On the Reconstitution Problem in the Multiple Time-Scale Method

摘要: Higher-order multiple-scale methods for general multiparameter mechanical systems are studied. The role played by the control and imperfection parameters in deriving perturbative equations is highlighted. definition of codimension problem, borrowed from bifurcation theory, extended to systems, excited either externally or parametrically. concept a reduced dynamical system then invoked. Different approaches followed literature deal with reconstituted amplitude discussed, both search steady-state solutions analysis stability. Four classes considered, based on consistency inconsistency approach, completeness incompleteness terms retained analysis. four critically compared conclusions drawn. Finally, three examples illustrated corroborate findings show quantitative differences between various approaches.