An improved generalized Lagrangian analysis method for attenuating waves

In this study, an improved generalized Lagrangian analysis method (LAM) is proposed for attenuating waves by means of mathematical derivations and numerical calculations. It addresses the difficulty of determining the stress and particle velocity from the measured strain histories, and it correlates the relationships among stress, strain, and particle velocity histories without the need for additional assumptions. Numerical errors encountered in the numerical calculations are analyzed, and feasible methods are proposed to reduce them, including optimized construction and multi-step iterative calculation. The accuracy of using the improved LAM is verified by a case study involving stress histories. By using error-control methods, the case study illustrates the feasibility and effectiveness of the improved LAM. Finally, a one-dimensional nonlinear viscoelastic bar model is established, and simulation results agree well with those of the improved LAM, thereby verifying again its validity and accuracy.