Oscillations Of Mechanical Systems Research Articles

Nonlinear dynamics of milling processes

In this article, dynamics and stability of milling operations with cylindrical end mills are investigated. A unified–mechanics–based model, which allows for both regenerative effects and loss–of–contact effects, is presented for study of partial–immersion, high–immersion and slotting operations. Reduced–order models that can be used for certain milling operations such as full–immersion operations and finishing cuts are also presented. On the basis of these models, the loss of stability of periodic motions of the workpiece–tool system is assessed by using Poincare sections and the numerical predictions of stable and unstable motions are found to correlate well with the corresponding experimental observations. Bifurcations experienced by periodic motions of the workpiece–tool system with respect to quasi–static variation of parameters such as axial depth of cut are examined and discussed. For partial–immersion operations, consideration of both time–delay effects and loss–of–contact effects is shown to have a significant influence on the structure of the stability boundaries in the space of spindle speed and axial depth of cut. The sensitivity of system dynamics to multiple–regenerative effects, mode–coupling effects and feed rate is also discussed.

A piecewise-conserved constant of motion for a dissipative system

We discuss a piecewise-conserved constant of motion for a simple dissipative oscillatory mechanical system. The system is a harmonic oscillator with sliding (dry) friction. The piecewise-conserved constant of motion corresponds to the time average of the energy of the system during one half-period of the motion, and changes abruptly at the turning points of the motion. At late times the piecewise-conserved constant of motion degenerates to a constant of motion in the usual sense.

Control, State Estimation and Laboratory Experiments with Oscillatory Mechanical System

In the article a problem of mathematical models construction for oscillatory mechanical systems (OMS) with complex (chaotic) dynamics is considered. The mathematical model of system is constructed with application of the aggregative method. The device for OMS control with use of the computer is described. Verification of the obtained model on the basis of laboratory experiments results is made. Pulse-number algorithm of OMS control is offered and checked with use of laboratory set-up. State estimation recursive algorithm is proposed.

IMPACT RESPONSE AND THE INFLUENCE OF FRICTION

Non-smooth stiffness and damping characteristics are commonly encountered in mechanical systems. The specific physical contacts considered in this paper are impact and friction. Although these individual effects have been the subject of quite intensive research it is their interaction and influence on the dynamic behavior of a mechanical oscillatory system that is the subject of the current work. Dynamical systems theory is used as a conceptual framework and comparisons are made between numerical and experimental results over a relatively wide range of parameters.

Natural oscillations of mechanical systems and the spectral theory of self-adjoint operators

In this paper, the following assertion is illustrated with some examples. In practically all cases, the problem on natural oscillations for linear holonomic nondissipative mechanical systems reduces to the problem of determining eigenvalues and eigenelements of the corresponding self-adjoint operator acting in the Hilbert space generated by the quadratic form of the kinetic energy. Bibliography: 1 title.

Quantum Phenomena in Small Antiferromagnets

We show that the most characteristic properties of mesoscopic antiferromagnets can be explained in terms of the response on a spatially inhomogeneous perturbation. This concept allows to explain the dynamic properties (quantum resonance, coherence and tunnelling rates) as well as static perturbations which, for increasing size of au antiferromagnet, leads to a transition from the quantum mechanical oscillating system to a classical antiferromagnet with well defined Neel vectors.

Harmonic linearization of equations of forced oscillations of systems with dry-friction elements

A general method of the harmonic linearization of equations of forced oscillations of mechanical systems with dry-friction elements for arbitrary relationships between the intensity of the exciting forces and the limiting force of dry friction is explained. It is shown that the equation normally employed for harmonic linearization is valid only in the case when the limiting force of dry friction in the element is significantly lower than the reactive force that can be developed in the element in the absence of slip. A computational example for a system using a more precisely defined method of harmonic linearization is cited.

Chaotic oscillations in mechanical systems

Chaotic oscillations have now been observed in nonlinear mechanical systems using analytical, numerical, and experimental methods. Nevertheless, a more fundamental understanding of why and when such oscillations occur is of great importance. This goal will be pursued here by considering the relationship between chaos induced by forced oscillations versus self-excited oscillations, the relationship of indeterminancy of the final equilibrium state in the initial value problem to chaos in the sustained oscillation problem, comparison of theory to physical experiment, necessary and sufficient conditions for chaos to occur, and the question of convergence of systems of modal ordinary differential equations that derive from partial differential equations.

Chaotic oscillations in mechanical systems

Chaotic oscillations have now been observed in non-linear mechanical systems by analytical, numerical and experimental methods. Nevertheless a more fundamental understanding of why and when such oscillations occur is of great importance. This goal will be pursued here by considering the relationship between chaos induced by forced oscillations versus self-excited oscillations, the relationship of indeterminancy of the final equilibrium state in the initial value problem to chaos in the sustained oscillation problem, comparison of theory to physical experiment, necessary and sufficient conditions for chaos to occur, and the question of convergence of systems of modal ordinary differential equations which derive from partial differential equations.

