Module 9 : Forced Vibration with Harmonic Excitation; Undamped Systems and resonance; Viscously Damped                    Systems; Frequency Response Characteristics and Phase Lag; Systems with Base Excitation;                    Transmissibility and Vibration Isolation; Whirling of Shafts and Critical Speed.
Lecture 1 : Harmonic vibration of single DOF system
When (1) [ damping controlled]

 

 

In this region the excitation frequency is close to the natural frequency of the system and we see a huge build-up of dynamic response. It is this region that is critical and could cause potential damage to many structures and machine elements and needs to be avoided as far as possible. You now appreciate why it is important to accurately determine the natural frequencies of a system and make sure that the operating frequencies are not in the same range. When the excitation and the natural frequencies match, we call this phenomenon “resonance”.

 
(9.1.15)
 
Practical Implication

A real-life complex engineering system may have several natural frequencies and may be experiencing excitation at various frequencies. When any of these excitation frequencies comes close to any of the natural frequencies of the system, we can expect large amplitudes of vibration and this condition should be avoided as far as possible.
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