Viscoelastic Oscillator Research Articles

Generalization of KCC-theory to fractional dynamical systems and application to viscoelastic oscillations

As a geometrical method for analyzing the stability of dynamical systems, Kosambi–Cartan–Chern (KCC)-theory determines the Jacobi stability of a perturbation given to a trajectory based on the deviation curvature tensor. In this study, KCC-theory is generalized to dynamical systems with fractional derivatives, and the deviation curvature tensor is obtained from the fractional differential equation under the condition that the order of the fractional derivatives is close to an integer. Fractional KCC-theory is then applied to a one-dimensional spring–mass–damper model in which the damping force is expressed as a fractional derivative. In this case, three solution types are obtained depending on the damping coefficient and the fractional derivative order. One is damped oscillation with overshoot, which also appears in models with integer order derivatives, and another is damped oscillation without overshoot. The remaining one is overdamping, which neither oscillates nor overshoots. The deviation curvature tensor obtained from the fractional oscillatory model shows that both the damped oscillation without overshoot and the overdamping are Jacobi stable. When a discontinuous Jacobi instability appears on the solution curve, the solution type is classified as damped oscillation with overshoot. This result indicates that damped oscillation with overshoot and other solutions can be classified according to Jacobi stability.

Response analysis of the vibro-impact system under fractional-order joint random excitation

As a kind of good damping material, viscoelastic material is widely used in machinery, civil engineering, and other fields. In this paper, the viscoelasticity of the system is described by fractional differentiation. The dynamic response of a unilateral vibro-impact system with a viscoelastic oscillator under joint random excitation is studied, in which joint random excitation is composed of additive and multiplicative white noise. The fractional-order derivative was calculated based on Caputo’s definition, and the fractional derivative was equivalent to the corresponding linear damping force and linear restoring force. As a result, a new random system without fractional-order terms was obtained. A non-smooth transformation was introduced, which was equivalent to the original system to a new system without a velocity jump. The steady-state probability density functions of fractional-order vibro-impact systems under joint random excitation are solved by using the random average method and non-smooth transformation. In addition, the effects of parameters on the steady-state response of the system are analyzed.

Dynamics of a Flexible Disk Rotor under a Point Contact with Discrete Viscoelastic Oscillation Limiters

Dynamics of a Flexible Disk Rotor under a Point Contact with Discrete Viscoelastic Oscillation Limiters

Numerical simulation of tasks of vertical viscoelastic oscillation of suspension systems of frame, engine, cabin and seat

The analysis of the structures of the springing systems of modern vehicles showed that polymer composites are used in vehicles for which the decrease in curb weight is a critical indicator. The use of springs (suspensions) from polymer composites makes it possible to reduce the weight of the elastic element and increase durability while improving the smoothness of movement, reducing noise, and increasing traffic safety. When replacing the steel suspension with a polymer composite suspension, the mass of unsprung parts of the car decreases, and the economic performance of wheeled vehicles improves. The article discusses the problem of vertical viscoelastic oscillations of the suspension systems of the skeleton, engine, cabin, and seat. When considering the suspension's rheological properties, the Boltzmann-Volterra integral model is used. The Koltunov-Rzhanitsyn nucleus is used as a nucleus, which has weakly singular features of the Abel type. The system of integro-differential equations describing the studied process is solved by a method based on the use of quadrature formulas. The effect of the parameters of the hereditary-deformable properties of the suspension on the vibration shape is shown.

Numerical modeling of nonlinear viscoelastic vibrations of vehicles

Nonlinear viscoelastic oscillations of a vehicle in a vertical direction excited by static imbalance are considered. When taking into account the rheological properties of the suspension material and spring, the Boltzmann-Volterra principle was used. Mathematical models of the problem under consideration are obtained, which are described by systems of nonlinear integro-differential equations. A solution method based on quadrature formulas has been developed, and a computer program has been compiled on its basis. The results obtained are reflected in graphs. The influence of the material's rheological properties and the nonlinear characteristics of the suspension and spring on the amplitude and frequency of vertical vibrations of vehicles was investigated.

