Abstract
In this investigation, regular perturbation procedures in asymptotic expansions of the relevant variables are employed to discuss the static buckling analysis of a finite deterministically imperfect but viscously damped column resting on some quadratic–cubic nonlinear elastic foundations, but struck by a step load. The governing equation for the system under discussion is fully nonlinear, so that a closed form and easy solution to the problem is not possible. An approximate analytical solution to the problem is obtained using asymptotic and perturbation techniques and numerical results obtained show that increase in imperfection factors lower the static buckling loads of the column.
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