Computational Inverse Procedure for Identification of Structural Dynamic Loads

It is generally difficult to measure dynamic loads directly in the case of the complexity of the structure or the variant forms of the loads, such as wave source, road excitation. A computational inverse procedure is a promising way to determine these transient loads. This procedure recovers the time history and the distribution functions of both concentrated and extended loads based on the knowledge of displacement responses at only one receiving point on a surface of the structure. This procedure assumed that the time and spatial domain dependencies of the loading function are separable. Two time-discrete kernel functions, dynamic Green’s function and the response function of Heaviside step excitation are obtained using the FEM method. By applying the kernel functions, the displacement responses for a dynamic load with an arbitrary time function can be expressed in a form of convolution integral and the extended loading source is treated as a linear superposition of point sources. These continuous convolution functions are then temporally and spatially discretized. Since the Green’s or Heaviside’s function matrix is generally ill-conditioned, we can not simply use the conventional matrix operation for deconvolution. To overcome this difficulty, error function (objective function) is constructed and the optimization scheme is employed to recover both the loading time history and the distribution function. Numerical examples for both concentrated and extended load demonstrate the efficiency and accuracy of the proposed procedure.