It is generally assumed that the energy dissipation takes place due to viscous type of damping where the damping force is proportional to velocity. But there are systems where the damping takes place in many other ways.
For example, one may take surface to surface contact in vibrating systems and take Coulomb friction into account. Also in many cases energy is dissipated in joints also, which is a form of structural damping.
In these cases one may still use the derived equations by considering an equivalent viscous damping. This can be achieved by equating the energy dissipated in the original and the equivalent system.
The primary influence of damping on the oscillatory systems is that of limiting the amplitude at resonance. Damping has little influence on the response in the frequency regions away from resonance. In case of viscous damping, the amplitude at resonance is
For other type of damping, no such simple expression exists. It is possible to however, to approximate the resonant amplitude by substituting an equivalent damping Ceq in the foregoing equation. The equivalent damping Ceq is found by equating the energy dissipated by the viscous damping to that of the non-viscous damping with assumed harmonic motion.
where Wd must be evaluated from the particular type of damping.
Structural Damping :
When materials are cyclically stressed, energy is dissipated internally within the material itself.
Experiments by several investigators indicate that for most structural metals such as steel and aluminium, the energy dissipated per cycle is independent of the frequency over a wide frequency range and proportional to the square of the amplitude of vibration. Internal damping fitting this classification is called solid damping or
Structural damping. With the energy dissipation per cycle proportional to the square of the vibration amplitude, the loss coefficient is a constant and the shape of the hysteresis curve remains unchanged with amplitude and independent of the strain rate. Energy dissipated by structural damping can be written as
where 
is a constant with units of force displacement.
By the concept of equivalent viscous damping
or 
Coulomb Damping :
Coulomb damping is mechanical damping that absorbs energy by sliding friction, as opposed to viscous damping, which absorbs energy in fluid, or viscous, friction. Sliding friction is a constant value regardless of displacement or velocity. Damping of large complex structures with non-welded joints, such as airplane wings, exhibit coulomb damping.
Work done per cycle by the Coulomb force Fd
For calculating equivalent viscous damping
From the above equation equivalent viscous damping is found
Modes of Coulomb Damping
Coulomb damping absorbs energy with friction, which converts that kinetic energy into thermal energy or heat.
The Coulomb friction law is associated with two aspects. Static and kinetic frictions occur in a vibrating system undergoing Coulomb damping. Static friction occurs when the two objects are stationary or undergoing no relative motion. For static friction, the friction force F exerted between the surfaces having no relative motion cannot exceed a value that is proportional to the product of the normal force N and the coefficient of static friction μs.
Kinetic friction occurs when the two objects are undergoing relative motion and they are sliding against each other. The friction force F exerted between the moving surfaces is equal to a value that is proportional to the product of the normal force N and the coefficient of kinetic friction μk.
In both of these cases, the frictional force always opposes the direction of motion of the object. The normal force is perpendicular to the direction of motion of the object and equal to the weight of the object sliding.
Services: - Equivalent Viscous Damping Homework | Equivalent Viscous Damping Homework Help | Equivalent Viscous Damping Homework Help Services | Live Equivalent Viscous Damping Homework Help | Equivalent Viscous Damping Homework Tutors | Online Equivalent Viscous Damping Homework Help | Equivalent Viscous Damping Tutors | Online Equivalent Viscous Damping Tutors | Equivalent Viscous Damping Homework Services | Equivalent Viscous Damping