Effects of viscoelasticity on the stability and bifurcations of nonlinear energy sinks

Due to the increasing use of passive absorbers to control unwanted vibrations,many studies have been done on energy absorbers ideally,but the lack of studies of real environmental conditions on these absorbers is felt.The present work investigates the effect of viscoelasticity on the stability and bifurcations of a system attached to a nonlinear energy sink(NES).In this paper,the Burgers model is assumed for the viscoelasticity in an NES,and a linear oscillator system is considered for investigating the instabilities and bifurcations.The equations of motion of the coupled system are solved by using the harmonic balance and pseudo-arc-length continuation methods.The results show that the viscoelasticity affects the frequency intervals of the Hopf and saddle-node branches,and by increasing the stiffness parameters of the viscoelasticity,the conditions of these branches occur in larger ranges of the external force amplitudes,and also reduce the frequency range of the branches.In addition,increasing the viscoelastic damping parameter has the potential to completely eliminate the instability of the system and gradually reduce the amplitude of the jump phenomenon.

Rheological Behavior for Polymer Melts and Concentrated Solutions——Part Ⅶ: A Quantitative Verification for the Molecular Theory of Non-linear Viscoelasticity with Entanglement Constraints in Polymer Melts

Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and <(<upsilon>)over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.

A viscoelastic metamaterial beam for integrated vibration isolation and energy harvesting

Locally resonant metamaterials have low-frequency band gaps and the capability of converging vibratory energy in the band gaps at resonant cells.It has been demonstrated by several researchers that the dissipatioin of vibratory energy within the band gap can be improved by using viscoelastic materials.This paper designs an integrated viscoelastic metamaterial for energy harvesting and vibration isolation.The viscoelastic metamaterial is achieved by a viscoelastic beam periodically arrayed with spatial ball-pendulum nonlinear energy harvesters.The nonlinear resonator with an energy harvesting function is achieved by placing a free-rolling magnetic ball in a spherical cavity with an additional induction coil.The dynamic equations of viscoelastic metamaterials under transverse excitation are established,and the energy harvesting and vibration isolation characteristics within the dispersion relation of viscoelastic metamaterials are analyzed.The results show that the vibrations of the main body of the viscoelastic metamaterial beam are significantly suppressed in the frequency range of the local resonance band gap.At the same time,the elastic waves are limited in the nonlinear resonator with an energy harvesting function,which improves the energy output.Finally,an experimental platform of viscoelastic metamaterial vibration is established for validation purposes.

A robust viscoelastic surfactant tolerating 20% HCl up to 150℃ for oil well stimulation

Viscoelastic surfactants(VES)are often used as viscous diverters in acidizing stimulation to prolong the acid consumption time and maximize zonal coverage of the acid for improving well productivity.However,the ceiling temperature of commercial VES cannot exceed 120℃in practical use because of the poor thermal stability and fragile molecular structure,hindering their implementation in hightemperature oil reservoirs,i.e.,≥150℃.Here we synthesized a novel C22-tailed diamine,N-erucaminopropyl-N,N-dimethylamine(EDPA),and examined comparatively its rheological behavior,assemblies morphology and molecular stability in 20 wt%HCl with a commercial VES,erucyl dimethyl amidopropyl betaine(EDAB).The feasibility of EDPA for acidizing stimulation was assessed by acid etching of carbonate rock with its HCl solution at 150℃.Rheological results showed that the 2.5 wt%EDPA—20 wt%HCl solution maintains stable viscosity of 90 m Pa s at 150℃for 60 min,while that of 2.0 wt%EDAB HCl solution is just 1 m Pa s under identical conditions.1H NMR spectra and cryo-TEM observations revealed that the chemical structure and self-assembled architectures of EDPA remained intact in such context,but the EDAB suffered from degradation due to the hydrolysis of the amide group,accounting for the poor heat-resistance and acid-tolerance.The reaction rate of 2.5 wt%EDPA HCl solution with carbonate rock was one order of magnitude lower than that of 20 wt%HCl solution at 150℃,underpinning the potential of EDPA to be used in the high-temperature reservoirs acidizing.This work improved the thermal tolerance of VES in highly concentrated HCl solution,paving a feasible way for the acidization of high-temperature reservoir environments(~150℃).

