A unified approach for the vibration analysis of cylindrical shells with general boundary conditions

Cylindrical shells are widely used in engineering practice; in particular, one of the special applications is a tire, which can be modeled as a cylindrical shell on an elastic foundation (CSEF). To investigate influences of related parameters on the dynamic characteristics of the shell and help engineers to gain insights into the tire dynamics, a unified formulation for vibration analysis of the cylindrical shell with general boundaries has been developed; this unified formulation includes (i) formulations for CSEF governing equations based on the Donnell–Mushtari theory and Hamilton’s principle; (ii) a unified approach for the solutions of the characteristic equation; and (iii) a general treatment of the boundary conditions by adjusting the foundation spring coefficients. All nine sets of possible solutions of the characteristic equation are clarified and examined. Five case studies have been conducted to validate and verify the developed algorithm. The results based on the developed method generally have good agreement with those of the finite element method and experiment; missed solutions can be recovered.