Rayleigh’s dissipation function

Rayleigh s dissipation function is applied in order to properly handle the viscous component of the given dynamic system. In this case, it is assumed that the viscous nature of the dashpot will be linearly dependent upon the velocity of the mass. More specifically, the viscous damping force is considered to be proportional to the velocity of the mass and is given by the following relation. 

Equation (7.9) is expressed in terms of the generalized coordinate r, where c is defined as the coefficient of proportionality for viscous damping. Rayleigh s dissipation function is defined as... 

Further information concerning the definition and use of Rayleigh s dissipation function can be found in the references. 

The steps needed to determine the equations of motion for this system are essentially the steps for the previous system in Fig. 7.2. In this example, the effects of viscous damping are neglect, thereby omitting Rayleigh s dissipation function within the solution. This is a simple omission where removal of the dissipation function from Lagrange s equation will have an impact on the final solutions. 

Classical Viscous Damping The model of damping based on Rayleigh s dissipation function where the damping force depends on instantaneous velocities. 

This positively determined quadratic expression is referred to as the Rayleigh Onsager dissipative function, d S... 

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