On the Use of the Convolution Integral for Calculating the Response of Flexible Structures

Accurate prediction of structural response under moving loads remains a challenging problem, particularly for flexible systems such as prestretched cables. This study introduces a new formulation of utilizing convolution integral to calculate the response of a field structure points due to moving loads with different rates. In addition, this work compares two complementary modeling approaches to evaluate the dynamic response induced by a moving point load. The first, termed the Analytical Moving-Load Model (ANMDL), employs a convolution integral formulation to obtain closed-form analytical responses. The second, the Finite Element Moving-Load Model (FEMDL), uses a finite element framework to simulate the same loading conditions numerically. Both models assume linear system behavior, allowing the application of the superposition principle. A prestretched cable subjected to a moving point load is investigated as a case study to validate and assess the two formulations. The results demonstrate strong agreement between ANMDL and FEMDL, confirming the reliability of the analytical approach for dynamic cable analysis. A parametric investigation reveals that the velocity of the moving load significantly affects the cable response, whereas the load magnitude has a comparatively smaller influence. The proposed framework provides new insights into the dynamic behavior of cable systems and offers an efficient alternative to fully numerical simulations for moving-load problems.