Demonstrates the relationship between vibration amplitude and frequency variation in systems with nonlinear spring characteristics, suggesting instability under certain parameters.
This paper deals with the steady vibration in a system with a periodically varying nonlinear spring characteristics of a symmetrical broken-linear type. Using an approximate analytical method, the relation between the amplitude of the vibration and the frequency of variation of the spring characteristics under several conditions are obtained. It is made clear that when the system parameters take certain values, no steady vibration extending over the ranges of nonlinear characteristics can exist. From this consideration, an approximate formula giving the boundary of the unstable region in the stability chart of a linear system with a periodic system parameter is obtained.
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Saburo Aiba (1958) studied this question.
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