scholarly journals An Analytical Solution for Non-Linear Viscoelastic Impact

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1849
Author(s):  
Stelian Alaci ◽  
Constantin Filote ◽  
Florina-Carmen Ciornei ◽  
Oana Vasilica Grosu ◽  
Maria Simona Raboaca
Keyword(s):  
Analytical Solution ◽  
Hysteresis Loop ◽  
Viscoelastic Model ◽  
First Integral ◽  
Coefficient Of Restitution ◽  
Contact Period ◽  
Maximum Deformation ◽  
Impact Parameters ◽  
Simplified Algorithm ◽  
The Moment

The paper presents an analytical solution for the centric viscoelastic impact of two smooth balls. The contact period has two phases, compression and restitution, delimited by the moment corresponding to maximum deformation. The motion of the system is described by a nonlinear Hunt–Crossley equation that, when compared to the linear model, presents the advantage of a hysteresis loop closing in origin. There is only a single available equation obtained from the theorem of momentum. In order to solve the problem, in the literature, there are accepted different supplementary hypotheses based on energy considerations. In the present paper, the differential equation is written under a convenient form; it is shown that it can be integrated and a first integral is found—this being the main asset of the work. Then, all impact parameters can be calculated. The effect of coefficient of restitution upon all collision characteristics is emphasized, presenting importance for the compliant materials, in the domain of small coefficients of restitution. The results (variations of approach, velocity, force vs. time and hysteresis loop) are compared to two models due to Lankarani and Flores. For quasi-elastic collisions, the results are practically the same for the three models. For smaller values of the coefficient of restitution, the results of the present paper are in good agreement only to the Flores model. The simplified algorithm for the calculus of viscoelastic impact parameters is also presented. This algorithm avoids the large calculus volume required by solving the transcendental equations and definite integrals present in the mathematical model. The method proposed, based on the viscoelastic model given by Hunt and Crossley, can be extended to the elasto–visco–plastic nonlinear impact model.

Modeling and Simulation of the Sulfur Dioxide Adsorption Process in Natural Zeolites

2015 ◽  
Vol 811 ◽  
pp. 35-42 ◽  
Author(s):  
Susana Sfechiş ◽  
Mihail Abrudean ◽  
Diana Monica Sas ◽  
Mihaela Ligia Ungureşan ◽  
Iulia Clitan ◽  
...  
Keyword(s):  
Sulfur Dioxide ◽  
Analytical Solution ◽  
Modeling And Simulation ◽  
Adsorption Process ◽  
Original Form ◽  
Dynamical Regime ◽  
Natural Zeolites ◽  
Time Period ◽  
Process Work ◽  
The Moment

The paper presents a solution for modeling and simulation of the adsorption process of the sulfur dioxide in natural zeolites. The adsorption process is modeled as a distributed parameter process, its dynamics depending on three independent variables: time and two spatial variables. In order to simulate the adsorption process, an original form of the approximating analytical solution which describes the process work in dynamical regime is proposed and used. The coefficients of the approximating analytical solution are determined using experimental data obtained from the real plant. A direct practical application, resulted through the simulation of the obtained mathematical model, is the approximation of the time period in which the saturation of the zeolites of different dimensions occurs. Having the mentioned time period, the operators from the industrial field can decide with precision the moment when a zeolite block has to be replaced in order to avoid the environment pollution.

Analytical Solution of 1-D Viscoelastic Consolidation of Soft Soils with Fractional Maxwell Model

2012 ◽  
Vol 157-158 ◽  
pp. 419-423
Author(s):  
Ya Peng Zhang ◽  
Feng Gao
Keyword(s):  
Analytical Solution ◽  
Soft Soil ◽  
Soil Layer ◽  
Viscoelastic Model ◽  
Integral Form ◽  
Maxwell Model ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Fractional Maxwell Model ◽  
The One

Considering the rheological characteristics of soil, think the fractional maxwell with viscoelastic model can be described, the fractional maxwell model into integral form of saturated soft soil layer, the one dimensional compression, through the Laplace transform problems get instantaneous loading and single stage, the analytical solution of the loading conditions.

Fractional Derivative Viscoelastic Model for the Analysis of Two Colliding Spherical Shells

2012 ◽  
Author(s):  
Yury A. Rossikhin ◽  
Marina V. Shitikova
Keyword(s):  
Fractional Derivative ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Wave Fronts ◽  
Spherical Shells ◽  
Reflected Waves ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Moment ◽  
Contact Domain

The collision of two isotropic spherical shells is investigated for the case when the viscoelastic features of the shells represent themselves only in the place of contact and are governed by the standard linear solid model with fractional derivatives. Thus, the problem concerns the shock interaction of two shells, wherein the generalized fractional-derivative standard linear law instead of the Hertz contact law is employed as a low of interaction. The pans of the shells beyond the contact domain are assumed to be elastic, and their behavior is described by the equations of motion which take rotary inertia and shear deformations into account. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. Due to the short duration of contact interaction, the reflected waves are not taken into account. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. To determine the desired values behind the wave fronts, one-term ray expansions are used, as well as the equations of motion of the contact domains for the both spherical shells.

