Summary In this paper, the dynamic response of a damaged double‐beam system traversed by a moving load is studied, including passive control using multiple tuned mass dampers. The double‐beam system is composed of two homogeneous isotropic Euler–Bernoulli beams connected by a viscoelastic layer. The damaged upper beam is simulated using a double‐sided open crack replaced by an equivalent rotational spring between two beam segments, and the lower primary beam is subjected to a moving load. The load is represented by a moving Dirac delta function and by a quarter car model, respectively. Road surface roughness (RSR) is classified as per ISO 8606:1995(E). The effect of vehicle speed of the moving oscillator and variable RSR profiles on the dynamics of this damaged double Euler–Bernoulli beam system for different crack‐depth ratios (CDRs) at various crack locations is studied. It is observed that coupling of two beams leads to a vehicular effect on the damaged beam, even when no vehicle on it is present. The effects of single and multiple tuned mass dampers to control the vibrational responses of the primary beam due to damage on the secondary beam is studied next. The performance of tuned mass dampers to reduce the transverse vibrations of the damaged double‐beam system and of the quarter car is investigated. The paper links the coupling between the two levels of double beam with the inertial coupling of the vehicle to the double‐beam system.

This article generalizes the implementation of higher order corrections to state transition matrices during instantaneous reversals in hybrid dynamical systems impacting a discontinuity boundary transversally. A closed form expression for saltation terms in systems possessing a degree of smoothness zero is derived. The difference in flight times of two closely initiated trajectories in state space to the impacting surface has been estimated up to O (2). A comparison of the times of impact estimated with the first order approximation reveals that higher order corrections lead to a significant improvement of estimates. Next, two new algorithms to estimate the Lyapunov spectrum and Floquet multipliers for piecewise-smooth systems have been presented using the derived second order corrections. Stability analyses are subsequently carried out using the proposed framework for two representative cases i.e., of a hard impact oscillator and a pair impact oscillator. It is established that the obtained Floquet multipliers and Lyapunov spectrum accurately predict the stability of the dynamical states, as validated by their corresponding bifurcation diagrams.