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Structural Dynamic Analysis with Generalized Damping Models: Analysis by Sondipon Adhikari

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Chapter 5Linear Systems with General Non-Viscous Damping

In Chapter 4, a symmetric state-space approach for exponentially damped linear systems was proposed. It was shown that the dynamic response of the system can be obtained in a manner similar to undamped or viscously damped systems provided that the eigenvalues and eigenvectors are available. Calculation of the eigensolutions in the state-space is computationally expensive as the dimension of the system can be very large due to the additional internal variables. The purpose of this chapter is to consider methods based on the configuration space. We also consider general non-viscous damping model for analytical developments. The exponential model discussed in Chapter 4 can be considered as a special case. We express the equation of motion of forced vibration of an N degrees-of-freedom linear system with general non-viscous damping as

[5.1] images

The initial conditions associated with the above equation are

[5.2] images

In section 1.3, currently available methods for analyzing such systems were discussed. The majority of the available methods employ additional dissipation coordinates and then use the state-space formalism. This approach is not only computationally more involved but also physical insight is lost in such approach. For this reason, ...

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