Explict form of an implicit method for inverse force identification

Most existing time domain force identification methods are based on the state space method, which has the disadvantage of large discretization error with a low sampling frequency or a long sampling duration. This work transforms the conventional implicit Newmark-β algorithm into an explicit form for the solution of the Ax=b equations, which is an equivalent transformation, and it exhibits the same characteristics of Newmark-β algorithm as an implicit method. The accuracy of this method for the dynamic force identification is illustrated with two shear-frame buildings and a planar truss structure. Numerical results are compared with reference analytical responses. The new method gives more accurate identified force time histories compared with those from the conventional state space method for multiple sinusoidal and white noise excitations with 10% measurement noise in the responses.