The recovery of external force in nonlinear system by using a weak-form integral method

Abstract

For the recovery of unknown external force in the inverse vibration problems, we first transform the linear ordinary differential equation of motion into a linear parabolic-type partial differential equation and then use the Green second identity to derive a boundary integral equation in terms of the adjoint Trefftz test functions. It results in a weak-form integral method to recover the external force for nonlinear structures, of which only the data of displacements and two velocities at initial and final times are specified. The advantages gained in this transformation to a weak-form integral formulation can be seen when we test some nonlinear inverse vibration problems within a long time span and under a large noise.