# Vibration amplitude

A structure withstands a vibration of amplitude x and frequency y for z number of cycles. How many number of cycles the structure will withstand if the vibration amplitude is doubled. How many number of cycles the structure will withstand if the vibration frequency is doubled?

Gokul43201
Staff Emeritus
The number of cycles to failure (N) is related to the cycle amplitude through an exponential relation $N = A \cdot S^{-k}$ which is typically plotted as a linear fit on a half-log plot, known as an S-N curve. (google "S-N curve fatigue" and look at images). The exponent in the relation is highly material dependent. Also, this behavior is only one possible kind of fatigue known as high-cycle fatigue (where loading is essentially restricted to the elastic regime). If stresses, are much higher (into the plastic regime), you have low-cycle fatigue, for which the cycles to failure (N) is related to the amplitude of plastic strain (again, by an exponential plot), and you can not relate this to a stress amplitude without a stress-strain curve.