Free vibration analysis of stringer stiffened general shells of revolution using a meridional finite strip method

•Mid-surface of the shell may have arbitrary shape as well as variable thickness.•The stiffeners may have an arbitrarily variable section in the meridian direction.•The adopted element permits the analysis of both thin and moderately thick shells.•So, the moment MζMζ and shear force have negligible effects on the strain energy of stiffeners.•Stiffening a shell with stringers may decrease or increase the natural frequency.

A deep doubly curved shell element is developed for free vibration analysis of general shells of revolution. The mid-surface of the shell may have an arbitrary shape as well as a variable thickness, and the shell can be closed circumferentially or not. For both the circumferential and meridian directions of the shell element, Lagrange polynomials are used to interpolate the displacement variables. Stringer stiffeners are modeled as discrete curved beams to investigate the free vibration of stiffened shells. The frequencies are compared with the published data, and new examples of axisymmetric shells with positive and negative Gaussian curvature are presented.

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