Wavelet-Galerkin method for reconstruction of structural dynamic responses

Abstract

In this article, the wavelet-Galerkin method is adopted for calculating structural dynamic responses under the framework of multiresolution analysis. At first, the second-order differential equation of motion is transformed into wavelet domain through function expansion with scaling function at the chosen resolution level. The number of basis function is uniquely determined, and the corresponding coefficients are approximated by numerical quadrature method. And then the two-term connection coefficients are derived and computed at various scales. After this, the dynamic responses of the system with single degree of freedom subjected to sinusoidal excitation are obtained and validated. Subsequently, the proposed method is extended to multidegree-of-freedom systems based on mode-superposition method. Finally, the parametric study is performed, and the simulation results show that the identified dynamic responses match the true responses very well with appropriate choice of the resolution level and the wavelet order.