STRUCTURAL SIMILITUDE FOR AXIAYMMETRIC FREE VIBRATION OF STIFFENED SHALLOW SPHERICAL SHELLS BY ENERGY METHOD

The general similitude conditions and scaling laws are derived by directly applying the similitude transformation to the total energy of a structural system. On this basis, partial similitude of vibration is mainly investigated based on innovative introduction of the formulas for stiffness parameters. A reinforced orthotropic shallow spherical shell is taken as an example for analysis. The frequency equations are obtained based on linear strain-displacement relations and maximum kinetic energy. Completely and partially similar vibrations are performed. The results show that completely similar models can predict the behavior of the prototype accurately. Section types of stiffeners of the model can be different from the ones of the prototype, when the ratios of the cross-sectional area, first and second moment of the stiffener area to their spacing are similar. This is convenient for the design of experiment models. A scaling law of partial similarity is derived when the Poisson's ratio of the model is equal or near to the value of the prototype, and the model can predict well the vibration of the prototype. The method and results of this paper have good practical value for relevant experiments and design.