Fractal equation of motion of a non-Gaussian polymer chain: investigating its dynamic fractal response using an ancient Chinese algorithm.

The mechanical response of dielectric elastomers can be influenced or even controlled by an imposed electric field. It can, for example, cause mechanical stress or strain without any applied load; this phenomenon is referred to as electrostriction. There are many purely phenomenological hyperelastic models describing this electroactive response of dielectric elastomers. In this contribution, we propose an electromechanical constitutive model based on molecular chain statistics. The model considers polarization of single polymer chain segments and takes into account their directional distribution. The latter results from non-Gaussian chain statistics, taking finite extensibility of polymer chains into account. The resulting (one-dimensional) electric potential of a single polymer chain is further generalized to the (three-dimensional) network potential. To this end, we apply directional averaging on the basis of numerical integration over a unit sphere. In a special case of the eight-direction (Arruda–Boyce) model, directional averaging is obtained analytically. This results in an invariant-based electroelastic constitutive model of dielectric elastomers. The model includes a small number of physically interpretable material constants and demonstrates good agreement with experimental data, with respect to the electroactive response and electrostriction of dielectric elastomers.

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A NOTE ON THE MODE COUPLING THEORY OF POLYMER MELT DYNAMICS

Modern Physics Letters B ◽

10.1142/s0217984990001124 ◽

1990 ◽

Vol 04 (14) ◽

pp. 913-916 ◽

Cited By ~ 10

Author(s):

KYOZI KAWASAKI

Keyword(s):

Potential Energy ◽

Polymer Chain ◽

Mode Coupling ◽

Polymer Melt ◽

Equation Of Motion ◽

Coupling Theory ◽

Mode Coupling Theory ◽

The Matrix

The mode coupling theory of polymer melt dynamics put forward recently by Schweizer is combined with the curvilinear displacement invariance of the potential energy. The resulting equation of motion of a tagged polymer chain is shown to be consistent with the reptation picture when the matrix surrounding the tagged chain is frozen.

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Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain

Physical Review E ◽

10.1103/physreve.99.052502 ◽

2019 ◽

Vol 99 (5) ◽

Cited By ~ 4

Author(s):

Vahid Morovati ◽

Roozbeh Dargazany

Keyword(s):

Polymer Chain ◽

Single Polymer Chain ◽

Non Gaussian

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Non-Gaussian additive and multiplicative noise-induced chaos in the lateral vibration of a viscoelastic plate: A fully analytic approach

Journal of Vibration and Control ◽

10.1177/1077546320971379 ◽

2020 ◽

pp. 107754632097137

Author(s):

Ali Reza Asnafi

Keyword(s):

Analytical Approach ◽

Multiplicative Noise ◽

Chaotic Behavior ◽

Viscoelastic Plate ◽

Equation Of Motion ◽

Lateral Vibration ◽

Bounded Noise ◽

Noise Characteristics ◽

Additive And Multiplicative Noise ◽

Non Gaussian

In this study, the chaotic behavior of a viscoelastic plate under integrated non-Gaussian additive and multiplicative bounded noise is investigated with an analytical approach. First, the governing equation of motion of the system was derived by introducing a set of dimensionless parameters. After that, the modified version of Melinkov’s function in terms of statistical indices was obtained, and then, for a spectrum of bounded noises, the boarder curves of chaotic areas were obtained. The model of sine/cosine Wiener was chosen for the bounded noise which enables the researcher to produce a range of wide and narrowband noises. For the case that the excitation is only additive, or only multiplicative, and that both excitations exist simultaneously, the effect of variations in structural properties and noise characteristics on the chaos area were investigated. It was shown that at frequencies close to the natural frequency of the corresponding linear system, narrowband excitations affected the chaotic behavior more than the wideband ones and vice versa. To validate the results, a numerical simulation was also made.

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