Fluidisation of yield stress fluids under vibration

<h2>Abstract</h2> Motivated by the industrial processing of chocolate, we study experimentally the fluidisation of a sessile drop of yield-stress fluid on a pre-existing layer of the same fluid under vertical sinusoidal oscillations. We compare the behaviours of molten chocolate and Carbopol which are both shear-thinning with a similar yield stress but exhibit very different elastic properties. We find that these materials spread when the forcing acceleration exceeds the same threshold which is determined by the initial deposition process. However, the height reduction due to spreading is typically at least three times greater in chocolate than in Carbopol under similar forcing. Moreover, the two materials exhibit very different spreading behaviours: whereas chocolate exhibits slow long-term spreading, the Carbopol drop rapidly relaxes its stress by spreading to a new equilibrium shape with an enlarged footprint. This spreading is insensitive to the history of the forcing. In addition, the Carbopol drop performs large-amplitude oscillations with the forcing frequency, both above and below the threshold. We investigate these viscoelastic oscillations and provide evidence of complex nonlinear viscoelastic behaviour in the vicinity of the spreading threshold. In fact, for forcing accelerations greater than the spreading threshold, our drop automatically adjusts its shape to remain at the yield stress. We discuss how our vibrated-drop experiment offers a new and powerful approach to probing the yield transition in elastoviscoplastic fluids.

A new mechanism of viscoelastic fluid for enhanced oil recovery: Viscoelastic oscillation

This report summarizes our recent experimental findings [Xie et al., Phys. Rev. Lett., 2022] and pore-scale simulation results [Xie et al., Phys. Rev. Fluids., 2020] on viscoelastic oscillation, which is a new observation of viscoelastic instability in the multiphase flow state. The viscoelastic oscillation causes trapping of droplets in contraction-expansion micro-channels regardless of the injection rate. Based on the force balance analysis on the viscous, capillary and elastic forces, the oscillation amplitude is found to linearly increase with viscoelasticity, and the trapped droplet size is determined by the elasto-capillary number. The oscillation also helps to extract droplets from their originally trapped positions such as dead-ends once a critical Deborah number is reached. These results successfully explain the phenomenon that the alternative injection of viscoelastic and inelastic fluids continually produces additional oil, indicating that the viscoelastic oscillation is a new important mechanism of viscoelastic fluid for enhanced oil recovery. Cited as: Xie, C., Xu, K., Qi, P., Xu, J., Balhoff, M. T. A new mechanism of viscoelastic fluid for enhanced oil recovery: Viscoelastic oscillation. Advances in Geo-Energy Research, 2022, 6(3): 267-268. https://doi.org/10.46690/ager.2022.03.10

Stochastic Response of Nonlinear Viscoelastic Systems with Time-Delayed Feedback Control Force and Bounded Noise Excitation

In this paper, an approximate analytical procedure is proposed to derive the stochastic response of nonlinear viscoelastic systems with time-delayed feedback control force and bounded noise excitation. The viscoelastic force and the time-delayed control force depend on the past histories of the state variables, which will result in infinite-dimensional problem in theoretical analysis. To resolve these difficulties, the viscoelastic force and the time-delayed control force are approximated by the current state variable based on the quasi-periodic behavior of the systematic response. Then, by using the stochastic averaging method for strongly nonlinear systems subjected to bounded noise excitation, an averaged equation for the equivalent system is derived. The Fokker–Plank–Kolmogorov (FPK) equation of the associated averaged equation is solved to derive the stochastic response of the equivalent system. Finally, two typical nonlinear viscoelastic oscillators are worked out and the results demonstrated the effectiveness of the proposed procedure. By utilizing the quasi-periodic behavior and stochastic averaging method of the strongly nonlinear system, the time-delayed control force and the viscoelastic terms can be simplified with equivalent damping force and equivalent restoring force and the resonant response under bounded noise excitation can be obtained analytically. The numerical results showed the accuracy of the proposed method.

