On the Cauchy problem of the standard linear solid model with Cattaneo heat conduction

2021 ◽  
pp. 1-33
Author(s):  
Marta Pellicer ◽  
Belkacem Said-Houari
Keyword(s):  
Heat Conduction ◽  
Expansion Method ◽  
Decay Rates ◽  
Solid Model ◽  
Fourier Space ◽  
Standard Linear Solid Model ◽  
The Cauchy Problem ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Appl Math

In the present paper we consider the Standard Linear Solid model in R N coupled with the Cattaneo law of heat conduction. We show the well-posedness and asymptotic stability of the problem, giving decay rates for a norm related to the solution. These results are compared with those given for the Fourier problem in (Pellicer and Said-Houari (2020)) and the ones of the problem without heat conduction (see previous work (Appl Math. Optim 80 (2019) 447–478)). The main difference is that the Cattaneo system exhibits the well-known regularity-loss phenomenon. The methods used to prove these results are the energy method in the Fourier space and the eigenvalues expansion method.

scholarly journals Asymptotic behaviour for the vibrations modeled by the standard linear solid model with a thermal effect

2013 ◽  
Vol 399 (2) ◽  
pp. 472-479 ◽  
Author(s):  
Margareth S. Alves ◽  
Celene Buriol ◽  
Marcio V. Ferreira ◽  
Jaime E. Muñoz Rivera ◽  
Mauricio Sepúlveda ◽  
...  
Keyword(s):  
Asymptotic Behaviour ◽  
Thermal Effect ◽  
Solid Model ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear

Experimental identification of the material standard linear solid model parameters by means of dynamical measurements

2021 ◽  
pp. 107754632110371
Author(s):  
Stefano Amadori ◽  
Giuseppe Catania
Keyword(s):  
Frequency Domain ◽  
Solid Material ◽  
Model Parameters ◽  
Solid Model ◽  
Material Parameters ◽  
Experimental Identification ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Material Standard

A procedure for the experimental identification of the material standard linear solid model parameters by means of dynamic mechanical analysis test instrument measurements is presented. Since the standard linear solid material stress–strain functional D( ω) relationship in the frequency domain formally depends on the standard linear solid material parameters, a procedure able to identify these parameters from test measurement estimates is proposed in this work. Nevertheless, a critical, nonlinear and non-parametric approach is to be followed since the number of the material standard linear solid block components is generally unknown, and the material D( ω) shows a highly nonlinear dependency on the unknown standard linear solid material parameters. For these reasons, measurement and test model noise is expected to strongly influence the accuracy of the identification results. A multi-step procedure is presented, consisting first in the non-parametric identification of a frequency dependent, two degrees of freedom model instrument frame by means of a polynomial rational function, where polynomial order and parameters, such as polynomial coefficients and pole-residue couples, are optimally identified by means of an algebraic numerical technique and of an iterative stabilization procedure. Another procedure able to identify the material D( ω) polynomial rational functional relationship in the frequency domain is also proposed, taking into account the dynamic contribution of the instrument frame, of the inertial contribution of the distributed mass of the beam and of the lumped mass of the instrument force measuring system. An effective procedure, able to identify the standard linear solid material model parameters in the time domain from the identified material physical poles, is finally proposed. Some application examples, concerning the identification of the standard linear solid model of a known material and of an unknown composite material, are shown and discussed as well.

Viscoelastic Properties of Phagocytes in Arteriosclerotic Origin

2014 ◽  
Vol 540 ◽  
pp. 321-325
Author(s):  
Wei Zeng ◽  
Yan Rong Shi ◽  
Xiao Yan Deng
Keyword(s):  
Experimental Data ◽  
Viscoelastic Properties ◽  
Important Implication ◽  
Research Field ◽  
Solid Model ◽  
Initial Stage ◽  
Standard Linear Solid Model ◽  
Aspiration Technique ◽  
Standard Linear Solid ◽  
Standard Linear

A micropipette aspiration technique was adopted to investigate the viscoelastic properties of phagocytes of arteriosclerotic origin. A standard linear solid model was employed to fit the experimental data and three viscoelastic coefficients were used to compare the mechanical properties of the phagocytes in different phases during arteriosclerostic development. The experimental results indicated that prior to the formation of arteriosclerosis, the mobility and deformability of the marcopahges matured from monocytes decreased, and their rigidity increased. At the initial stage of arteriosclerosis formation, the mobility and deformability of the foam-cells further decreased. This finding may have important implication in the research field of arteriosclerosis.

