The Numerical Method for Natural Frequencies Analysis of Simply Supported Ring-Stiffened Cylinder

Abstract:

Based on frequency equation of simply supported ring-stiffened cylinder, an alternative approach for calculating natural frequencies of ring-stiffened cylinder is proposed. Using some transformation techniques, the frequency equation is converted to determinant form of matrix pencil. Thus, solving frequency equation is equivalent to calculating generalized eigenvalues of matrix pencil. Then the natural frequencies of ring-stiffened cylinder are acquired with QR method. The result of QR method agrees well with that of bisection method and finite element method. By reducing order of the determinant, a simplified formula for calculating the minimum natural frequency of ring-stiffened cylinder is given. It proves that the simplified formula meets accuracy requirements when rings have small stiffness through comparing results from QR method and simplified formula. Using the approach of this paper, natural frequency’s curves of ring-stiffened shell are compared with that of unstiffened cylinder, while the effects of ring’s number and stiffness on natural frequencies are investigated.

• Periodical: Applied Mechanics and Materials (Volume 248)
• Pages: 133-139
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.248.133
• Online since: December 2012
• Authors: An Fu Zhang, Mei Ping Sheng
• Keywords: Generalized Eigenvalue, Natural Frequency, Ring-Stiffened Cylinder, Simplified Formula

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