Analysing modal coupling in non-classically damped systems: beyond Rayleigh’s damping hypothesis—a comparative study

This research delves into the consequences of neglecting modal coupling in non-classically damped systems, particularly within Rayleigh's lightly non-classical damping assumption. Damping devices are introduced into multi-degree-of-freedom frame systems to assess the impact of modal coupling on energy transfer in linear dynamic non-classical damping systems. Three distinct approaches for decoupling non-classically damped systems are introduced: the state-space approach for exact solutions, the lightly non-classical method for addressing the undamped complex eigenvalue problem, and the formulation of the quadratic eigenvalue problem to tackle the original eigenvalue problem. Modal coupling is evaluated using the modal assurance criterion. The study identifies instances of modal coupling in non-classically damped systems by analysing two scenarios. The proposed methodologies establish a robust foundation for exploring modal characteristics and advancing engineering solutions in various applications.