Abstract
The present analysis uses multi-timing regular perturbations in straight line expansions to research a precise equation having a cubic-quintic nonlinearity. The equation contains slowly-varying expressly time-dependent coefficients moreover as some tiny parameters upon that straight line expansions ar initiated. The formulation is seen to be typical of a precise mass-spring arrangement (with geometric imperfection), treed by a loading history that's expressly time-dependent and slowly variable, however endlessly decreasing in magnitude, whereas the restoring force on the spring encompasses a cubic-quintic nonlinearity. The dynamic buckling load of the elastic model structure is decided analytically and is said to the corresponding static buckling load. To the amount of the accuracy maintained, it's ascertained that the dynamic buckling load depends, among others, on the worth of the primary spinoff of the loading perform evaluated at the initial time. All results ar straight line and underlying the load amplitude.
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The present analysis uses multi-timing regular perturbations in straight line expansions to research a precise equation having a cubic-quintic nonlinearity. The equation contains slowly-varying expressly time-dependent coefficients moreover as some tiny parameters upon that straight line expansions ar initiated. The formulation is seen to be typical of a precise mass-spring arrangement (with geometric imperfection), treed by a loading history that's expressly time-dependent and slowly variable, however endlessly decreasing in magnitude, whereas the restoring force on the spring encompasses a cubic-quintic nonlinearity. The dynamic buckling load of the elastic model structure is decided analytically and is said to the corresponding static buckling load. To the amount of the accuracy maintained, it's ascertained that the dynamic buckling load depends, among others, on the worth of the primary spinoff of the loading perform evaluated at the initial time. All results ar straight line and underlying the load amplitude.
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