Analytical approximation of weakly nonlinear continuous systems using renormalization group method

摘要: Abstract A direct method based on renormalization group (RGM) is proposed for determining the analytical approximation of weakly nonlinear continuous systems. To demonstrate application method, we use it to analyze some examples. First, vibration a beam resting elastic foundation with distributed quadratic and cubic nonlinearities in cases primary subharmonic resonances n th mode. We apply RGM discretized governing equation also directly partial differential equations (PDE). The results are full agreement those previously obtained multiple scales method. Second, obtain higher order free vibrations nonlinearities. applied as well PDE. capable producing It shown that discretization methods not general equal. Finally, previous problem case expressed complex-variable form. second form agreement. observe systems, must be treated