Derivation of Effective Ratio of Acoustic Impedance for Impacting Viscoelastic Slug (Standard Linear Solid Model) and Elastic Rod

2014 ◽  
Vol 554 ◽  
pp. 701-711
Author(s):  
Abu Bakar Musa
Keyword(s):  
Acoustic Impedance ◽  
Multiple Scales ◽  
Numerical Results ◽  
Viscoelastic Materials ◽  
Elastic Rod ◽  
Time Constants ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Impact ◽  
Viscoelastic Rod

The study is about impact of a short viscoelastic slug on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when a viscoelastic slug moving at a speed impacts a semi-infinite stationary viscoelastic rod. In order to validate the numerical results, we derive the effective ratio of acoustic impedance for impacting rods which will be used in the viscoelastic discontinuity analysis. The objective of this study is to investigate how the viscosity time constants in the slug and in the rod give rise to different interface stresses and interface velocities following wave transmission in the slug. After modeling the impact and solving the governing system of partial differential equations in the Laplace transform domain, we invert the Laplace transformed solution numerically to obtain the stresses and velocities. In inverting the Laplace transformed equations we used the complex inversion formula (Bromwich contour). In validating the numerical results, the method of viscoelastic discontinuity analysis is engaged to determine the first discontinuity jump at the interface. Finally, we discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the viscoelastic impacts obtained numerically and the predictions acquired using the multiple scales in perturbation.

Experimental Study of Concrete Aging Effect on the Contact Force and Contact Time During the Impact Interaction of an Elastic Rod with a Viscoelastic Beam

2016 ◽  
Vol 33 (3) ◽  
pp. 317-322 ◽  
Author(s):  
I. I. Popov ◽  
T.-P. Chang ◽  
Yu. A. Rossikhin ◽  
M. V. Shitikova
Keyword(s):  
Contact Force ◽  
Contact Time ◽  
Low Velocity Impact ◽  
Solid Model ◽  
Elastic Rod ◽  
Average Maximum ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Impact

AbstractIn the present paper, the low-velocity impact of an elastic rod with a flat end upon a viscoelastic Timoshenko type beam has been considered. Viscoelastic properties of the beam out of the contact zone are described by the standard linear solid model with integer derivatives, while inside this zone they are governed by the fractional derivative standard linear solid model. The contact force for a concrete target has been defined experimentally at the concrete age of 7, 14, 28, 56, and 91 days. It has been found that an average maximum of the contact force increases with concrete age, whereas the contact duration decreases. Moreover, the most remarkable changes of both, contact force and contact time, occur at the concrete age earlier than 14 days, after that the rate of changes slows down. Experimental results have a good coincidence with theoretical expectations.

Predicting the Impact Response of a Nonlinear Single-Degree-of-Freedom Shock-Absorbing System From the Measured Step Response

1997 ◽  
Vol 119 (3) ◽  
pp. 221-227 ◽  
Author(s):  
S. N. Robinovitch ◽  
W. C. Hayes ◽  
T. A. McMahon
Keyword(s):  
High Energy ◽  
Degree Of Freedom ◽  
Step Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impact Forces ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Impact ◽  
Measured Response

We measured the step response of a surrogate human pelvis/impact pendulum system at force levels between 50 and 350 N. We then fit measured response curves with four different single-degree-of-freedom models, each possessing a single mass, and supports of the following types: standard linear solid, Voigt, Maxwell, and spring. We then compared model predictions of impact force during high-energy collisions (pendulum impact velocity ranging from 1.16 to 2.58 m/s) to force traces from actual impacts to the surrogate pelvis. We found that measured peak impact forces, which ranged from 1700 to 5600 N, were best predicted by the mass-spring, Maxwell, and standard linear solid models, each of which had average errors less than 3 percent. Reduced accuracy was observed for the commonly used Voigt model, which exhibited an average error of 10 percent. Considering that the surrogate pelvis system used in this study exhibited nonlinear stiffness and damping similar to that observed in simulated fall impact experiments with human volunteers, our results suggest that these simple models allow impact forces in potentially traumatic falls to be predicted to within reasonable accuracy from the measured response of the body in safe, simulated collisions.