Fluidisation of yield stress fluids under vibration

Motivated by the industrial processing of chocolate, we study experimentally the fluidisation of a sessile drop of yield-stress fluid on a pre-existing layer of the same fluid under vertical sinusoidal oscillations. We compare the behaviours of molten chocolate and Carbopol which are both shear-thinning with a similar yield stress but exhibit very different elastic properties. We find that these materials spread when the forcing acceleration exceeds the same threshold which is determined by the initial deposition process. However, the height reduction due to spreading is typically at least three times greater in chocolate than in Carbopol under similar forcing. Moreover, the two materials exhibit very different spreading behaviours: whereas chocolate exhibits slow long-term spreading, the Carbopol drop rapidly relaxes its stress by spreading to a new equilibrium shape with an enlarged footprint. This spreading is insensitive to the history of the forcing. In addition, the Carbopol drop performs large-amplitude oscillations with the forcing frequency, both above and below the threshold. We investigate these viscoelastic oscillations and provide evidence of complex nonlinear viscoelastic behaviour in the vicinity of the spreading threshold. In fact, for forcing accelerations greater than the spreading threshold, our drop automatically adjusts its shape to remain at the yield stress. We discuss how our vibrated-drop experiment offers a new and powerful approach to probing the yield transition in elastoviscoplastic fluids.

Nonlinear viscoelastic oscillations of single-mass system at power excitation

Nonlinear oscillations of single-mass system at force excitation of vibration connected with fixed base by weightless viscoelastic spring are considered. To take into account the rheological properties of the spring material, the Boltzmann-Volterr principle was used. Mathematical models of the problem in question are obtained, which are described by nonlinear integro-differential equations. A solution method based on the use of quadrature formulas has been developed and a computer program has been compiled on its basis, the results of which are reflected in the form of graphs. Influence of nonlinear and rheological properties of spring on amplitude and phase of mass oscillations is investigated.

Sedimentation behavior of a spherical particle in a Giesekus fluid: A CFD–DEM solution

Abstract The sedimentation of a spherical solid particle in viscoelastic fluids was studied using a Giesekus model by development of a direct numerical simulation solver based on fully-resolved and immersed boundary methods to understand the complex non-Newtonian fluid flow and spherical particle dynamics. Two benchmark problems were modeled to evaluate the accuracy of the developed solver and excellent agreement with prior experimental and simulation results were obtained. In addition, the temporal and spatial order of convergence of the transient and advection discretization schemes were studied. The aim is to provide a clearer picture for the effect of confinement and rheology of the viscoelastic fluid on the sedimentation phenomenon of a spherical particle in a Giesekus fluid. We report that the negative wake occurs at Weissenberg number Wi ≥ 2.45 at all blockage ratios a ∕ R = 0 . 243 , 0.390, 0.464, and 0.538. At Wi = 1 . 00 , the negative wake occurs mainly at blockage ratio a ∕ R ≥ 0.390 when the effect of confinement is enhanced. There is a linear relationship between the sphere overshoot/steady-state velocity and blockage ratio due to shear-thinning effects. The oscillations in the sphere velocity were reported at all Wi for blockage ratios a ∕ R ≤ 0.464. The sphere velocity oscillations disappear at the highest blockage ratio a ∕ R = 0 . 538 except at Wi = 0 . 01 and 1.00. The viscoelastic fluid velocity oscillations were reported at Wi ≥ 1.00 at all blockage ratios. The viscoelastic fluid velocity oscillations become more damped with blockage ratio a ∕ R which the mutual effects of shear-thinning and wall effects become more dominant.

Viscoelastic flow-induced oscillations of a cantilevered beam in the crossflow of a wormlike micelle solution

