The use of vibration to reduce residual stress levels in fabrications is potentially an attractive alternative to thermal annealing. The application of the process has hitherto been limited by the lack of coherent theory of operation. In this study, residual stresses were introduced into a low-alloy steel EN3b by rolling. It was shown that prolonged low-amplitude vibration at 100 Hz induced a stress relaxation of as much as 40 per cent, where the original level was close to yield. A model has been developed to explain the diverse effects resulting from low-amplitude vibration; the model involves the motion of dislocations under the influence of the combined residual and external cyclic stress fields. This model, which has been validated by detailed X-ray line profile analysis and elasticity measurements, is an extension to the currently available explanation for VSR (vibratory stress relief). The standard model, which assumed the need to exceed the local yield stress, only comes into operation at the higher levels of applied stress amplitude. The development of accurate and validated methods for the application of VSR may now be contemplated.

In this paper, we describe and illustrate the application of a novel approximation technique for coupled, nonlinear dynamic systems. The technique begins by obtaining the analytical (or approximate analytical) solutions to the uncoupled system. Then, these solutions are used to approximate particular terms in the fully-coupled, nonlinear system in such a way that the target system is amenable to (approximate) analytical solution algorithms. This work forms part of a larger effort to develop robust control systems for large-scale industrial manipulators. To this end, the final example examined in this work considers the FutureForge manipulator: a state-of-the-art manipulator which forms part of a next-generation forging platform under development at the Advanced Forming Research Centre in Glasgow. To show the breadth of applications of our approach, we also apply it to more widely-recognised models like the Rayleigh and Van der Pol oscillators. In both of these cases, we consider a system of two oscillators each having dynamic behaviour described by Rayleigh/Van der Pol oscillators and coupled together through the resulting damping matrices.

In this paper, we describe and illustrate the application of a novel approximation technique for coupled, nonlinear dynamic systems. The technique begins by obtaining the analytical (or approximate analytical) solutions to the uncoupled system. Then, these solutions are used to approximate particular terms in the fully-coupled, nonlinear system in such a way that the target system is amenable to (approximate) analytical solution algorithms. This work forms part of a larger effort to develop robust control systems for large-scale industrial manipulators. To this end, the final example examined in this work considers the FutureForge manipulator: a state-of-the-art manipulator which forms part of a next-generation forging platform under development at the Advanced Forming Research Centre in Glasgow. To show the breadth of applications of our approach, we also apply it to more widely-recognised models like the Rayleigh and Van der Pol oscillators. In both of these cases, we consider a system of two oscillators each having dynamic behaviour described by Rayleigh/Van der Pol oscillators and coupled together through the resulting damping matrices.