Broadband Random Excitation Research Articles

Response of a non-linearly damped oscillator to combined periodic parametric and random external excitation

An analytical solution, using the Fokker-Planck-Kolmogorov equation, is obtained for the problem of response of a non-linearly damped oscillator to combined periodic parametric and random external excitation. The solution yields first-order probability densities of amplitude and phase. These expressions are employed to distinguish between oscillations excited by external and parametric periodic forces in the presence of additional broadband random external excitation. Through decoupling of fast and slow motions an approximate expression is obtained for expected value of time to phase “switch”.

Accelerated vibration fatigue life testing of leads and soldered joints

The prediction of vibration fatigue life of leads and solder joints at low excitation from that obtained during high-level testing is possible but the extrapolation exponent depends not only on the S- N curve of the failed material, but also on the type of excitation and on whether failure is due to component or to support resonance. For single-frequency excitation the exponent for copper lead-wire failures is 8 if the circuit board resonates, 3.2 or, more realistically, 2.6 if the forcing frequency is constant at the initial value of component resonance, and 1.5 if it tracks the component resonance. For swept frequency the exponent is approximately 8 if failure is due to board resonance, 2.3 if due to component resonance, and this difference prevents extrapolation from swept-frequency tests which in the one sweep cover both component and support resonances. A similar problem exists for broadband random excitation. For 50/50 solder joints the exponent was 5.6 for non-resonant excitation, failure times being approximately log-normally distributed. The resonant frequency of components drops as vibration damage accumulates in the leads. The chenge in f n can serve as a measure of damage before fracture occurs, but also leads to incorrect, optimistic conclusions from fixed-frequency, initially resonant, testing, owing to the component's detuning.

Response Spectra for Nonlinear Oscillators

Methods are presented for calculating the response spectrum of a nonlinear oscillator with broadband random excitation. A perturbation approach is used for oscillators with slightly nonlinear spring elements to show that the effect of the nonlinearity is a slight shift in the spectrum peak. A new heuristic approach is used for oscillators with large nonlinearities and small damping to show that in addition to a shift in the peak an increase in spectral bandwidth also occurs. The Duffing oscillator is studied as a specific example.

An Investigation of Fatigue Failure of Materials under Broad Band Random Vibrations

I the present paper the fatigue life of material under the multifactor influence of broad band random excitations was investigated. Parameters which affect the fatigue life were postulated to be peak stress, variance of stress, and the natural frequency of the system. Experimental data were processed by the hybrid computer. Based on the experimental results and the regression analysis, a best predicting model has been found. All values of the experimental fatigue lives are within the 95% confidence intervals of the predicting equation. Research results in narrow band random fatigue have been reported.'

On the optimization of saturating servomechanisms subjected to random disturbances

Using power balance equations for nonlinear second-order systems subjected to broad-band random excitation, the average response of some typical servomechanisms is derived. The results are quantitative in limitating cases and provide a strong qualitative understanding of the systems in intermediate cases. The notion that a time-optimal feedback system provides satisfactory behavior when external disturbances are present is shown to be not true in some cases.