Multiple scales analyses of the dynamics of weakly nonlinear mechanical systems

摘要: This review article starts by addressing the mathematical principles of perturbation method multiple scales in context mechanical systems which are defined weakly nonlinear ordinary differential equations. At this stage paper investigates some different forms typical nonlinearities frequently encountered machine and structural dynamics. leads to conclusions relating relevance scope popular versatile method, its strengths, adaptability potential for variant forms, also weaknesses. Key examples from literature used develop consolidate these themes. In addition examines role term-ordering, integration so-called small (ie, perturbation) parameter within system constants, nondimensionalization time-scaling, series truncation, inclusion exclusion higher order nonlinearities, problems handling secular terms. general discussion is then applied models dynamics space tethers given that necessarily highly susceptible modelling accuracy, thus offering a rigorous testing applications case-study area method. The concludes with comments on use variants constraints can bring expectations accuracy.