scholarly journals Underground main pipeline behaviour under a travelling impulse in the form of a triangle

2021 ◽  
Vol 264 ◽  
pp. 01006
Author(s):  
Barna Rakhmankulova ◽  
Sayibdjan Mirzaev ◽  
Rakhmatjon Khusainov ◽  
Saparboy Khusainov
Keyword(s):  
Wave Front ◽  
Viscoelastic Model ◽  
Elastic Interaction ◽  
Viscosity Coefficient ◽  
Underground Pipeline ◽  
Main Pipeline ◽  
Soil System ◽  
Maximum Deformation ◽  
Viscous Interaction ◽  
Deformed State

The article presents an analysis of the dynamic response of an underground main pipeline under the action of a longitudinal wave, propagating in soil along the pipe. It is assumed that the elastic pipe has a finite length. A linear viscoelastic model of the "pipe-soil" system interaction is considered. The influence of a pulse in the form of a triangle on the deformed state of an underground main pipeline is investigated. The article presents a comparative analysis of the results obtained for some values of the coefficients of elastic and viscous interaction, the propagation velocity, and the duration of the pulse. In the case of elastic interaction of the "pipe-soil" system, the reflection of the wave propagating in the underground pipeline on the boundaries of the pipeline when it coincides with the wave propagating in the soil leads to an increase in the maximum deformation of the underground pipeline, the value of deformation can double. The viscosity coefficient of interaction at the pipe-soil system contact leads to the wave front attenuation in the underground pipeline. For soils with the coefficient of viscous interaction higher than 100 kN∙s/m2, this leads to complete attenuation of the bursts at the wave front in the pipeline. The influence of the wave propagation in soil on the deformation values at the wave front was also studied.

Mechanical Behavior of Active and Passive Strain Sections in CFRP Laminate under Uniaxial Tension

2021 ◽  
Vol 410 ◽  
pp. 680-685
Author(s):  
Pavel B. Severov
Keyword(s):  
Hysteresis Loop ◽  
Uniaxial Tension ◽  
Mechanical Energy ◽  
Nonlinear Behavior ◽  
Cfrp Laminate ◽  
Maximum Deformation ◽  
Maximum Expansion ◽  
Development Stages ◽  
Maximum Angle ◽  
Mechanical Energy Dissipation

This study investigates the nonlinear behavior of quasi-isotropic CFRP laminate under uniaxial tension. To verify the convergence of the calculated and experimental deviations, the approximating nonlinear equations describing the upper and lower hysteresis loop branches were found. The formation of a hysteresis loop in the active and passive strain sections in CFRP laminate has been studied. The open hysteresis loop development stages are shown from maximum expansion to stabilization, and to the tendency of branches to connect and narrow the loop. The point of the maximum angle between the upper and lower branches of the loop is determined – the apex of the hysteresis loop at maximum deformation. The strain region is found, in which the branches of the loop are parallel. The equations are determined, describing the nonlinear behavior of modules of Ex(ε) in the sections of increasing and decreasing strain. The dependence between mechanical energy dissipation per unit volume and strain was obtained.

scholarly journals Theoretical Bending Collapse of Hat-Section Tubes

2018 ◽  
Vol 7 (4.26) ◽  
pp. 153
Author(s):  
Hafizan Hashim ◽  
Hanita Hashim ◽  
Arif Affendi Jamal ◽  
M. A.M. Jusoh
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Plastic Region ◽  
Tubular Structures ◽  
Pure Bending ◽  
Analysis Technique ◽  
Collapse Model ◽  
The Moment ◽  
Relationship Of ◽  
Good Agreement

This paper presents an attempt to modify an existing theoretical model to predict the bending collapse response of hat-section tubular structures. The analytical collapse model was based on Kim and Reid. Additional hinge lines created during deformation of the tube were examined and integrated with existing model to forming a modified analytical solution. Variation of the hinge moments were solved using limit analysis technique. Procedure for developing the finite element (FE) models of tube specimens was also presented. Moment-rotation characteristics from pure bending simulation were compared with analytical model and good agreement was achieved. The average of differences between simulation and calculation were found to be <5% within plastic region. In conclusion, the modified analytical solution has adequate capability to predict the moment-rotation relationship of hat-section tubes subject to pure bending.. 

Coefficient of Restitution for Collinear Collisions of Elastic-Perfectly Plastic Spheres

1997 ◽  
Vol 64 (2) ◽  
pp. 383-386 ◽  
Author(s):  
C. Thornton
Keyword(s):  
Theoretical Model ◽  
Analytical Solution ◽  
Yield Stress ◽  
Impact Velocity ◽  
Contact Interaction ◽  
Material Properties ◽  
Coefficient Of Restitution ◽  
Normal Contact ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Based on a simplified theoretical model for the normal contact interaction of two elastic-perfectly plastic spheres, an analytical solution is provided for the coefficient of restitution. The solution is expressed in terms of the ratio of impact velocity to yield velocity rather than in terms of material properties such as the yield stress which is difficult to reliably ascertain for many materials.

