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[rajbeermalhotra]

�
Considering the response of a single degree of freedom system to harmonic excitation with viscous damping , following conclusions can be drawn:

Now,

The response of a single degree of freedom system to harmonic excitation can be split into:

a) Steady Sate response (or vibration) which is a result of the applied force.
b)Transient vibration which is the the result of the free vibration and is dependent on the initial conditions.Right?

Now, the transient vibration decays with time as a consequence of damping.Right?

But, it is also observed that the amplitude of the steady state response incraeses with time.This can be mathematically be proved easily as a consequence of the solution of the differential equation.

My question is:

1)What is the physical reasoning for the amplitude of the steady state response increasing with time?

Besides,
It is also found that the amplitude of the steady stae response is more in systems without damping (a theoretical case though) and is less in systems with damping.Right?

My question is:

2)That means, damping palys a role in reducing the amplitude of both steady state response as well as transient response?But, the transient (free vibration) response eventually decays completely as a consequence of dapming.Right?
Can anyone throw some more light on this???

Posted via Email

[Akshaya.Das]

Dear Mr Rajbeer,

I have understand your question. It will be easier for me to answer your question, if you elaborate the context.

Dr A K Das

-----Original Message-----
Message From rajbeermalhotra[AT]red... [mailto:rajbeermalhotra[AT]red...]
Sent: Monday, November 27, 2006 10:56 PM
To: Das, Akshaya
Subject: Effect of Damping on Steady State Vibration:Harmonic Excitation

�
Considering the response of a single degree of freedom system to harmonic excitation with viscous damping , following conclusions can be drawn:

Now,

The response of a single degree of freedom system to harmonic excitation can be split into:

a) Steady Sate response (or vibration) which is a result of the applied force.
b)Transient vibration which is the the result of the free vibration and is dependent on the initial conditions.Right?

Now, the transient vibration decays with time as a consequence of damping.Right?

But, it is also observed that the amplitude of the steady state response incraeses with time.This can be mathematically be proved easily as a consequence of the solution of the differential equation.

My question is:

1)What is the physical reasoning for the amplitude of the steady state response increasing with time?

Besides,
It is also found that the amplitude of the steady stae response is more in systems without damping (a theoretical case though) and is less in systems with damping.Right?

My question is:

2)That means, damping palys a role in reducing the amplitude of both steady state response as well as transient response?But, the transient (free vibration) response eventually decays completely as a consequence of dapming.Right?
Can anyone throw some more light on this???

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Posted via Email

[rajbeermalhotra]

Thanks or the response.Basically, am reading the book "Dynamics of Structures" by Anil K.Chopra and had the clearifications mentioned.I elaborate below as you required:

1)The response of a single degree of freedom system to harmonic excitation can be split into:

a) Steady Sate response (or vibration) which is a result of the applied force.
b)Transient vibration which is the the result of the free vibration and is dependent on the initial conditions.Right?

Now, the transient vibration decays with time as a consequence of damping.Right?

My questions:

1)It is observed that the amplitude of the steady state response is more in a systen without damping and less in a system with damping.What is the reason for this?

2)Also, it is observed that, if we make a plot between the no. of cycles on the x axis and the amplitude of oscillation on the y axis, it is observed that lighter the damping greate is the number of cycles required to acieve a certain percentage of steady state amplitude.What is the reason for this?

Please help!!

�

On Mon, 27 Nov 2006 Akshaya.Das[AT]ake... wrote :

[Akshaya.Das]

Please find my reply below:

1)

a) In simple words, damping in vibrating structure results resisting force against vibration. It is the reason that the system without damping (which is pactically impossible)having more responses than system with damping. This is not only true for transient state , also for steady state.

b) I would like to mention that tansient vibration is not equivalent to free vibration, as you stated. Transient vibration is a state where vibrating body is accelerating before reaching uniform velocity or steady state.

C) If a system is exited by momentary force and subseqently force is withdrawn, and allow the sytem to vibrate freely without damping, is termed as Free Vibration.

2) Ligthly damped system always take more nos of cycles to achieve steady state amplitude than heavily damped system. Heavy damping reduces the duration of transient vibration and leads to steady state amplitude faster.

I hope I have understand your this question properly.

Regards,

Dr A K Das

-----Original Message-----
Message From rajbeermalhotra[AT]red... [mailto:rajbeermalhotra[AT]red...]
Sent: Tuesday, November 28, 2006 2:16 AM
To: Das, Akshaya
Subject: Effect of Damping on Steady State Vibration:Harmonic Excitation

Thanks or the response.Basically, am reading the book "Dynamics of Structures" by Anil K.Chopra and had the clearifications mentioned.I elaborate below as you required:

1)The response of a single degree of freedom system to harmonic excitation can be split into:

a) Steady Sate response (or vibration) which is a result of the applied force.
b)Transient vibration which is the the result of the free vibration and is dependent on the initial conditions.Right?

Now, the transient vibration decays with time as a consequence of damping.Right?

My questions:

1)It is observed that the amplitude of the steady state response is more in a systen without damping and less in a system with damping.What is the reason for this?

2)Also, it is observed that, if we make a plot between the no. of cycles on the x axis and the amplitude of oscillation on the y axis, it is observed that lighter the damping greate is the number of cycles required to acieve a certain percentage of steady state amplitude.What is the reason for this?

Please help!!

�

On Mon, 27 Nov 2006 Akshaya.Das[AT]ake... wrote :