Forced Axisymmectric Motion of Shallow Spherical Shells

by Herbert Reismann,
Paul M. Culkowski,

Serial Information: Journal of the Engineering Mechanics Division, 1968, Vol. 94, Issue 2, Pg. 653-670

Document Type: Journal Paper


A formal solution is presented for the dynamic response of a shallow spherical shell under axisymmetric but otherwise arbitrarily distributed, time-dependent surface tractions, for arbitrary initial conditions and (admissible) homogeneous boundary conditions. The solution is obtained in terms of the eigen-functions associated with the free vibration of the shell, and appropriate orthogonality and normalization conditions are formulated. The free vibration problem for a clamped shell is solved, and an example of shell response to a transient loading condition is presented. The theoretical development and its application are carried out within the framework of a theory which accounts for the effect of shear deformation and rotatory inertia. A comparison with the theory which neglects these effects is presented. Significant differences in the predictions of the two theories are noted.

Subject Headings: Motion (dynamics) | Arbitration | Vibration | Transient loads | Shear deformation | Dynamic response | Spherical shells | Axisymmetry

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