An analysis of nonlinear damping and stiffness effects in force-limited random vibration testing

The effects of both stiffness and damping nonlinearities on force-limited, random vibration test specifications are investigated. The response of the source-load vibratory system to a random, Gaussian excitation is analyzed using the modal- and residual-mass two degree-of-freedom system. The technique of statistical linearization is used in conjunction with the frequency shift method to derive force-limiting specifications for a nonlinear load mass modeled as a Duffing, Rayleigh damped, and linear plus quadratically damped oscillator, respectively. The normalized force-limiting specification for each nonlinear system is determined for a range of nonlinear stiffness and damping coefficients and compared with its linear counterpart over the same range of effective mass parameters. In general, deviations in the force-limiting spectrum arising from nonlinear stiffness effects will be apparent only at low frequencies on systems that are lightly damped, have large nonlinear stiffness parameters, and that experience moderately high input excitations. Deviations in the force-limiting spectrum arising from nonlinear damping effects will be apparent at lower frequencies on systems that are lightly damped, but having smaller nonlinear damping parameters and input excitations than their nonlinear stiffness counterparts. Case studies are presented to illustrate the methodology for deriving both linear and nonlinear force-limiting specifications for use in the test laboratory.