Download or read book Wave Propagation in the Linear Theory of Viscoelasticity written by George M. C. Fisher and published by . This book was released on 1964 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was shown in AD-436 823 that, in the linear theory of viscoelasticity, the speed of propagation of an acceleration wave is a solution of a particular eigenvalue problem. It is demonstrated that this eigenvalue problem governs, not only the speed of propagation of acceleration waves, but also the propagation speeds of shocks and all higher order waves. Solutions which contain discontinuities of arbitrary order N are easily exhibited.
Download or read book Wave Propagation in the Linear Theory of Viscoelasticity written by George Myles Cordell Fisher and published by . This book was released on 1966 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Decay of Plane Waves in the Linear Theory of Viscoelasticity written by George Myles Cordell Fisher and published by . This book was released on 1965 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is the sequel to AD-604 661 in which we have derived a necessary propagation condition governing the wavespeeds with which shocks and all higher order singular surfaces must propagate in a material subject to linear viscoelastic behavior. Of obvious interest is the manner in which the wave front varies with time. This subject, in the case of nonlinear, one-dimensional acceleration waves, has been treated by Coleman and Gurtin. Their work on general materials with memory includes onedimensional linear viscoelastic wave propagation as a special case. They show that when the stressstrain law is non-linear, the strength of an acceleration wave may either grow or decay; but it always decays in the linear theory providing the initial slope of the relaxation function is negative. These same results were established simultaneously by Varley for a slightly less general constitutive assumption (a constitutive equation of integral type), but for more general motions (plane, cylindrical, and spherical waves). Chen has also treated this problem. (Author).
Download or read book Theory of Viscoelasticity written by R. M. Christensen and published by Courier Corporation. This book was released on 2013-04-26 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integration of theoretical developments offers complete description of linear theory of viscoelastic behavior of materials, with theoretical formulations derived from continuum mechanics viewpoint and discussions of problem solving. 1982 edition.
Download or read book Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition written by Francesco Mainardi and published by World Scientific. This book was released on 2022-08-16 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition keeps the structure of the first edition but each chapter has been revised and expanded, and new additions include a novel appendix on complete monotonic and Bernstein functions that are known to play a fundamental role in linear viscoelasticity.This book is suitable for engineers, graduate students and researchers interested in fractional calculus and continuum mechanics.
Download or read book Mathematical Problems in Linear Viscoelasticity written by Mauro Fabrizio and published by SIAM. This book was released on 1992-01-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.
Download or read book The Theory of Linear Viscoelasticity written by David Russell Bland and published by Pergamon. This book was released on 1960 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wave Propagation in Viscoelastic Media written by Francesco Mainardi and published by Pitman Advanced Publishing Program. This book was released on 1982 with total page 1022 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Viscoelastic Waves in Layered Media written by Roger D. Borcherdt and published by . This book was released on 2009 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a rigorous, self-contained exposition of the mathematical theory for wave propagation in layered media with arbitrary amounts of intrinsic absorption. The theory, previously unpublished in book form, provides solutions for fundamental wave-propagation problems and corresponding numerical results in the context of any media with a linear response (elastic or anelastic). It provides new insights regarding the physical characteristics for two- and three-dimensional anelastic body and surface waves. The book is an excellent graduate-level textbook. It permits fundamental elastic wave propagation to be taught in the broader context of wave propagation in any media with a linear response. The book is a valuable reference text. It provides tools for solving problems in seismology, geotechnical engineering, exploration geophysics, solid mechanics, and acoustics. The numerical examples and problem sets facilitate understanding by emphasizing important aspects of both the theory and the numerical results.
Download or read book Wave Propagation in Viscoelastic and Poroelastic Continua written by Martin Schanz and published by Springer Science & Business Media. This book was released on 2012-11-27 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave propagation is an important topic in engineering sciences, especially, in the field of solid mechanics. A description of wave propagation phenomena is given by Graff [98]: The effect of a sharply applied, localized disturbance in a medium soon transmits or 'spreads' to other parts of the medium. These effects are familiar to everyone, e.g., transmission of sound in air, the spreading of ripples on a pond of water, or the transmission of radio waves. From all wave types in nature, here, attention is focused only on waves in solids. Thus, solely mechanical disturbances in contrast to electro-magnetic or acoustic disturbances are considered. of waves - the compression wave similar to the In solids, there are two types pressure wave in fluids and, additionally, the shear wave. Due to continual reflec tions at boundaries and propagation of waves in bounded solids after some time a steady state is reached. Depending on the influence of the inertia terms, this state is governed by a static or dynamic equilibrium in frequency domain. However, if the rate of onset of the load is high compared to the time needed to reach this steady state, wave propagation phenomena have to be considered.
Download or read book Theory of waves in materials written by and published by Bookboon. This book was released on with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wave Propagation in Elastic Solids written by Jan Achenbach and published by Elsevier. This book was released on 2012-12-02 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: The propagation of mechanical disturbances in solids is of interest in many branches of the physical scienses and engineering. This book aims to present an account of the theory of wave propagation in elastic solids. The material is arranged to present an exposition of the basic concepts of mechanical wave propagation within a one-dimensional setting and a discussion of formal aspects of elastodynamic theory in three dimensions, followed by chapters expounding on typical wave propagation phenomena, such as radiation, reflection, refraction, propagation in waveguides, and diffraction. The treatment necessarily involves considerable mathematical analysis. The pertinent mathematical techniques are, however, discussed at some length.
Download or read book Wave Propagation in Viscoelastic Media written by and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical formulations of the wave propagation problem in a linear viscoelastic solid are reviewed from the point of view of constitutive equations and the theory of linear physical systems. Various general results from the theory of propagating singular surfaces and from the mathematical theory of hyperbolic equations are applied to the analysis of the wave propagation process. The impulse responses of three viscoelastic media are analyzed by use of asymptotic methods. The three material models are the standard linear solid, the standard linear solid with a continuous spectrum of relaxation times, and the power law solid. The standard linear solid with a continuous spectrum of relaxation times and the power law solid have a nearly constant quality factor, Q, over the seismic frequency band. The impulse responses of these two viscoelastic solids are compared. The results show significant and discernible features in the wave profile. It is concluded that differentiation of the models can be made by comparing wave shapes and that a complete knowledge of Q over the entire frequency range is required to determine the wave propagation problem when initiated by an impulsive process. 11 figures, 1 table.
Download or read book Waves in Elastic and Viscoelastic Solids written by Clifford Truesdell and published by . This book was released on 1984 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Viscoelasticity Plasticity Elastic Waves and Elastic Stability written by Clifford Truesdell and published by Springer. This book was released on 1984 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Wave Propagation in Linear Viscoelasticity written by W. J. Hrusa and published by . This book was released on 1984 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document discusses the initial value problem in one-dimensional linear visco-elasticity with a step-jump in the initial data. If the memory kernel is sufficiently smooth on (infinity), the solution exhibits discontinuities propagating along characteristics and a (higher order) stationary discontinuity at the position of the original step-jump. For a singular memory kernel, the propagating waves are smoothed in a manner depending on the nature of the singularity in the kernel, but the stationary discontinuity remains. Also discussed are the effects of these phenomena on the regularity of solutions with arbitrary initial data.
Download or read book Theory of Viscoelasticity Plasticity Elastic Waves and Elastic Stability written by Clifford Truesdell and published by Springer. This book was released on 1984 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:
