An isogeometric FSDT approach for the study of nonlinear vibrations in truncated viscoelastic conical shells

• Published in: Engineering with computers Vol. 40; no. 3; pp. 1637 - 1651
• Main Authors: Shafei, Erfan, Faroughi, Shirko, Reali, Alessandro
• Format: Journal Article
• Language: English
• Published: London Springer London 01-06-2024; Springer Nature B.V
• Subjects: B spline functions; Basis functions; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Civil engineering; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Conical shells; Control; Deformation; Equations of motion; Knots; Math. Applications in Chemistry; Mathematical and Computational Engineering; Nonlinear equations; Original Article; Shear deformation; Systems Theory; Viscoelasticity; First-order shear deformation theory; NURBS-based isogeometric analysis; Periodic knot vector; Viscoelastic conical shell; Nonlinear vibration
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-023-01885-w

Nonlinear vibrations of truncated viscoelastic conical shell (TVCS) structures are studied using an isogeometric formulation based on non-uniform rational B-spline (NURBS) basis functions. The governing equations of motion for the TVCS are formulated in terms of meridional, circumferential, and transverse deformation components, using the first-order shear deformation theory (FSDT). The TVCS domain is modeled using a non-periodic knot vector along its meridional direction due to its bounded form and a periodic knot vector along the circumferential direction due to its periodicity. Assuming the generalized form of the Maxwell model for visco-elastic material, a system of coupled nonlinear equations for the isogeometric patch is obtained. Displacement functions are approximated using
C
1
quadratic and
C
2
cubic NURBS resulting in a generalized time-varying nonlinear problem. The effects of patch refinements, partial loading, and asymmetric hysteresis behavior on the nonlinear vibration of the TVCS structures with different geometries and load functions are investigated.