Simple Vibration Neutraliser Notes - Mechanical Engineering

Mechanical Engineering: Simple Vibration Neutraliser Notes - Mechanical Engineering

The document Simple Vibration Neutraliser Notes - Mechanical Engineering is a part of Mechanical Engineering category.
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Dynamic Vibration Absorbers

Basic Concept

Dynamic Vibration Absorbers (DVA) are based on the concept of attaching a secondary mass to a primary vibrating system such that the secondary mass dissipates the energy and thus reduce the amplitude of vibration of the primary system.

There are many application of DVA, A few are noted below:

  • vibration control of transmission cables
  • control of torsional oscillation of crankshaft
  • control of rolling motion of ships
  • chatter control of cutting tools
  • control of noise in aircraft cabin
  • vibration control of hand held devices

DVAs are generally of three types

  • Vibration Neutralizer :

Here, a secondary mass is connected to the primary using a spring element.

  • Auxiliary Mass Damper :

Here the secondary mass is connected to the primary by a damper/dashpot.

  • Dynamic Vibration Absorber:

A general case where both spring and damper are used to connect the secondary mass, with the primary system.

Model of a Simple Vibration Neutralizer

The primary system is assumed to be an undamped single-degree-of-freedom system of mass mand stiffness k1. The secondary system (the neutralizer) consists of mass m2 attached to the primary using a spring of stiffness k2 . The primary system is subjected to a harmonic excitation as shown in figure 16.1.

Simple Vibration Neutraliser Notes - Mechanical Engineering

The responses of the masses from their respective equilibrium positions are denoted as x1 for m1 and x2 for m2 . The equations of motion for the masses can be written as
 

Simple Vibration Neutraliser Notes - Mechanical Engineering
 

In the steady state, the solutions of the governing equations are assumed to be x1 = x1ejwt and x2 = x2ejwt . Substituting these in eqns (16.1) and (16.2), we get

Simple Vibration Neutraliser Notes - Mechanical Engineering
 

Solving eqns. (16.3) and (16.4), we obtain

Simple Vibration Neutraliser Notes - Mechanical Engineering

From eqns. (16.5) and (16.6), you may note that if the secondary system is tuned to the excitation frequency, i.e., its natural frequency  Simple Vibration Neutraliser Notes - Mechanical Engineering   is made equal to , then  Simple Vibration Neutraliser Notes - Mechanical Engineering  and  Simple Vibration Neutraliser Notes - Mechanical Engineering  This implies that the primary system comes to rest, after tuning.

 

Design Considerations

  • It should be noted that a tuned neutralizer makes the response of the primary system zero only at one frequency, namely, w2. So, the application of such a neutralizer is very much limited.
  • Eventhough the tuned mass damping system could successfully neutralize the vibration response of the primary system when the excitation frequency is w2; it also introduces two new resonating frequencies to the original system. Hence, care should be taken such that the two new frequencies are kept sufficiently away from the expected excitation frequency.
  • From equation 16.6, you may note that at w=w2 , displacement of the secondary mass,  Simple Vibration Neutraliser Notes - Mechanical Engineering  . In fact in many system, there is a constraint on maximum permissible value of x2. This is known as rattle space.
The document Simple Vibration Neutraliser Notes - Mechanical Engineering is a part of Mechanical Engineering category.
All you need of Mechanical Engineering at this link: Mechanical Engineering

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