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.

scholarly journals Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions

2016 ◽  
Vol 7 ◽  
pp. 554-571 ◽  
Author(s):  
Santiago D Solares
Keyword(s):  
Atomic Force Microscopy ◽  
Computational Study ◽  
Plane Surface ◽  
Material Behavior ◽  
Dynamic Mode ◽  
Viscoelastic Materials ◽  
Force Microscopy ◽  
Atomic Force ◽  
Standard Linear Solid ◽  
Standard Linear

Significant progress has been accomplished in the development of experimental contact-mode and dynamic-mode atomic force microscopy (AFM) methods designed to measure surface material properties. However, current methods are based on one-dimensional (1D) descriptions of the tip–sample interaction forces, thus neglecting the intricacies involved in the material behavior of complex samples (such as soft viscoelastic materials) as well as the differences in material response between the surface and the bulk. In order to begin to address this gap, a computational study is presented where the sample is simulated using an enhanced version of a recently introduced model that treats the surface as a collection of standard-linear-solid viscoelastic elements. The enhanced model introduces in-plane surface elastic forces that can be approximately related to a two-dimensional (2D) Young’s modulus. Relevant cases are discussed for single- and multifrequency intermittent-contact AFM imaging, with focus on the calculated surface indentation profiles and tip–sample interaction force curves, as well as their implications with regards to experimental interpretation. A variety of phenomena are examined in detail, which highlight the need for further development of more physically accurate sample models that are specifically designed for AFM simulation. A multifrequency AFM simulation tool based on the above sample model is provided as supporting information.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

scholarly journals Impact of COVID-19 Pandemic on Retail Structure in Barcelona: From Tourism-Phobia to the Desertification of City Center

2021 ◽  
Vol 13 (15) ◽  
pp. 8215
Author(s):  
Lluís Frago Clols
Keyword(s):  
Multiple Scales ◽  
Real Estate Market ◽  
Structured Interviews ◽  
City Center ◽  
Urban Theory ◽  
The Real Estate ◽  
Tourist Flows ◽  
Before And After ◽  
The Impact ◽  
The City

COVID-19 has meant major transformations for commercial fabric. These transformations have been motivated by the collapse of consumer mobility at multiple scales. We analyzed the impact of the collapse of global tourist flows on the commercial fabric of Barcelona city center, a city that has been a global reference in over-tourism and tourism-phobia. Fieldwork in the main commercial areas before and after the pandemic and complementary semi-structured interviews with the main agents involved highlight the relationship between global tourist flows and commercial fabric. The paper shows how the end of global tourism has meant an important commercial desertification. The end of the integration of the city center into global consumer flows has implications for urban theory. It means a downscaling of the city center and the questioning of traditional center-periphery dynamics. It has been shown that the tourist specialization of commerce has important effects on the real estate market and makes it particularly vulnerable. However, the touristic specialization of commercial activities as a strategy of resilience has also been presented. This adaptation faces the generalized commercial desertification that drives the growing concentration of consumption around the online channel.

scholarly journals The Impacts of Groundwater Chemistry on Wetland Vegetation Distribution in the Northern Qinghai–Tibet Plateau

2019 ◽  
Vol 11 (18) ◽  
pp. 5022 ◽  
Author(s):  
Junju Zhou ◽  
Juan Xiang ◽  
Lanying Wang ◽  
Guoshuang Zhong ◽  
Guofeng Zhu ◽  
...  
Keyword(s):  
Multiple Scales ◽  
Groundwater Chemistry ◽  
Ion Concentration ◽  
Tibet Plateau ◽  
Distribution Data ◽  
Vegetation Distribution ◽  
Chemical Parameters ◽  
Weakly Alkaline ◽  
Artemisia Frigida ◽  
The Impact

Groundwater chemistry has an important impact on the vegetation distribution in inland areas. An in-depth understanding of the impact of groundwater chemistry on vegetation can help in developing an effective management strategy to protect the inland ecosystem. The aim of this study was to identify the influence of groundwater chemicals on species diversity and the distribution characteristics of wetland plants at multiple scales based on the groundwater chemical data from 15 sampling points and the distribution data of 13 plants in the Sugan Lake Wetland in 2016. The results show that the groundwater of the Sugan Lake Wetland is weakly alkaline, with high salinity and hardness; the water chemical type is Na-SO4-Cl; the concentration of the major water chemical parameters is significantly different and is the highest in the northwest, followed by the southwest, and is the lowest in the east; with an increase in the groundwater depth, the concentration of major water chemical parameters first showed an increasing trend followed by a decreasing trend; Artemisia frigida Willd, Poa annua L. and Triglochin maritimum L. were adapted to the environment with a higher ion concentration of the groundwater, and their salt resistance was the strongest; Blysmus sinocompressus and Polygonum are more adapted to the environment with lower salinity and hardness of groundwater; Thermopsis lanceolata has stronger adaptability to the ion concentration, salinity, and hardness of groundwater; other plants are adapted to environments where the ion concentration, salinity, and hardness of the groundwater are moderate.

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