Dynamic stiffness formulation for circular rings

• Published in: Computers & structures 2012-12, Vol.112-113, p.258-265
• Main Authors: Tounsi, D., Casimir, J.B., Haddar, M.
• Format: Article
• Language: English
• Subjects: Circular ring; Civil Engineering; Continuous element method; Curved beam; Dynamic stiffness method; Dynamical systems; Dynamics; Dynamique, vibrations; Engineering Sciences; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical models; Physics; Rings (mathematics); Solid mechanics; Stiffness; Stiffness matrix; Structural and continuum mechanics; Structural members; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2012.08.005

► We present a procedure for calculating the dynamic stiffness matrix of circular rings. ► The numerical validation is achieved thanks to comparisons with FE results. ► The performances of the method are evaluated in the case of thick circular rings. ► Harmonic responses for two kinds of load cases are estimated. This paper describes a procedure for calculating the dynamic stiffness matrix of a circular ring. The basis of the dynamic stiffness method resides in determining the dynamic stiffness matrix of such structural elements. The solution of the elementary problem is derived using Hamilton’s principle and a Fourier series expansion of the solution. Concentrated and distributed loads are applied to the ring along several directions in order to determine the response of the system. The performances of the method are evaluated using comparisons with the harmonic responses of a circular ring obtained using the finite element method.