Vibration control performance of linear and nonlinear mass damping systems under stochastic excitation

This paper investigates the vibration control performance of both linear and nonlinear mass damping system devices under stochastic excitation. These devices are installed atop a primary structure, modeled as a typical linearly elastic single-degree-of-freedom (SDOF) system, and subjected to Gaussian White Noise (GWN) ground acceleration. To estimate the stochastic response of the nonlinear system, the Statistical Linearization (SL) method is employed. This approach approximates the original nonlinear system with an equivalent linear one by minimizing the mean-square error between their respective statistical properties. As a result, it facilitates the application of linear stochastic system theory to analyze the complex dynamics of nonlinear systems under random excitation. The SL method proves particularly effective in estimating the mean and variance of system responses in nonlinear dynamic systems. Several case studies are presented to illustrate the method's application and to demonstrate its computational efficiency and accuracy in comparison with Monte Carlo (MC) simulations. Furthermore, the results provide valuable insights into the stochastic response characteristics of both linear and nonlinear mass damping systems. Notably, a key finding challenges the prevailing belief: stiffness nonlinearity does not improve the passive device's capacity to absorb and dissipate energy from the primary structure.