ALL-OPTICAL HYSTERESIS SWITCHING USING MOBIUS CONFIGURATION MICRORING RESONATOR CIRCUIT

2015 ◽  
Vol 74 (8) ◽  
Author(s):  
Ahmad Fakhrurrazi Ahmad Noorden ◽  
Azam Mohamad ◽  
Mahdi Bahadoran ◽  
Kashif Chaudhary ◽  
M. S. Aziz ◽  
...  
Keyword(s):  
Phase Shift ◽  
Analytical Solution ◽  
Hysteresis Loop ◽  
Optical Bistability ◽  
Ring Resonator ◽  
Microring Resonator ◽  
The Novel ◽  
Matrix Methods ◽  
Switching Power ◽  
All Optical

The novel twisted ring resonator called add-drop Mobius microring resonator is introduced and modelled with the analytical solution of transfer matrix methods for the generation of optical bistability. Simulated results show that, the add-drop Mobius configuration provides greater phase shift due to the longer length of propagation per roundtrip than add-drop filter configuration. In add-drop Mobius system, drop port generated the optical bistable hysteresis loop with 19.25 mW output switching power and through port generated lower switching power as 5.55 mW. The drop port of the system is found as the suitable port for the operating the all-optical hysteresis switching.

Evaluation of Nonlinear Damping Properties of Magnetorheological Gels Under Shear Loading

2013 ◽  
Author(s):  
Yotsugi Shibuya ◽  
Hiroshi Nasuno ◽  
Hirohisa Sakurai ◽  
Katsuaki Sunakoda
Keyword(s):  
Magnetic Field ◽  
Dynamic Response ◽  
Hysteresis Loop ◽  
Viscoelastic Model ◽  
Shear Loading ◽  
Material System ◽  
Damping Properties ◽  
Stress Strain ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Model

Rheological properties of magnetorheological gels can be changed reversibly by applied magnetic fields. Magnetorheological gels with different material system are characterized the dynamic response of the material by shearing test in magnetic field. Nonlinear behavior is observed in the dynamic response of the material. To understand mechanism of the behavior, dynamic properties of magnetorheological gels are evaluated by experiment and nonlinear viscoelastic model. Magnetorheological gels used in this study consist of three types of paramagnetic particles and a cyclic-poly-siloxane gel matrix. Three material systems of magnetic particles are chosen: Fe-Si-Ni, Si-Fe and Fe-Si-B-Cr types. Shear testing is conducted in magnetic field 0mT, 105mT and 211mT. The stress-strain response under shear deformation is characterized by non-ellipsoidal hysteresis loop due to nonlinearity of the response. To identify the nonlinear properties, analysis in frequency domain is applied to identify the dynamic response of the material. Nonlinear viscoelastic model with high order components is made and phenomenon of the non-ellipsoidal hysteresis loop in the stress-strain relation and damping properties are illustrated.

scholarly journals Parameter identification and analysis of soluble chemical transfer from soil to surface runoff

2012 ◽  
Vol 9 (3) ◽  
pp. 3901-3931
Author(s):  
J. X. Tong ◽  
J. Z. Yang ◽  
B. X. Hu
Keyword(s):  
Analytical Solution ◽  
Water Content ◽  
Surface Runoff ◽  
Soil Depth ◽  
Volumetric Water Content ◽  
Related Parameter ◽  
Chemical Transfer ◽  
Study Results ◽  
The Moment ◽  
Experimental Soil

Abstract. A two-layer mathematical model is used to predict the chemical transfer from the soil into the surface runoff with ponding water. There are two incomplete infiltration-related parameter γ and runoff-related parameter α in the analytical solution to the model, which were assumed to be constant in previous studies (Tong et al., 2010). In this study, experimental data are used to identify the variable γ and α based on the analytical solution. The soil depth of the mixing zone is kept to be constant in different experiments, and the values of γ and α before the surface runoff occurs are constant and equal to their values at the moment the runoff starts. From the study results, it is found that γ will decrease with the increase of the surface runoff time, the increase of the ponding-water depth, hp, or with the decrease of the initial volumetric water content. The variability of γ will decrease with the increase of the initial volumetric water content. Similarly, α will decrease with time for the initially unsaturated experimental soils, but will increase with time for the initially saturated experimental soils. The larger the infiltration, the less chemical concentration in the surface runoff is. The analytical solution is not valid for experimental soil without any infiltration if α is expected to be less or equal to 1. The results will help to quantify chemical transfer from soil into runoff, a significant problem in agricultural pollution management.

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