Single Degree Of Freedom System:

This has been observed in the previous unit that the systems along mass and elasticity are prone to the vibrations, if they get excited. While a system is excited it begins vibrating and it vibrates at natural frequency if it executes natural vibration. The natural frequency of vibration based on mass and stiffness. If the system is continuously excited, the system vibrates along with forced vibration and frequency of the vibration is equivalent to the frequency of the exciting force. The excitation to the system might be because of the unbalance which always presents because complete balancing is never done because of the practical reasons.

If forcing frequency becomes equivalent to the natural frequency, the resonance takes place and amplitude of vibration becomes very high because of the resonance. High amplitude results in high stresses. The precaution needs to be taken so that failure does not take place because of these high stresses. Hence, known of natural frequency of the system must be known to the operator to save the system close resonance. If system needs to operate near the resonance, damping must be incorporated in the system to restrict the amplitude.

In a machine with rotating or reciprocating parts, the system is excited continuously by the force because of the unbalance in the machinery with rotating parts based on the executricity of the rotating mass. The exciting force based on the unbalance and the speed of rotation. In case of machine along reciprocating parts, the unbalance based on crank radius that is always larger than the eccentricity of rotating mass. Hence, reciprocating machine contains larger amplitude of vibration than a rotating machine due to larger exciting force.

Objectives

After learning this unit, you must be able to

• Study forced vibration of a machine,
• examine vibration of machine along rotating/reciprocating parts,
• analyse whirling of shafts,
• understand behaviour of machine because of the harmonic excitation.