Generalized solutions for the Euler-Bernoulli model with zener viscoelastic foundations and distributional forces
- Author
- G. Hörmann, S. Konjik and Ljubica Oparnica (UGent)
- Organization
- Abstract
- We study the initial-boundary value problem for an Euler-Bernoulli beam model with discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial force and an external load both of Dirac-type. The corresponding model equation is a fourth-order partial differential equation and involves discontinuous and distributional coefficients as well as a distributional right-hand side. Moreover the viscoelastic foundation is of Zener-type and described by a fractional differential equation with respect to time. We show how functional analytic methods for abstract variational problems can be applied in combination with regularization techniques to prove existence and uniqueness of generalized solutions.
- Keywords
- Generalized solutions, Colombeau generalized functions, fractional derivatives, functional analytic methods, energy estimates, BEAMS
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8644760
- MLA
- Hörmann, G., et al. “Generalized Solutions for the Euler-Bernoulli Model with Zener Viscoelastic Foundations and Distributional Forces.” ANALYSIS AND APPLICATIONS, vol. 11, no. 2, 2013, doi:10.1142/S0219530513500176.
- APA
- Hörmann, G., Konjik, S., & Oparnica, L. (2013). Generalized solutions for the Euler-Bernoulli model with zener viscoelastic foundations and distributional forces. ANALYSIS AND APPLICATIONS, 11(2). https://doi.org/10.1142/S0219530513500176
- Chicago author-date
- Hörmann, G., S. Konjik, and Ljubica Oparnica. 2013. “Generalized Solutions for the Euler-Bernoulli Model with Zener Viscoelastic Foundations and Distributional Forces.” ANALYSIS AND APPLICATIONS 11 (2). https://doi.org/10.1142/S0219530513500176.
- Chicago author-date (all authors)
- Hörmann, G., S. Konjik, and Ljubica Oparnica. 2013. “Generalized Solutions for the Euler-Bernoulli Model with Zener Viscoelastic Foundations and Distributional Forces.” ANALYSIS AND APPLICATIONS 11 (2). doi:10.1142/S0219530513500176.
- Vancouver
- 1.Hörmann G, Konjik S, Oparnica L. Generalized solutions for the Euler-Bernoulli model with zener viscoelastic foundations and distributional forces. ANALYSIS AND APPLICATIONS. 2013;11(2).
- IEEE
- [1]G. Hörmann, S. Konjik, and L. Oparnica, “Generalized solutions for the Euler-Bernoulli model with zener viscoelastic foundations and distributional forces,” ANALYSIS AND APPLICATIONS, vol. 11, no. 2, 2013.
@article{8644760,
abstract = {{We study the initial-boundary value problem for an Euler-Bernoulli beam model with discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial force and an external load both of Dirac-type. The corresponding model equation is a fourth-order partial differential equation and involves discontinuous and distributional coefficients as well as a distributional right-hand side. Moreover the viscoelastic foundation is of Zener-type and described by a fractional differential equation with respect to time. We show how functional analytic methods for abstract variational problems can be applied in combination with regularization techniques to prove existence and uniqueness of generalized solutions.}},
articleno = {{1350017}},
author = {{Hörmann, G. and Konjik, S. and Oparnica, Ljubica}},
issn = {{0219-5305}},
journal = {{ANALYSIS AND APPLICATIONS}},
keywords = {{Generalized solutions,Colombeau generalized functions,fractional derivatives,functional analytic methods,energy estimates,BEAMS}},
language = {{eng}},
number = {{2}},
title = {{Generalized solutions for the Euler-Bernoulli model with zener viscoelastic foundations and distributional forces}},
url = {{http://doi.org/10.1142/S0219530513500176}},
volume = {{11}},
year = {{2013}},
}
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