Stateczność i Drgania Powłok w Oparciu o Wyniki Badan Modelowych

The author introduces certain assumptions enabling the determination of the form of buckling and the fundamental mode of vibration of a shell. The first assumption is, that the form of buckling of the system is similar to its deflection under the action of a concentrated force. The second assumption is that the fundamental mode of vibration is similar to the form of buckling.
After the determination of the deflection, calculations of the critical load or the frequency of vibration of the given shell cam be proceeded with.
Buckling of cylindrical and spherical shells is considered. In the case of a spherical shell the first assumption leads to the following value of critical load (or local stability loss):

(1) [...]

where E = Youngs's modulus, h = shell thickness, R = radius of curvature and  = Poisson's ratio.
The force method is used for the computation of the mode and frequency of resonance vibration of the shell. The result obtained confirms the second assumption. In the case of shells the deformation of which cannot be computed theoretically recourse can be made to model tests.
For this purpose, equations determining similarity laws for problems of stability and vibration are derived by means of dimensional analysis. Assuming geometrical similarity between the model and the real body and disregarding Poisson's ratio, the following simple equations for
shells are obtained:
(a) The similarity law for buckling,

(2) […]

where q is the critical load. One prime refers to the model, two primes to the real body. (b) The similarity law for vibration,

(3)  […]

where n vibration frequency, L linear dimensions of model and M specific mass (per unit volume). As an example of application of the Eqs. (2) and (3), a conoidal shell is discussed. Results of investigations and photographs of model tests by means of the author's method are included.