Stability and Free Vibrations of Thin Cylindrical and Conical Shells of a Circular Cross Section under Various Boundary Conditions

摘要

After a survey of numerous papers by other authors dealing with the stability and free vibrations of thin isotropic supported cylindrical and conical shells under various boundary conditions, the present authors come to the conclusion that the formulas so far suggested for the determination of the frequencies of vibrations of the conical shells are cumbersome, and that their applicability range is not well defined. The present paper investigates the stability and small extra-axial free vibrations of structurally orthotropic cylindrical and conical shells under the action of axial compression and external pressure under various boundary conditions: six types of clamping for the cylindrical and three types for conical shells. The inertial forces in the normal and circular directions are taken into account, and the effect of the boundary conditions on the lowest frequency of the free vibrations of the shell is studied. The results of the calculations agree within the calculation errors, with the results of other authors. (Author)