期刊
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
卷 23, 期 6, 页码 1570-1604出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/fca-2020-0079
关键词
fractional derivatives; constitutive equation; thermodynamical restrictions; wave propagation; stochastic process; stochastic excitation; Karhunen-Loeve expansion
资金
- Ministry of Education, Science and Technological Development of the Republic of Serbia
- Bulgarian Academy of Sciences
- Serbian Academy of Sciences and Arts through the project Operators, Differential Equations and Special Functions of Fractional Calculus - Numerics and Applications
Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loeve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.
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