Journal ArticleDOI
Linear models of dissipation in anelastic solids
Michele Caputo,Francesco Mainardi +1 more
- Vol. 1, Iss: 2, pp 161-198
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The article was published on 1971-04-01. It has received 726 citations till now. The article focuses on the topics: Dissipation.read more
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On abstract Cauchy problems in the frame of a generalized Caputo type derivative
Fahd Jarad,Thabet Abdeljawad +1 more
TL;DR: In this paper , the authors considered a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional and discussed the existence and uniqueness of mild solutions.
Dynamic response of the fractional driving force
TL;DR: In this article, the authors show that the dynamic response of a sinusoidal forcing system exhibits some characteristics of a regular relaxor, and for the range 1 < D < 2, some properties of a damped harmonic oscillator, and the two phase lags approach each other in the limit o D 1 from either side of 1.
Book ChapterDOI
Viscoelasticity of Solids (Old and New)
TL;DR: The approach adopted here is essentially historical, with technicalities kept to a minimum as discussed by the authors, and it is a branch of continuum mechanics which fostered the expansion of a good general thermo-mechanics of continua (first with Duhem and Eckart) and favored the creation of rational continuum mechanics in the sense of Truesdell, Noll and Coleman.
Book ChapterDOI
Wavelet-Based Laplace Transformation for Initial- and Boundary-Value Problems
TL;DR: In this article, the Laplace transform of a function is defined on a domain of s, and the integral of the function is obtained by converging in a Laplace domain.
Proceedings ArticleDOI
Response Dynamics in the Continuum Limit of the Lattice Dynamical Theory of Viscoelasticity (Fractional Calculus Approach)
TL;DR: In this paper, a fractional diffusion-wave equation is derived in the continuum limit of the lattice dynamical equations of motion of a chain of coupled fractional oscillators obtained from the integral equation of motion for simple harmonic oscillators by generalization of the ordinary integrals into ones involving fractional integrals.
References
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Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Book
Stress Waves in Solids
TL;DR: A large and growing number of original papers on both the experimental and the theoretical aspects of stress wave propagation is appearing in the scientific literature, and two international conferences solely concerned with the subject have been held during the last five years as mentioned in this paper.