Harmonic response calculation of viscoelastic structures using classical normal modes: An iterative method

•Only classical normal modes are used in the proposed iterative method.•The method only needs to iteratively solve a diagonal dynamic equation.•The convergence condition of the iterative procedure is given.•The influence of higher modes is considered by using a mode correction technique.•The method is illustrated in terms of different types of viscoelastic materials.

An efficient iterative method, which only requires normal modes, is presented to calculate the harmonic response of viscoelastic structures. The method only needs to iteratively solve a diagonal dynamic equation instead of solving the dynamic equation directly such that it takes O(N2) instead of O(N3). However, the iterative procedure based on lower normal modes cannot be converged to the exact result. A modal correction technique is therefore introduced to improve the accuracy of iterative results. Finally, the efficiency and applicability of the method are illustrated in terms of sandwich plates with different types of viscoelastic core.