Authors - Chhavi Kumari, Upendra Dani, Tushar Chavan, Pragati Chilwarwar, Chhavi Kalra

MECHANICAL VIBRATION 

 - Guided by Prof. Umesh Chavan

Introduction

Mechanical vibration is the motion of a particle or body which oscillates about a position of equilibrium. Most vibrations in machines and structures are undesirable due to increased stresses and energy losses. It deals with the relationship between forces acting on the mechanical system and the oscillatory motion of mechanical system about a point within the system. 

The main reasons of vibration are as follows :

1. Unbalanced centrifugal force in the system. This is caused because of nonuniform material distribution in a rotating machine element.
2. Elastic nature of the system.
3. External excitation applied on the system.
4. Winds may cause vibrations of certain systems such as electricity lines, telephone lines, etc

Importance of Vibration Study

The structures designed to support the high-speed engines and turbines are subjected to vibration.

• Faulty design and poor manufacture can cause unbalance in the engines which results into excessive and unpleasant stresses in the rotating system because of vibration.

• Bearings and Gears wear of rapidly because of vibrations.

• Vibrations may cause loosening of parts from the machine

 

• Because of improper design or material distribution, the wheels of locomotive can leave the track due to excessive vibration which results in accident or heavy loss.
 

• Many buildings, structures and bridges fall because of vibration.
 

• If the frequency of excitation coincides with one of the natural frequencies of the system, a condition of resonance is reached, and dangerously large oscillations may occur which may result in the mechanical failure of the system.

Classification of Vibrations

Free and forced vibration

Free vibration- If a system, after an initial disturbance, is left to vibrate on its own, the ensuing vibration is known as free vibration. No external force acts on the system. For example: oscillation of simple pendulum

Forced vibration - If a system is subjected to an external force (often, a repeating type of force), the resulting vibration is known as forced vibration. For example: oscillation that arises in machines such as diesel engines.

Free and Forced Vibrations

Damped and Undamped vibration

Damped vibration - If any energy is lost or dissipated in friction or other resistance during oscillation, it is called damped vibration.
Undamped vibration - If no energy is lost, the vibration is known as undamped vibration. 

 

In many physical systems, the amount of damping is so small that it can be disregarded for most engineering purposes. However, consideration of damping becomes extremely important in analyzing vibratory systems near resonance.

Linear and nonlinear vibration

If all the basic components of a vibratory system the spring, the mass, and the damper behave linearly, the resulting vibration is known as linear vibration.
If, however, any of the basic components behave nonlinearly, the vibration is called nonlinear vibration.

If the vibration is linear, the principle of superposition holds, and the mathematical techniques of analysis are well developed. For nonlinear vibration, the superposition principle is not valid, and techniques of analysis are less well known.

- - - Linear Vibration | - non linear vibration

Types of Mechanical Vibrations

1. Torsional Vibration:

Torsional vibration is angular vibration of an object, commonly a shaft along its axis of rotation. It is often a concern in power transmission systems using rotating shafts or couplings where it can cause failures if not controlled. A second effect of torsional vibrations applies to passenger cars.

Torsional vibrations can lead to seat vibrations or noise at certain speeds. Both reduce the comfort.

2. Axial or Longitudinal Vibrations:

Axial vibration is a kind of longitudinal shafting vibration which occurs in the crankshaft because of the radial as well as tangential forces

 

3. Transverse Vibrations:

A vibration in which the element moves to and fro in a direction perpendicular to the direction of the advance of the wave.

Degree of Freedom

The minimum number of independent coordinates required to specify the motion of a system at any instant is known as degrees of freedom of the system.
• In general, it is equal to the number of independent displacements that are possible.
• This number varies from zero to infinity.
• The one, two degrees of freedom systems are shown in figure

 

Mechanical system of one degree of freedom

Mechanical system of two degree of freedom

Stages of Vibration Analysis

 

 

 

 

Parts of a Vibrating System

A vibratory system basically consists of three elements, namely the mass, the spring and damper. In a vibrating body, there is exchange of energy from one form to another. Energy is stored by mass in the form of kinetic energy (1/2 mv2), in the spring in the form of potential energy (1/2 kx ) and dissipated in the damper in the form of heat energy which opposes the motion of the system.

SINGLE DEGREE OF FREEDOM SYSTEM

One coordinate ( x ) is sufficient to specify the position of the mass at any time …. SDOF
No external force applied to the mass; hence the motion resulting from an initial disturbance ….. free vibration.
No element that causes dissipation of energy during the motion of the mass, so the amplitude of motion remains constant with time .. Un-damped system

 

 

If a particle is displaced through a distance xm from its equilibrium position and released with no velocity, the particle will undergo simple harmonic motion,

 

 

 

 

General solution is the sum of two particular solutions,

 

 

x is a periodic function and ωn is the natural circular frequency of the motion.

 

Further Cases -  

Viscous Damping Principle

Damping force is proportional to velocity and 

Damping Force = Damping Coefficient (C) times Velocity (dx/dt) 

-dissipates energy

  

Dashpots can de designed as in shock absorbers or the equivalent effect of energy dissipating capacity determined from tests to find the value of this coefficient C.

Damping from Shearing Action of a viscous medium

 

Conclusion

• Mechanical Vibrations is measurement of a periodic process of oscillations with respect to equilibrium point.
• We experience these mechanical vibration in everyday life
• There are useful as well as harmful vibration.
• There can Free/Forced, Damped/Undamped, Linear/Nonlinear  OR Deterministic/Random Vibration OR combinations of these mechanical vibrations.  
  
• Modeling of systems can be Single Degree of freedom, 2 DOF, Multi DOF and Continuous Systems.