Abstract We investigate the interactions between a cantilevered flexible beam and cross-flow of a viscoelastic fluid. Unlike Newtonian fluids, viscoelastic fluids exhibit elastic flow instabilities even in the absence of inertia. These elastic flow instabilities drive the oscillations of flexible structures placed in their flow path. In this work, the fluid–structure interactions between the flow of viscoelastic wormlike micelle solution and a flexible cantilevered beam is studied as a function of the Weissenberg number and the beam’s tip angle. At low Weissenberg numbers, the flow remained stable and the beam deflected in the direction of flow. As the Weissenberg number was increased, a separated vortex appeared upstream of the cantilever near its tip. At a critical Weissenberg number of W i = 11 , the flow became unstable. For beams with small tip angles of 0° and 25°, no oscillations were observed. However, for beams with larger tip angles of 45° and 65°, oscillatory motions coupled to the flow instability were observed, where the amplitude of the beam oscillations increased with increasing tip angle. Particle image velocimetry measurements showed that the elastic flow instability was characterized by the periodic formation of strong fluid jet that originated upstream of the beam in a region of strong extensional flow where it likely resulted from the local breakdown of the wormlike micelle solution. This jet was accompanied by a pair of counter-rotating vortices on its sides as it entrained fluid around the tip of the beam. The frequency of oscillations of the beams with large tip angles increased monotonically with Weissenberg number, while their amplitudes of oscillations initially increased with Weissenberg number before decaying to zero for W i > 20 , despite the fact that the flow remained unstable. Our results showed that oscillations were only possible when the tip of the cantilevered beam made a positive angle with respect to the primary incoming flow direction.

A fractional Maxwell approach for the shock response of viscoelastic oscillator

Viscoelastic damping structures under shock loading with variable amplitude and frequency are always in the multifactorial dynamic state, of which the shock response is obviously different from that under low strain rate. In order to accurately describe the impact mechanical properties of viscoelastic damped materials, a fractional order Maxwell model (FMM) is constructed. To verify the adopted model, the dynamic experiments for different strain rates (1800 s-1, 2500 s-1, 3500 s-1 and 4000 s-1) are performed by SHPB system. The experimental stress-strain curves should be divided into three stages: the linear stage, the strain-softening stage and the strain-hardening stage. As increase with the strain rate, the peak strain, the peak stress and the curvature of the curve in strain-softening stage increase, and the hardening effect in the strain-hardening stage tends to stronger, demonstrating a distinct strain rate effect in viscoelastic damped materials. The reason is that as increase of the strain rate, the action time of external loading gets closer to the relaxation time of the molecular chain segment, indicating the apparent strain rate-dependence of molecular slip and friction. The comparisons are made between the models of FMM, fractional Kelvin-Voight, ZWT and Ogden considering the strain rate-dependent. As a fractional-order model, FMM model has the minimum mean of RMSE 0.460 among the four models. The results indicate that FMM model could accurately describe the impact mechanical behavior characteristics of viscoelastic materials in a wider range of strain rate with comprehensive superiority of higher fitting precision, fewer parameters and clear physical meaning.

Response of fractional Maxwell viscoelastic oscillator subjected to impact load

ABSTRACT The prediction for the impact behavior of viscoelastic oscillator (VEO) has a great significance. The fractional Maxwell viscoelastic oscillator (FMVEO) model under impact load is derived by integrating the fractional Maxwell constitutive model into the system vibration equation and further involving the geometric factors of the isolators. The numerical algorithm based on Chebyshev operational matrix is derived. The Split Hopkinson Pressure Bar (SHPB) experiment is conducted to validate the proposed model. The results indicate that FMVEO can fully describe impact properties of the viscoelastic oscillator. The fractional orders α and β are critical to the elasticity-viscosity component of FMVEO and the first amplitude of the impact response, respectively. The response of FMVEO displays an under-damped state for α ≤ 0.5 and over-damped state for α > 0.5. FMVEO degenerates into a pure-elastic system for α = 0 and evolves into a pure-viscous system for α = 1. In frequency domain, there are resonant peaks for the amplitude-frequency response for α ≤ 0.5, while no pronounced peaks exist for α > 0.5. The fractional order β displays a positive correlation with the first amplitude and a weakly negative correlation with the damping. The geometric factor κ should be taken into full consideration in two ways, the relatively small amplitude and the limited installation space, which shows the significant effect of the geometric element on the system response.

Effects of pre-stretch on the oscillation and stability of dielectric elastomers

Pre-stretch affects the dynamic performance of the dielectric elastomers (DEs). In this paper, the effects of pre-stretch on the nonlinear viscoelastic oscillation and stability of the DE membrane actuator are investigated. Analytical model based on Euler-Lagrange method and homogeneity assumption is developed to describe the complex dynamic behaviour of the viscoelastic DE membrane actuator under equibiaxial and non-equibiaxial pre-stretches, respectively. Numerical calculations are applied to predict dynamic responses of the DE membrane actuator with different initial stretch ratios. The results indicate that the viscoelastic creep of the DE membrane actuator can be eliminated by specific initial stretch ratio. The phase paths and Poincaré maps reveal that proper pre-stretch helps to improve the stability of the DE membrane actuator. This work provides guidance for the structure design, stability control, and optimization of soft actuators and soft robots.

