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Indexed by:期刊论文

Date of Publication:2018-04-01

Journal:JOURNAL OF VIBRATION ENGINEERING & TECHNOLOGIES

Included Journals:SCIE

Volume:6

Issue:2

Page Number:107-115

ISSN No.:2321-3558

Key Words:Symplectic method; Hamiltonian system; Exact solution; Free vibration; Cylindrical shell

Abstract:Purpose In engineering applications, the vibration analysis of cylindrical shells is highly significant for the design of engineering structures subjected to external dynamic excitations. In practice, the explicit expression would make a better and more quick design comparing to the numerical results. However, the studies on analytical method were concentrated on the semi-inverse method. To overcome the limitation, we introduce a new analytical treatment for the free vibration of cylindrical shells.
   Methods Under the framework of the Hamiltonian system, an analytical symplectic approach is introduced into the free vibration of cylindrical shells. In the symplectic space, exact solutions are obtained in a rational and systematic way without any trial functions.
   Results Analytical frequency equation for arbitrary boundary conditions is derived. Highly accurate natural frequencies and analytical vibration mode functions are obtained simultaneously.
   Conclusion In this paper, the governing equations for Donnell's and Reissner's shell theories can be successfully transformed into the Hamiltonian form by introducing a full state vector. The free vibration of cylindrical shells is reduced into a symplectic eigenproblem. Numerical results are compared with those previously published in literature and good agreement is observed. In addition, the proposed method can be extended to micro/nanoscale cylindrical shells.