Quantum Statistics of the Toda Oscillator in the Wigner Function Formalism

AbstractClassical and quantum mechanical Toda systems (Toda molecules, Toda lattices, Toda quantum fields) recently found growing interest as nonlinear systems showing solitons and chaos. In this paper the statistical thermodynamics of a system of quantum mechanical Toda oscillators characterized by a potential energy V(q) = Vo cos h q is treated within the Wigner function formalism (phase space formalism of quantum statistics). The partition function is given as a Wigner‐ Kirkwood series expansion in terms of powers of h2 (semiclassical expansion). The partition function and all thermodynamic functions are written, with considerable exactness, as simple closed expressions containing only the modified Hankel functions Ko and K1 of the purely imaginary argument iζ with ζ = Vo/kT.

Influence of exponentially correlated centered stationary process on oscillations of mechanical systems with one degree of freedom

Influence of exponentially correlated centered stationary process on oscillations of mechanical systems with one degree of freedom

Multiple frequency oscillations in mechanical systems, with one degree of freedom, when subjected to ?white light? through a linear filter, having only pairs of purely imaginary characteristic numbers

Multiple frequency oscillations in mechanical systems, with one degree of freedom, when subjected to ?white light? through a linear filter, having only pairs of purely imaginary characteristic numbers

Nonlinear oscillations of mechanical systems with dry friction

Nonlinear oscillations of mechanical systems with dry friction

Nonlinear oscillations of mechanical systems

Nonlinear oscillations of mechanical systems

The impact of cardiac activity on triaxially recorded endogenous microvibrations of the body.

The influence of cardiac activity on the endogenous microvibrations of the body (MV) was studied in a total of 37 young, healthy subjects. The force oscillations and the rectified and integrated force-time function in the three space directions were simultaneously recorded with the ECG and the arterial pulse during quiet bipedal standing before (control) and after isoprenaline inhalation, a work load of 150 W, and mild cold stress. In the vertical force component (Fz) 27 out of the 37 subjects showed cardiac characteristics similar to the ballistocardiogram. After isoprenaline or exercise, all 37 subjects showed these cardiac characteristics in Fz, and the maximal amplitudes as well as the rectified impulse values were increased in the three directions, but particularly in the z-axis. The propagation of the MV through the body was independent of the arterial pulsation. The increase in muscle tone due to cold stress led to a significant increase of the rectified impulse only in the sideward direction (SY). It is concluded that the triaxially recorded MV arise from cardiac activity, mainly reflected in the vertical (z) axis, and from skeletal musculature representing a mechanical oscillating system with varying material constants (muscle tension, inertial forces, etc.).

Results of an investigation of an optoelectronic dynamic capacitor

Of the high-resistance modulators used in instruments for measuring small currents with input-signal transformation, the dynamic capacitor [I] is closest in its characteristics to an ideal modulator. However, the serious drawbacks of the dynamic capacitor are the low modulation frequency (usually not greater than 500 Hz), due to the mechanical oscillatory system, and also the re]atively large dimensions and mass.

Oscillations of mechanical systems that do not become linear when the parameter vanishes: PMM vol. 42, no. 6, 1978, pp. 1039–1048

The results of investigations in [1] are extended to multidimensional systems that become nonlinear at μ = 0. Two-dimensional mechanical systems were investigated in [2,3]. The characteristic equations of systems considered here contain in the critical system either a pair of pure imaginary roots or two zero roots with one or two groups of solutions and n roots with negative real parts in the adjoint system. It is shown that the investigation of such systems necessitates the imposition on the system of some constraints that supplement those specified in [1], The auxilliary function u (1) k ( θ) used in the determination of Liapunov's function is derived by a different method than in [1 – 3], In two of the three investigated cases the problem is reduced to the determination of roots of some integral real irrational function. An example is presented.

Anisotropy of KDP crystals containing traces of impurities

The magnetic properties of KDP crystals were experimentally investigated by measuring the torsional rigidity of a high-quality mechanical oscillating system in a magnetic field. It is shown that real KDP crystals, grown in laboratory and factory conditions, specially purified or containing traces of impurities (not more than 10−3 mole %), exhibit magnetic anisotropy. A relation is found between the anisotropy of the magnetic susceptibility (Δχ) and the magnetic field. The magnetic fields where Δχ becomes constant (H ≥ 400 Oe) were determined. The values of Δχ at these fields for different KDP specimens did not exceed 3·10−8. The method can be used to determine the magnetic anisotropy of any dielectric substance.

Problems of the dissipation of energy in oscillations. The 10th Conference on Problems of the Dissipation of Energy in the Oscillations of Mechanical Systems

Problems of the dissipation of energy in oscillations. The 10th Conference on Problems of the Dissipation of Energy in the Oscillations of Mechanical Systems

The Method of Averaging and Domains of Stability for Integral Manifolds

Liapunov’s direct method is a standard and effective approach to computing the domain of stability (or region of attraction) of an autonomous ordinary differential equation. In this paper the author investigates domains of stability of integral manifolds of solutions generated by nonlinear mechanical and electrical oscillatory systems with many degrees of freedom. These manifolds are families of solutions that exhibit stronger stability properties than individual solutions. The problem of estimating the domain of stability of an asymptotically stable integral manifold is reduced to computing the domain of stability of an associated autonomous system of differential equations. This is done by applying the method of averaging to the system generating the integral manifold thus removing angular and time dependences. The stability region of this associated system is then computed and a result is established showing that this region is contained in the stablity region of the original system. Several examples, ...