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

• 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
• ISSN: 1385-2000; 1573-2738
• DOI: 10.1007/s11043-021-09520-1

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.