# which mode shapes and frequecy the vibrating system will adopt?

• posted
Dear All,
I started studying vibration recently and getting confused as I go
deep n deep into it.
A multidegree system has n natural frequencies and hence n natural
shapes.
My confusion is
Which frequency (and hence the corressponding mode shape)will the
Or the system will act democratically and give chance to each of its
frequency to execute one by one and one after the other. :)
In other words what is the criteria for the system to execute certain
mode shape and frequency?
Also if a multidegree system is disturbed from its equillibrium
position , will it execute all the frequencies and mode shape before
coming to equillibrium once again?
(I referred the text book .They discuss about the general equation in
terms of 'n' and conclude that the system will have n number of
corressponding frequencies.)
Regards,
Yogesh Joshi
• posted
The frequency and mode shape is dependent on the forcing function. If there is no driving force the structure will not vibrate at all.
If there is a driving force at a frequency not too close to one of the natural frequencies of the structure, then the structure will vibrate at the driving frequency but will not resonate. Vibratory stresses will generally be low, and no coherent mode shape will develop.
If there is a driving force at frequency nearly equal to one of the natural frequencies of the structure, the resonant mode shape will be excited. Vibratory stresses may be high if there is not sufficient damping.
DGP
• posted
The answer is rather complex.
It depends in part on the location, frequency, and characteristics of the applied force or base excitation.
Furthermore, some modes are more "excitable" than other modes. The "effective modal mass" gives a comparison of the modes in this regard.
For example, consider a cantilever beam. The first mode tends to dominate the response regardless of the excitation source. The beam's first mode has the highest effective modal mass.
The cantilever beam's higher modes are increasingly difficult to excite. The effective modal mass tends to be inversely proportional to the mode number for this beam.
On the other hand, a string in tension has numerous modes that are readily excitable. Stringed musical instruments thus produce a blend of harmonics.
Tom Irvine