Transient Dynamic Analysis of Unconstrained Layer Damping Beams Characterized by a Fractional Derivative Model

Mikel Brun, Fernando Cortés and María Jesús Elejabarrieta
Additional contact information
Mikel Brun: Department of Mechanics, Design and Industrial Management, University of Deusto, Avda. de las Universidades 24, 48007 Bilbao, Spain
Fernando Cortés: Department of Mechanics, Design and Industrial Management, University of Deusto, Avda. de las Universidades 24, 48007 Bilbao, Spain
María Jesús Elejabarrieta: Department of Mechanics, Design and Industrial Management, University of Deusto, Avda. de las Universidades 24, 48007 Bilbao, Spain

Mathematics, 2021, vol. 9, issue 15, 1-18

Abstract: This paper presents a numerical analysis of the influence of mechanical properties and the thickness of viscoelastic materials on the transient dynamic behavior of free layer damping beams. Specifically, the beams consist of cantilever metal sheets with surface viscoelastic treatment, and two different configurations are analyzed: symmetric and asymmetric. The viscoelastic material is characterized by a five-parameter fractional derivative model, which requires specific numerical methods to solve for the transverse displacement of the free edge of the beam when a load is applied. Concretely, a homogenized finite element formulation is performed to reduce computation time, and the Newmark method is applied together with the Grünwald–Letnikov method to accomplish the time discretization of the fractional derivative equations. Amplitudes and response time are evaluated to study the transient dynamic behavior and results indicate that, in general, asymmetrical configurations present more vibration attenuation than the symmetrical ones. Additionally, it is deduced that a compromise between response time and amplitudes has to be reached, and in addition, the most influential parameters have been determined to achieve greater vibration reduction.

Keywords: transient analysis; finite element method; unconstrained damping beam; viscoelastic material; fractional derivative model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/15/1731/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/15/1731/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:15:p:1731-:d:599357

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().