On the critical instability wavelengths of rod morphologies containing an arbitrary sinusoidal perturbation

The critical instability wavelengths of an infinitely long rod containing an arbitrary sinusoidal perturbation are resolved by using the two dimensionless variables λ/(2πR) and δ/R (λ and δ are the wavelength and the amplitude of the perturbation introduced, respectively; R is the average radius of the perturbed rod). It is revealed that λc/(2πR) decreases linearly with an increasing (δ/R)2 (λc is the critical instability wavelength). A linear relationship exists as λc/(2πR) = 1.00 - 0.34 (δ/R)2 with the linear relativity as high as 0.999. This result provides a simple criterion for the instability of rod morphologies that contain a sinusoidal perturbation.