Perturbation analysis on the dynamic buckling of a lightly damped spherical cap modulated by a slowly varying sinusoidal load (1)

This investigation makes a conscious effort at analytical determination of the dynamic buckling load of an imperfect lightly damped spherical cap modulated by a sinusoidally slowly varying dynamic load. Essentially, the formulation is that of an elastic nonlinear oscillatory system, with small perturbations and with coefficients that are harmonically and dynamically slowly varying. The imperfection is discretized into an axisymmetric and a non-axisymmetric mode which are also the shapes of the equally discretized buckling modes. The dynamic buckling load is obtained and is related to the static buckling load. This by-passes the labour of repeating the entire process for different imperfection parameters. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 315-32