings can be effectively used for the design and control of this type of oscillators.

A Floating-Frame-of-Reference Formulation for Deformable Rotors Using the Properties of Free Elastic Vibration Modes

Formulations in rotordynamics are usually based on the assumption that the displacements of the bearings of the rotor are small, such that, besides the axial rotation, no large rigid-body motions have to be taken into account. This results in linear equations of motion with gyroscopic terms. When the axial angular speed of a rotor is increased, however, as well as for rapidly changing transient conditions, a non-linear coupling between the large axial rotation and the small rigid body motion induced by the compliance of the bearings and the small elastic deformation of the rotor body itself is to be expected. It is the scope of the present contribution to present a rational strategy for dealing with this situation. First, we present a problem-oriented version of the floating-frame-of-reference formulation (FFRF). We use a co-rotating rigid rotor as reference configuration, which allows using linear modes of the non-rotating elastic rotor as Ritz approximations. The position vector of the origin of a body-fixed coordinate system and three suitable Bryant angles are used as rigid body coordinates, and free elastic modes of the rotor are considered as elastic Ritz approximations. The properties of the latter and their consequences upon simplifying the necessary spatial integrals in the FFRF are addressed in some detail. The free modes are obtained from a Finite Elements pre-processing of the elastic rotor body. The non-linear equations of motion of the rotor are obtained afterwards by means of symbolic computation This formulation leads to a set of relations, in which the rigid-body degrees of freedom need not to be small, and which is integrated using an implicit scheme. Results for a rotor with unbalance forces, accelerated by external forces and having linear visco-elastic bearings are successfully compared to a commercial multi-body dynamics code.

MANY-BOSON DYNAMIC CORRELATIONS

In this paper we present an overview of a systematic development of the linear equations of motion for a dynamically correlated wave function that moves beyond the previous theories that include time-dependent pair correlations at most. We argue that these time-dependent pair correlations are insufficient to describe important physical effects in the energy/momentum regime of the 4 He roton; minimally, time-dependent three-body correlations are necessary to capture the relevant physics. For simplicity we illustrate this on the problem of atomic impurities in 4 He .