New exact free vibration solution of two-dimensional decagonal quasicrystal cylindrical shells in the symplectic framework

Abstract

An accurate free vibration analysis of two-dimensional decagonal quasicrystal (QC) cylindrical shells is performed under the framework of symplectic mechanics. Unlike the classical Lagrangain system, the governing equations are reduced into a set of lower order ordinary differential equations, and therefore exact solutions of displacements, rotation angles, internal forces and bending moments in the phonon and phason fields are simultaneously obtained and expressed in terms of symplectic vectors. The present results are compared with existing literature and finite element solutions, and excellent agreements are observed. Furthermore, the effects of key influencing factors on the free vibration characteristics are revealed also.

Keywords:

• Natural frequency
• vibration mode shapes
• free vibration
• quasicrystal cylindrical shell
• symplectic method
• analytical solution

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Natural Science Foundation of Liaoning Province [grant number 2023-MS-118] and the Fundamental Research Funds for the Central Universities [grant number DUT22LK16].