Studying the modal coupling effect on the FRF response to the non-classically damped structures

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Abstract This research aims to study the effect of neglecting modal decoupling due to Rayleigh's lightly non-classical damping hypothesis when investigating the frequency response functions of the non-classically damped systems. Also, the present work examines how modal coupling impacts the energy transfer between the different damped modes of these systems. This study considers the modal analysis of non-classically damped linear dynamic systems by introducing damping devices into multi-degree freedom frame systems. This study presents three methods for solving the quadratic eigenvalue problem of the non-classically damped systems: The state-space method for obtaining the exact solution, the lightly non-classical method for the undamped complex eigenvalue problem, and Adhikari's iteration method to solve the original space problem. The results of decoupling the modes of the non-classically damped system using the modal assurance coefficient and plotting the frequency and phase responses are discussed. This study proposes an example of a multi-degree freedom frame system with an introduced external damper with three variations to illustrate the modal decoupling of non-classically damped systems.

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