On viscoelasticity and methods of measuring dynamic mechanical properties of linear viscoelastic solids

Representation of viscoelastic characteristics -- Measurement of dynamic mechanical properties of materials -- The vibrating reed test -- Experimental determination of the complex young's modulus of solid plastics -- Method and theory -- Vibrating reed apparatus -- Results and discussion -- Experimental determination of the complex poisson's ratio of solid plastics -- Method -- Apparatus and technique -- Results and discussion

The Nonstationary Effects On A Softening Duffing Oscillator

This paper presents a numerical study for the bifurcations of a softening Duffing oscillator subjected to stationary and nonstationary excitation. The nonstationary inputs used are linear functions of time. The bifurcations are the results of either a single control parameter or two control parameters that are constrained to vary in a selected direction on the plane of forcing amplitude and forcing frequency. The results indicate: 1. Delay (memory, penetration) of nonstationary bifurcations relative to stationary bifurcations may occur. 2. The nonstationary trajectories jump into the neighboring stationary trajectories with possible overshoots, while the stationary trajectories transit smoothly. 3. The nonstationary penetrations (delays) are compressed to zero with an increasing number of iterations. 4. The nonstationary responses converge through a period-doubling sequence to a nonstationary limit motion that has the characteristics of chaotic motion. The Duffing oscillator has been used as an example of the existence of broad effects of nonstationary (time dependent) and codimensional (control parameter variations in the bifurcation region) inputs which markedly modify the dynamical behavior of dynamical systems. © 1994

Non-Stationary Responses Of Self-Excited Driven System

This is the first attempt to determine the effects of a broad range of linear non-stationary regimes related to the frequencies of external excitation v(t) ranging from evolving to robust, on dynamic responses of self-excited systems, governed by the Van der Pol differential equation. The results obtained, time histories and phase plane plots, are revealing. Because of continuous variations of v(t), a representative point in the (v, K) plane, where K is the amplitude of excitation, continually crosses various regions and boundaries of periodic, aperiodic, stable, and unstable system motions, thus exhibiting a variety of new dynamic forms, which lead in some cases to a possible chaotic motion. The non-stationary responses are sensitive to the sweep rates α: the faster the sweep, the earlier are the appearances of new waveforms (patterns) and the shorter are the time intervals between the changed patterns. The responses are also sensitive to the variations of other system parameters: ε{lunate}, which indicates the degree of non-linearity; K, amplitude of external excitation; σ, detuning, and σ0, initial (t=0) detuning; and p0, initial amplitude of the response. The Rayleigh-Van der Pol oscillator is the basis of a model for a number of physical, biological, chemical, and engineering phenomena. This paper is an initial contribution to further theoretical and applied studies in non-stationary processes. © 1990

The Effects Of Non-Stationary Processes On Chaotic And Regular Responses Of The Duffing Oscillator

This paper deals with the effects of non-stationary regimes on stationary chaotic motions and non-linear attractors: (1) linear variations of the excitation frequency, v = vin0 + αvt, and the amplitude B = B0 + αBt; (2) cyclic variations of the excitation frequency, v = v0 + γ sin αct. It was shown in (1) that for very small values of αv or αB, i.e. for slow sweeps, the non-stationary responses initially coincide with the stationary chaotic, but then they depart. The faster the sweep, the earlier is the departure from the stationary and from other non-stationary responses. An observation is made that for sufficiently fast sweeps, the initially chaotic motion may be changed into a structured one. In (2) initially stationary chaotic motion is changed instantaneously to another type of motion. The stationary attractors transit into different attractors. Many dynamic phenomena in the real world are modelled mathematically by the non-stationary Duffing differential equation. This paper presents the first attempt to apply non-stationary processes to chaotic motion. It is the objective of this study to contribute to the theory of dynamics and technical design. © 1990

Nonstationary Process: Nonstationary Bifurcation Maps, Evolutionary Dynamics

The study presented in this paper is one of a series of papers published by the authors on nonstationary problems. It addresses itself to the characterization of the types of dynamical responses and their ranges contained in the time flow of the Duffing nonlinear, nonstationary, dissipative, forced oscillator. A new effective method - a Nonstationary Bifurcation Map (EI-Lu map) - has been introduced by the authors that allows us to do precisely this. This new technique is by far more advantageous than the customary methods in use: the phase portrait or Poincare maps. The latter may give inadequate information because of the overlapping dynamical responses contained within ranges of time. The main feature of nonstationary processes is that the nonstationary responses are transient. The phenomena of the transiency are presented in detail. Significant cases are those when the non-stationary transmission of the signals crosses different nonstationary bifurcation boundaries. This is significant because most of dynamical-biological activities occur in the regions between order and chaos. It characterizes nonstationary dynamical processes. The possibility of constructing responses for arbitrary small nonstationary inputs may be used as nonstationary perturbations, replacing customary perturbations of integrable Hamiltonians

Transitions Through Period Doubling Route To Chaos

The Duffing driven, damped, \u27softening\u27 oscillator has been analyzed for transition through period doubling route to chaos. The forcing frequency and amplitude have been varied in time (constant sweep). The stationary 2T, 4T...chaos regions have been determined and used as the starting conditions for nonstationary regimes, consisting of the transition along the Ω(t) = Ω0± α/2 t, f ≡ const., Ω-line, and along the E-line: Ω(t) = Ω0 ± α/2 t; f(t) = f0 ± α/2 t. The results are new, revealing, puzzling and complex. The nonstationary penetration phenomena (delay, memory) has been observed for a single and two-control nonstationary parameters. The rate of penetrations tends to zero with increasing sweeps, delaying thus the nonstationary chaos relative to the stationary chaos by a constant value. A bifurcation discontinuity has been uncovered at the stationary 2T bifurcation: the 2T bifurcation discontinuity drops from the upper branches of (a,Ω) or (a,f) curves to their lower branches. The bifurcation drops occur at the different control parameter values from the response χ(t) discontinuities. The stationary bifurcation discontinuities are annihilated in the nonstationary bifurcation cascade to chaos-they reside entirely on the upper or lower nonstationary branches. A puzzling drop (jump) of the chaotic bifurcation bands has been observed for reversed sweeps. Extreme sensitivity of the nonstationary bifurcations to the starting conditions manifests itself in the flip-flop (mirror image) phenomena. The knowledge of the bifurcations allows for accurate reconstruction of the spatial system itself. The results obtained may model mathematically a number of engineering and physical systems