A distinct property of the natural frequency spectrum of a class of thin elastic shells is considered. New combinational frequencies and corresponding modes can be generated in the frequency spectrum with time due to increasing load. Those new frequencies and modes are equal to the natural ones of the shell. Generation of such combinational frequencies is known as internal resonance. This feature is illustrated by the example of a spherical shell under radial compression and a cylindrical shell under axial compression. A situation when a resonant frequency is the sum of two natural frequencies (and the same is true for corresponding modes) is analyzed. Formation of resonant frequencies can lead to buckling when small nonlinear factors are taken into consideration. This effect is demonstrated using examples of simple discrete models.
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