Intraocular pressure before and after capsulorhexis using two viscoelastic substances and two surgical approaches in enucleated porcine eyes

AIM:To investigate the influence of ophthalmic viscoelastic devices(OVDs)and different surgical approaches on the intraocular pressure(IOP)before and after creation of the curvilinear circular capsulorhexis(CCC)as a measure for anterior chamber stability during this maneuver.METHODS:Prospective experimental WetLab study carried out on enucleated porcine eyes.IOP was measured before and after CCC with the iCare Rebound tonometer(iCare ic200;iCare Finland Oy,Vantaa,Finland).The OVDs used were a cohesive one[Z-Hyalin,Carl Zeiss Meditec AG,Germany;hyaluronic acid(HA)]and a dispersive[Z-Celcoat,Carl Zeiss Meditec AG,Germany;hydroxy propylmethylcellulosis(HPMC)].The CCC was created using Utrata forceps or 23 g microforceps in different combinations with the OVDs.RESULTS:Using the Utrata forceps the IOP dropped from 63.65±6.44 to 11.25±3.63 mm Hg during the CCC.The use of different OVDs made no difference.Using the 23 g microforceps the IOP dropped from 65.35±8.15 to 36.55±6.09 mm Hg.The difference between IOP drop using either Utrata forceps or 23 g microforceps was highly significant regardless of the OVD used.CONCLUSION:Using the sideport for the creation of the capsulorhexis leads to a lesser drop in IOP during this maneuver compared to the main incision in enucleated porcine eyes.The use of different OVD has no significant influence on IOP drop.

Development of a Three-Dimensional Multiscale Octree SBFEM for Viscoelastic Problems of Heterogeneous Materials

The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms(DOFs).A basic framework of the Multiscale Scaled Boundary Finite Element Method(MsSBFEM)was presented in our previous works,but those works only addressed two-dimensional problems.In order to solve more realistic problems,a three-dimensional MsSBFEM is further developed in this article.In the proposed method,the octree SBFEM is used to deal with the three-dimensional calculation for numerical base functions to bridge small and large scales,the three-dimensional image-based analysis can be conveniently conducted in small-scale and coarse nodes can be flexibly adjusted to improve the computational accuracy.Besides,the Temporally Piecewise Adaptive Algorithm(TPAA)is used to maintain the computational accuracy of multiscale analysis by adaptive calculation in time domain.The results of numerical examples show that the proposed method can significantly reduce the DOFs for three-dimensional viscoelastic analysis with good accuracy.For instance,the DOFs can be reduced by 9021 times compared with Direct Numerical Simulation(DNS)with an average error of 1.87%in the third example,and it is very effective in dealing with three-dimensional complex microstructures directly based on images without any geometric modelling process.

The effect of reactive plasticizer on viscoelastic and mechanical properties of solid rocket propellants based on different types of HTPB resin

Conventional plasticizers deteriorate mechanical and viscoelastic properties of the propellants due to their migration upon aging and long-term storage,which affects reliability and safety properties during exploitation.To address this issue,conventional plasticizer,dioctyl adipate(DOA),is replaced by reactive one,castor oil(CO).In addition,three different types of HTPB were used to obtain propellants with designed viscoelastic and mechanical properties.The CO increased propellants viscosity,without a significant impact on the propellant processability,regardless to the type of prepolymer.Conversely,mechanical properties were different depending on the type of resin,which were further analyzed by gel permeation chromatography(GPC).Addition of CO formed a denser polymer network and shifted T_(g) to higher values,compared to the compositions with DOA.The tensile strength of CO-containing propellants was lower at +20℃ and +50℃ compared to the reference compositions,while the strain at maximum load and strain at break were significantly increased with pronounced plastic deformation,especially for samples at -30℃.The inclusion of CO in the propellants composition gives more room for adjusting a wide range of mechanical properties.

Tensile Shock Physics in Compressible Thermoviscoelastic Solid Medium

This paper addresses tensile shock physics in thermoviscoelastic (TVE) solids without memory. The mathematical model is derived using conservation and balance laws (CBL) of classical continuum mechanics (CCM), incorporating the contravariant second Piola-Kirchhoff stress tensor, the covariant Green’s strain tensor, and its rates up to order n. This mathematical model permits the study of finite deformation and finite strain compressible deformation physics with an ordered rate dissipation mechanism. Constitutive theories are derived using conjugate pairs in entropy inequality and the representation theorem. The resulting mathematical model is both thermodynamically and mathematically consistent and has closure. The solution of the initial value problems (IVPs) describing evolutions is obtained using a variationally consistent space-time coupled finite element method, derived using space-time residual functional in which the local approximations are in hpk higher-order scalar product spaces. This permits accurate description problem physics over the discretization and also permits precise a posteriori computation of the space-time residual functional, an accurate measure of the accuracy of the computed solution. Model problem studies are presented to demonstrate tensile shock formation, propagation, reflection, and interaction. A unique feature of this research is that tensile shocks can only exist in solid matter, as their existence requires a medium to be elastic (presence of strain), which is only possible in a solid medium. In tensile shock physics, a decrease in the density of the medium caused by tensile waves leads to shock formation ahead of the wave. In contrast, in compressive shocks, an increase in density and the corresponding compressive waves result in the formation of compression shocks behind of the wave. Although these are two similar phenomena, they are inherently different in nature. To our knowledge, this work has not been reported in the published literature.

