The restriction of KB averaging method is discussed and asymptotic solution of the weakly nonlinear and forced oscillation u″+ω20u=εkcos ωt-εu3 is obtained by Struble technique. The conclusion about this oscillat...The restriction of KB averaging method is discussed and asymptotic solution of the weakly nonlinear and forced oscillation u″+ω20u=εkcos ωt-εu3 is obtained by Struble technique. The conclusion about this oscillation derived with other method is discussed. The results show that KB method will break down when a and θ in the zeroth solution of above eqation are not slowly varying functions of time t. The stationary solution of weakly nonlinear oscillation, u″+ω20u=εkcosω(ε)t-εu3 is also analysed.展开更多
文摘The restriction of KB averaging method is discussed and asymptotic solution of the weakly nonlinear and forced oscillation u″+ω20u=εkcos ωt-εu3 is obtained by Struble technique. The conclusion about this oscillation derived with other method is discussed. The results show that KB method will break down when a and θ in the zeroth solution of above eqation are not slowly varying functions of time t. The stationary solution of weakly nonlinear oscillation, u″+ω20u=εkcosω(ε)t-εu3 is also analysed.
