Damping In Vibration Slide Presentation 
The concept of proportional damping is critically examined and a generalized form of proportional damping is proposed. It is shown that the proportional damping can exist even when the damping mechanism is non-viscous.Classical modal analysis is extended to deal with general non-viscously damped multiple degree-offreedom linear dynamic systems. The new method is similar to the existing method with some modifications due to non-viscous effect of the damping mechanism. The concept of (complex) elastic modes and nonviscous modes have been introduced and numerical methods are suggested to obtain them. It is further shown that the system response can be obtained exactly in terms of these modes. Mode orthogonality relationships, known for undamped or viscously damped systems, have been generalized to non-viscously damped systems. Several useful results which relate the modes with the system matrices are developed.These theoretical developments on non-viscously damped systems, in line with classical modal analysis,give impetus towards understanding damping mechanisms in general mechanical systems. Based on a first-order perturbation method, an approach is suggested to the identify non-proportional viscous damping matrix from the measured complex modes and frequencies. This approach is then further extended to identify non-viscous damping models. Both the approaches are simple, direct, and can be used with incomplete modal data.

Dynamics of Undamped Systems 
Equation of Motion
Modal Analysis
Models of Damping 
Single Degree-of-freedom Systems 
Continuous Systems 
Multiple Degrees-of-freedom Systems
Other Studies
Modal Analysis of Viscously Damped Systems 
The State-Space Method 
 Methods in Configuration Space 
Analysis of Non-viscously Damped Systems
Identification of Viscous Damping 
Single Degree-of-freedom Systems Systems 
Multiple Degrees-of-freedom Systems 
Identification of Non-viscous Damping 
Open Problems
Outline of the Dissertation
The Nature of Proportional Damping
Dynamics of Non-viscously Damped Systems
Symmetry Preserving Methods
Experimental Identification of Damping

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