Nonwetting droplet oscillation and displacement by viscoelastic fluids

Simulations and theory reveal oscillations of droplets when driven by viscoelastic fluids because of their elastic memory effect. The viscoelastic oscillation helps release trapped droplets from hard-to-displace positions.

A strongly-coupled cell-based smoothed finite element solver for unsteady viscoelastic fluid–structure interaction

This paper describes a cell-based smoothed finite element method (CS-FEM) for computing unsteady viscoelastic fluid–structure interaction (VFSI) within the arbitrary Lagrangian–Eulerian framework. The incompressible Navier–Stokes equations incorporating the Oldroyd-B constitutive relation are decoupled via the smoothed characteristic-based split scheme that allows equal low-order interpolations for the triple primitive variables. The elastodynamics equation of a geometrically nonlinear solid is solved by the modified Newton–Raphson method in conjunction with the generalized-α method. Following an efficient moving mesh strategy, the block-Gauss–Seidel procedure is utilized to tightly couple three interacting fields. In particular, CS-FEM is adopted to spatially discretize the global VFSI system where all gradient related terms are readily smoothed. The cell-based smoothing concept is also introduced to evaluate viscoelastic fluid forces acting on the deformable body. Two transient VFSI examples are analyzed to demonstrate the enlarged applicability of CS-FEM. The main characteristics of viscoelastic flow-induced oscillations are successfully captured.

Melt Rheological Behavior and Morphology of Poly(ethylene oxide)/Natural Rubber-graft-Poly(methyl methacrylate) Blends.

The influence of morphology on the rheological properties of poly(ethylene oxide) (PEO) and natural rubber-graft-poly(methyl methacrylate) (NR-g-PMMA) blends in the melt was investigated. The blends were prepared at different blend compositions by a solution-casting method. Linear viscoelastic shear oscillations measurements were performed in order to determine the elastic and viscous properties of the blends in the melt. The rheological results suggested that the blending of the two constituents reduced the elasticity and viscosity of the blends. The addition of an even small amount of NR-g-PMMA to PEO changed the liquid-like behavior of PEO to more solid-like behavior. Morphological investigations were carried out by optical microscopy to establish the relationship between morphology and melt viscosity. Depending on the blend compositions and viscosities, either droplet–matrix or co-continuous morphologies was observed. PEO/NR-g-PMMA blends exhibited a broad co-continuity range, and phase inversion was suggested to occur at the PEO/NR-g-PMMA blend with a mass ratio of 60/40 (m/m), when NR-g-PMMA was added to PEO as a matrix.

Shape oscillations of a viscoelastic droplet suspended in a viscoelastic host liquid

The small-amplitude oscillation of a liquid droplet suspended in an immiscible host liquid is studied, where both liquids are assumed viscoelastic. An analytical characteristic equation is derived, and the damping rate and angular frequency that describe the droplet oscillation are numerically solved. The effect of the properties of the host liquid, including its density, viscosity and elasticity, on the viscoelastic droplet oscillation is examined for the quadrupole mode. The host liquid is found to make the droplet oscillation more complex and the mechanisms behind that are discussed.

Vibrations of the plate with elastic core resting on the Winkler foundation caused by a moving oscillator

In the paper a structure consisting of two Kirchhoff plates connected by an elastic Winkler layer is considered. The structure rests on the Winkler foundation and is subjected to a one-mass visco-elastic oscillator, moving at a constant speed on the upper plate, parallel to one of the plate sides. Forced and free vibrations of the plates and the oscillator are analysed. In the case of such a complex system vibration of the plates is described by two coupled differential equations, or one differential equation with elevated order. In addition, due to the nature of the moving load (inertial load), these equations have variable, time-dependent coefficients. The solutions are illustrated by numerical examples.