A flexible multiscale algorithm based on an improved smoothed particle hydrodynamics method for complex viscoelastic flows

Viscoelastic flows play an important role in numerous engineering fields,and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids.However,traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time,and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids.In this paper,a universal multiscale method coupling an improved smoothed particle hydrodynamics(SPH)and multiscale universal interface(MUI)library is presented for viscoelastic flows.The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain.We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows.In the first example,the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions.The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain.In the second example,the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics(DPD)method.The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain.Moreover,transferring different physical quantities has an important effect on the numerical results.

Hermite Finite Element Method for Vibration Problem of Euler-Bernoulli Beam on Viscoelastic Pasternak Foundation

Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Euler-Bernoulli beam on viscoelastic Pasternak foundation can be used to analyze the deformation and response of buildings under complex geological conditions. In this paper, we use Hermite finite element method to get the numerical approximation scheme for the vibration equation of viscoelastic Pasternak foundation beam. Convergence and error estimation are rigourously established. We prove that the fully discrete scheme has convergence order O(τ2+h4), where τis time step size and his space step size. Finally, we give four numerical examples to verify the validity of theoretical analysis.

Effect of viscoelasticity on nonlinear vibration of single microbubble

Based on the Church-Hoff model, the nonlinear oscillations of a single encapsulated microbubble with a finite thickness shell are theoretically studied. The effects of viscoelasticity on radial oscillations and the fundamental and harmonic components are researched. The peaks of radial oscillations and magnitudes of power spectra of the fundamental and harmonic components all increase gradually with the shear modulus of shell varying from 0 to 10 MPa by an interval of 0. 1 MPa at the same shear viscosity, while they decrease as the shear viscosity increases from 0 to 1 Pa · s by an interval of 0. 01 Pa · s at the same shear modulus. The fluctuation ranges of subharmonic and ultraharmonic signals are much larger than both the fundamental and second harmonic components. It means that the effect of viscoelasticity on the subharmonic and ultraharmonic signals is greater than that on the fundamental and second harmonic components. So adjusting the viscoelasticity of the shell is a potential method to obtain a perfect microbubble contrast agent used for the subharmonic and ultraharmonic imaging. Four points with significant fundamental and harmonic components are chosen as an example： a shear viscosity of 0. 39 Pa · s with shear modulus of 3.9, 6. 6, and 8.6 MPa, respectively; a shear modulus of 6.6 MPa with a shear viscosity of 0.42 Pa · s.

NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS

The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.

The Dynamic Viscoelasticity of Polyethylene Based Montmorillonite Intercalated Nanocomposites

The viscoelastic behavior of melts for two systems composed of intercalated nanocomposites based on low density polyethylene and 3 wt% loading of cetyltrimethyl- ammonium bromide modified montmorillonite was studied. The results obtained through examining the dynamic storage module G' and dynamic loss module G' values of the composite revealed that the dynamic viscoelastic properties of composite strongly depended on intercalation of polymer, and exhibited dramatically change with altering intercalation conditions. Only when modified montmorillonite content was about 3 wt%, the composite showed a trend of pseudo-solidlike at lower frequencies.

Effect of starch particles on foam stability and dilational viscoelasticity of aqueous-foam

Surface dilational rheological behavior and foam stability of starch/surfactant mixed solutions were studied at different starch concentrations and constant surfactant concentration. The results show that dilational viscoelasticity modulus, dilational elasticity modulus and dilational viscosity modulus increase with the concentration of starch particles. Foam stability increases with dilational viscoelasticity. Foam strength also increases with starch concentration. Starch particles play a positive effect on foam stability and dilational viscoelasticity and the effect becomes more significant as drainage proceeds. Film pictures indicate that the film with 20%(by mass) starch particles is thicker than that without starch. Starch particles gather in Plateau border and resist drainage, making the foam more stable.

