vibration subject

1. STANI MEMORIAL COLLEGE OF ENGINEERING & TECHNOLOGY, PHAGI - JAIPUR
LECTURE PLAN FOR THE ACADEMIC YEAR 2020-21
BRANCH: Mechanical Engineering YEAR/ SEMESTER: II year IV Semester
TEACH METHODOLOGY: Lecture / O.H.P/ LCD/ Case Study/ Role Play / Any Other
FACULTY NAME: Vikram Singh, Asst. proff. Dept.-ME DATE: ___/____/____LT NO.:
SUBJECT: Mechanical vibration
TOPIC: Damped vibrations of single degree of freedom systems: Viscous damping
1. INTRODUCTION:-
If any energy is lost or dissipated in friction or other resistance during oscillation, the
vibration is damped vibration.
2. THEORY:-
The oscillatory motions considered so far have been for ideal systems, i.e. systems
that oscillate indefinitely under the action of linear restoring force. In real systems,
dissipative forces, such as friction, are present and retard the motion. Consequently,
the mechanical energy of the system diminishes in time, and the motion is said to be
damped.
Mainly four types of damping system
1. Viscous damping
2. Couloumb damping
3. Structural damping
4. Non linear damping
1.Viscous damping:-
One common type of retarding force is proportional to the speed and acts in the
direction opposite to the motion. The damping caused by fluid friction is
called viscous damping. The presence of this damping is always modelled by a
dashpot, which consists of a piston A moving in a cylinder B as shown in Fig. The
frictional force is proportional to velocity and is denoted by cx˙ and the constant c is
called the coefficient of viscous damping.

2. Consider the damped free vibration of a springÐmass damper system shown in Fig.
3.2. Using DÕAlembertÕs principle, a dynamic problem can be converted to a static
problem by considering inertia force.
Mx+cx+kx = 0 - - - - -1
Equation 1 is a linear, second order, homogeneous differential equation. It has the
solution of the form

3. There are three special cases of damping that can be distinguished with respect to
the critical damping coefficient.
Over-damped system
When c > cc and ρ > 1
x  A e
λ
1t
 Be
λ
2t
…. 3.11
There are two constants A and B which can be evaluated using initial conditions
There are two constants A and B which can be evaluated using initial conditions
xt=0 = x0; vt=0 = v0.
As t increases x decreases. This motion is non-vibratory or a periodic as shown in
Fig. 3.3.
Critically damped system
When c = cc and ρ = 1
This motion is also non-vibratory but it is of special interest because x decreases at
the fastest possible rate without oscillation of the mass and is shown in Fig. 3.3.

4. Under-damped system
When c < cc and ρ < 1. The roots shown in Eq. 3.7 are complex.
SUMMARY:- here we discusses various types of damping system and viscous damping.
5. IMPORTANT QUESTIONS:-
Q1. Explain viscous damping with example.
6. REFEREMCES:
BOOK: 1. V.P SINGH
2.
INTERNET: www.wikipedia .com , www.braincart.com
7. FACULTY NAME: Vikram Singh