Rayleigh’s Classical Damping Revisited
نویسندگان
چکیده
Proportional damping is a widely used approach to model dissipative forces in complex engineering structures and it has been used in various dynamic problems for more than ten decades. A major limitation of the mass and stiffness proportional damping approximation is the lack of generality of the model to allow for experimentally observed variation of damping factors with respect to vibration frequency in complex structures. To remedy this, a new generalized proportional damping model is proposed. The proposed method requires only the measurements of natural frequencies and modal damping factors which can be obtained using a point measurement of the frequency response function (FRF). Simulation examples are provided to illustrate the proposed method. Verification of the proposed technique in lab scale experiments is presented. It is concluded that the present method has significant potential in modelling damping in industrial scale structures. INTRODUCTION Modal analysis is the most popular and efficient method for solving engineering dynamic problems. The concept of modal analysis, as introduced by Lord Rayleigh (1877), was originated from the linear dynamics of undamped systems. The undamped modes or classical normal modes satisfy an orthogonality relationship over the mass and stiffness matrices and uncouple the equations of motion, i.e., if Φ is the modal matrix then Φ MΦ and Φ KΦ are both diagonal matrices. This significantly simplifies the dynamic analysis because complex multiple degree-of-freedom (MDOF) systems can be effectively treated as a collection of single degree-of-freedom oscillators. Real-life systems are not undamped but possess some kind of energy dissipation mechanism or damping. In order to apply modal analysis of undamped systems to damped systems, it is common to assume the proportional damping, a special type of viscous damping. The proportional damping model expresses the damping matrix as a linear combination of the mass and stiffness matrices, that is
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