A Complex Modal Analysis Method for Damped Vibration Systems (The Representation in the Second Order Differential Form of a Modal Equation and its Use for Practical Application)

Abstract

Second order uncoupled differential equations for the general damped vibration systems are derived theoretically. The equations are written in a form similar to the classical real modal equations by using the natural frequency, the modal damping ratio, and the newly defined complex modal mass. Introducing supplementary variables, the response analysis is carried out in a similar manner to the real modal analysis. By comparing these equations to the classical ones, physical meanings of the derived equations are clarified. For the vibration problems near the resonant point, approximate complex modal equations are derived which have almost the same form as the classical one. Some applications of the proposed method to vibration problems are discussed.