Parametric Vibration of Viscoelastic Moving Belts Using Standard Linear Solid Model

2001 ◽  
Author(s):  
Zhichao Hou ◽  
Jean W. Zu
Keyword(s):  
Order Approximation ◽  
Dynamic Responses ◽  
Solid Model ◽  
Nontrivial Solutions ◽  
Closed Form Solutions ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Stability ◽  
First Order Approximation

Abstract By using a standard linear solid model to describe the viscoelasticity of the belt material, a vibration analysis of a parametrically excited moving belt is performed. Closed-form solutions at principal resonance and summation resonance are derived at the first order approximation. The existence conditions and stability are discussed for the nontrivial solutions, yielding explicit expressions of the existence and the stability conditions in terms of the detuning parameter. Numerical examples clearly show the effects of tension fluctuations and translating speeds on the amplitudes of dynamic responses, the corresponding existence domains and the stability of the solutions. It is also demonstrated that the stability domains of the nontrivial solutions are different from those corresponding to elastic models.

The generalized standard-linear-solid model and the corresponding viscoacoustic wave equations revisited

2019 ◽  
Author(s):  
Qi Hao ◽  
Stewart Greenhalgh
Keyword(s):  
Frequency Domain ◽  
Relaxation Function ◽  
Wave Equations ◽  
Complex Modulus ◽  
Spectral Element ◽  
Solid Model ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Forward And Inverse Modeling

Summary The generalized standard-linear-solid model, also called the Zener model, is widely used in viscoacoustic/viscoelastic wavefield forward and inverse modeling, because the wave equations in this model can be written in differential equation form, which can be solved efficiently by time-domain numerical methods such as finite difference method, spectral element method, etc. For this model, however, two different expressions for the relaxation function (or complex modulus) appear in the literature somewhat confusingly. In addition to this confusion, the time- and frequency-domain versions of the wave equations for the generalized standard-linear-solid model are scattered throughout the literature. Here, we revisit the generalized standard-linear-solid model and seek to overcome the confusion concerning the expression for the relaxation function (or modulus). We present a unified approach to derive the viscoacoustic wave equations. We start with the time- and frequency-domain formulations separately to derive two sets of viscoacoustic wave equations. All these viscoacoustic wave equations are expressed in a simple and compact form. The two sets of viscoacoustic wave equations are equivalent to each other. The proposed method to derive the appropriate viscoacoustic wave equations can be extended to derive wave equations for other dissipative media.

Comparison of 2-D numerical viscoelastic waveform modeling with ultrasonic physical modeling

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 862-871 ◽  
Author(s):  
Genmeng Chen
Keyword(s):  
Physical Model ◽  
Physical Modeling ◽  
Wave Attenuation ◽  
Numerical Study ◽  
Solid Model ◽  
Viscoelastic Materials ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Voigt Model

The objective of the study is to test the validity of theoretical models of wave attenuation by comparing their predictions of attenuation against physical model results. The study is confined to a 2-D geometry, and the viscoelastic materials used in physical modeling are those commonly used in the experiment. The physical modeling data of homogeneous media are compared with the numerical results in the frequency domain. The time‐domain comparisons between numerical modeling and physical modeling are also shown by three examples. The theoretical viscoelastic models used in the numerical study are the Kelvin‐Voigt model, the standard linear solid model, and the standard linear solid model with a continuous spectrum of relaxation time. On the comparison of a single model, all the models simulate the physical model fairly well, but the standard linear solid model gives the best result among them. The Kelvin‐Voigt model is easy to use as a quick first‐order simulation of the viscoelastic materials because it has fewer viscosity parameters than the other two models. The disadvantage of the Kelvin‐Voigt model is that it predicts too much attenuation of the high‐frequency components. It is also shown that neglecting the viscosity of some materials like polyvinylcloride plastic (PVC), which has high viscosity, will produce incorrect results in synthetic seismograms.

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