Dynamic response of viscoelastic functionally graded barrel and hyperboloidal coil springs with variable cross-sectional area

This paper investigates the dynamic response of viscoelastic axially functionally graded (AFG) barrel and hyperboloidal coil springs with variable cross-sectional area. Equations governing the dynamic behaviour of spatial rods are obtained via Timoshenko beam theory. The viscoelastic characteristics...

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Bibliographic Details
Published in:Mechanics of time-dependent materials 2022-12, Vol.26 (4), p.923-937
Main Authors: Cuma, Yavuz Cetin, Calim, Faruk Firat
Format: Article
Language:English
Subjects:
Algorithms
Beam theory (structures)
Characterization and Evaluation of Materials
Classical Mechanics
Coils
Cross-sections
Damping ratio
Dynamic response
Engineering
Forced vibration
Functionally gradient materials
Matrix methods
Polymer Sciences
Solid Mechanics
Springs (elastic)
Stiffness matrix
Timoshenko beams
Transfer matrices
Vibration analysis
Viscoelasticity
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Summary:This paper investigates the dynamic response of viscoelastic axially functionally graded (AFG) barrel and hyperboloidal coil springs with variable cross-sectional area. Equations governing the dynamic behaviour of spatial rods are obtained via Timoshenko beam theory. The viscoelastic characteristics of the material are described by Kelvin’s model. The transfer matrix method and stiffness matrix methods are used in combination in the numerical solution of the problem. Stiffness matrices are determined by the transfer matrix method (TMM). Solutions are obtained in the Laplace domain; the results are transformed into the time domain by Durbin’s inverse Laplace transform algorithm. A benchmark solution for verifying non-cylindrical geometry is successfully integrated into the damped forced vibration analysis. A parametric study is conducted in which cylinder radius ratio, damping ratio, material gradient and cross-sectional area are varied for both helical rod geometries mentioned above.
ISSN:1385-2000
1573-2738
DOI:10.1007/s11043-021-09520-1