Spillover, nonlinearity and flexible structures

It is suggested that a partial differential equation should not be linearized until after its reduction to a finite-dimensional ordinary differential equation. This idea can be implemented by means of an analytical procedure involving the Lyapunov-Schmidt bifurcation equations. A rigorous reduction of a singular infinite-dimensional implicit equation to the problem of an equivalent, merely finite-dimensional implicit equation is carried out. As an illustration, the auxiliary equation and bifurcation equations for the problem of deflection of an intension extensible beam is considered, including viscous damping and Balakrishnan-Taylor damping