The viscoelasticity of lipid shell and the hysteresis of subharmonic in liquid containing microbubbles

The viscoelasticity and subharmonic generation of a kind of lipid ultrasound contrast agent are investigated. Based on the measurement of the sound attenuation spectrum, the viscoelasticity of the lipid shell is estimated by use of an optimization method. Shear modulus Gs=10MPa and shear viscosity μs=1.49N.S/m^2 are obtained. The nonlinear oscillation of the encapsulated microbubble is studied with Church＇s model theoretically and experimentally. Especially, the dependence of subharmonic on the incident acoustic pressure is studied. The results reveal that the development of the subharmonic undergoes three stages, i.e. occurrence, growth and saturation, and that hysteresis appears in descending ramp insonation.

THE EFFECTS OF BLOOD VISCOELASTICITY ON THE PULSE WAVE IN ARTERIES

Based on Womersley' s theory, the frequency equation satisfied by a complex wave velocity of a pulse wave in arteries war generalized to viscoelastic blood, a general formula of the complex wave velocity with regard to both linearly viscoelastic arteries and linearly viscolelastic blood was obtained, and the effects of the viscoelastic property of blood on the phase velocity and the wave attenuation of the pulse wave using the formula systematically was discussed. It is concluded that the influence of the blood elasticity on the wave propagation of a pulse wave in arteries is weaker than that of the arterial viscosity and may be neglected in larger arteries.

Complex variable element-free Galerkin method for viscoelasticity problems

Based on the complex variable moving least-square （CVMLS） approximation, the complex variable element-free Galerkin （CVEFG） method for two-dimensional viscoelasticity problems under the creep condition is presented in this paper. The Galerkin weak form is employed to obtain the equation system, and the penalty method is used to apply the essential boundary conditions, then the corresponding formulae of the CVEFG method for two-dimensional viscoelasticity problems under the creep condition are obtained. Compared with the element-free Galerkin （EFG） method, with the same node distribution, the CVEFG method has higher precision, and to obtain the similar precision, the CVEFG method has greater computational efficiency. Some numerical examples are given to demonstrate the validity and the efficiency of the method.

Dynamic Viscoelasticity of Polyester/Rubber Composites under Cyclic Loading

This paper focuses on the influence of dynamic viscoelasticity and surface temperature on the fatigue mechanism and fatigue lifetime of polyester/rubber composites. Rubber composites show significant viscoelasticity during fatigue process. The variations of dynamic elastic modulus, mechanical loss angle, loss energy per cycle exhibit different trend in fatigue initial stage and final stage. Due to high viscoelasticity high heat generation occurs under cyclic loading, which leads to a high surface temperature. It is found that the variation of specimen surface temperature depends strongly on cycling frequency and stress amplitude. SEM (scanning electron microscopy) observation and static residual stiffness studies reveal that the surface temperature affects fracture morphology and fatigue lifetime of rubber composites strongly because of heat aging.

Comparison of viscoelasticity between normal human sciatic nerve and amniotic membrane

Sciatic nerve tissue was obtained from the gluteus maximus muscle segment of normal human cadavers and amniotic membrane tissue was obtained from healthy human puerperant placentas. Both tissues were analyzed for their stress relaxation and creep properties to determine suitability for transplantation applications. Human amniotic membrane and sciatic nerve tissues had similar tendencies for stress relaxation and creep properties. The stress value of the amniotic membrane stress relaxation group decreased to a greater extent compared with the sciatic nerve stress relaxation group. Similarly, the stress value of the amniotic membrane creep group increased to a greater extent compared with the sciatic nerve creep group. The stress relaxation curve for human amniotic membrane and sciatic nerve showed a logarithm correlation, while the creep curve showed an exponential correlation. These data indicate that amniotic membrane tissue has better stress relaxation and creep properties compared with sciatic nerve tissue.

Photoacoustic viscoelasticity imaging dedicated to mechanical characterization of biological tissues

Since changes in mechanical properties of biological tissues are often closely related to pathology,the viscoelastic properties are important physical parameters for medical diagnosis.A photoacoustic(PA)phase-resolved method for noninvasively characterizing the biological tissue viscoelasticity has been proposed by Gao et al.[G.Gao,S.Yang,D.Xing,\Viscoelasticity imaging of biological tissues with phase-resolved photoacoustic measurement,"Opt.Lett.36,3341–3343(2011)].The mathematical relationship between the PA phase delay and the viscosity–elasticity ratio has been theoretically deduced.Moreover,systems of PA viscoelasticity(PAVE)imaging including PAVE microscopy and PAVE endoscopy were developed,and high-PA-phase contrast images re°ecting the tissue viscoelasticity information have been successfully achieved.The PAVE method has been developed in tumor detection,atherosclerosis characterization and related vascular endoscopy.We reviewed the development of the PAVE technique and its applications in biomedical¯elds.It is believed that PAVE imaging is of great potential in both biomedical applications and clinical studies.