The Vibration problems occurs in most of areas like mechanical engineering, civil engineering and aerospace engineering etc.The vibration is not a desirable phenomenon. So in order to control these unwanted vibrations by the dissipation of vibration energy, this dissipation of energy called as damping phenomenon. Characterizing of these damping forces in any vibrating structures plays a very significant part in structural dynamics and controlling. In the year 1877 a literature review work carried out by the Lord Rayleigh who published the monograph on “Theory of sound”1.Damping phenomenon is not a new problem, this is an age old problem many researchers are working on damping phenomenon which is major role in vibration control.
Now a day’s Modern engineering methods have been developed and implemented to control of unwanted vibrations such as
(1)Automobiles working under random conditions
(2)Buildings when subjected to earthquake and shock loads
In the last two decades the innovative design method resulted in the development of improved composite structural materials and these materials are light in weight and also there is more requirement for the larger structures which have capacity to carryout maximum loads at very high speeds and at the same time the noise and vibration level should be safety and workability one.
In the year 1973 a detailed review work carried out on the damping phenomenon in material by Bert2.In the year 1977 a detail dissipation mechanism in the joints found by Earls3 and also in the year 1977 by Bears and Williams4.From the above literature review, the problem will arises to represent all these in the form of very small mechanisms exists in various parts in the structures with simplified manner.
In most of the cases the mechanism in an linear mode and requires similar linearization technique and also analysis can be carried out globally5.To get rid from above problems a well known method viscous damping method was introduced by the Rayleigh approach in the year 18771 using a famous dissipation function which is an quadratic expression and its represents the rate of change of energy dissipated along the symmetric coefficients with symmetric coefficients. A damping matrix consist of mass and stiffness matrices in linear combination mode pointed out by the Rayleigh that’s why it is called as Rayleigh damping or proportional damping and it is also called as classical damping one.