which mode shapes and frequecy the vibrating system will adopt?

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
system adopt?
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

Dear yogesh:

"yogesh" <[Only registered users see links. ]> wrote in message
news:f88a27e4.0408310102.7e90d6fa@posting.google.c om...

The structure will affect the shapes required to absorb the energy directed
into it. It will attempt to pick a mode that is closest to the driving
frequency, and sometimes based on the "point" of application of the driving
force. Usually, unless the disturbing force is special, the first resonant
mode will be "chosen".

David A. Smith

N:dlzc D:aol T:com (dlzc) wrote:



One mode can feed energy to another too, if conditions favor it. Many
systems will preferentially "ring" at one frequency, and as that decays
the energy will excite lower frequenct modes of the system. Modes can
even swap energy back and forth. This is easily seen in coupled resonant
systems, but can be seen in single objects with one dominant mode and
several submodes, like bells with non-circular cross-sections.

Then there're anisotropic dissipative effects. Asymmetrical
structures in particular will readily convert vibratory energy to heat
in certain directions, while vibrating nearly losslessly in others.

Also, external constraints on symmetrical vs. asymmetrical systems
can complicate things drastically. The OP might for instance look into
Chladni figures on drumheads, and compare with how and why quartz
crystal resonators are mounted the way they are.

Mark L. Fergerson

"yogesh" <[Only registered users see links. ]> wrote in message
news:f88a27e4.0408310102.7e90d6fa@posting.google.c om...


This sounds like the kind of problem physical chemists (and chemical
physicists) encounter regularly in studying molecular spectroscopy - the
science of analyzing the interaction of the complex structures of molecules
with EM radiation.


In general, a complex system will have many modes of vibration depending on
the available "degrees of freedom" of motion for the component parts. This
will be affected by geometric symmetry and other external constraints as
well. Some distinct modes of vibration may have totally different
appearances but identical frequencies and energies.

Google "normal modes of vibration"


The modes of motion 'excited' will depend on the exact nature of the
disturbance. If only one particle of a system of particles is disturbed,
then any and all modes in which that particular particle moves *can* be
excited.

In general any displacement from the equilibrium position of the system can
be represented as a linear combination of the normal modes, each with its
own amplitude coefficient. The simplest illustration of this is the
"coupled pendula." [Google that, too]

In [Only registered users see links. ] for example, there are two
coupled pendula in a two-dimensional system. There are two *normal* modes
of motion - "normal" is used in the *mathematical* sense of *independent* -
i.e. unable to influence each other. The two normal modes are 1) both
pendula swinging in *the same* direction simultaneously - "in synch," and 2)
both pendula swinging in *opposite* directions - "out of synch."

Displacement of *one* pendulum simultaneously energizes BOTH modes of
motion. The only way to energize *only one* mode would be to simultaneously
move both pendula from the equilibrium position by the same amount, in
*either* the same *or* the opposite directions, thus selectively energizing
only one of the modes.

In the applet on the page cited, click "Reset", then type in the same value
(10 is good) for BOTH initial positions (red and blue), then click start.
This is the "in synch" mode - the 'sym' mode, as molecular spectroscopists
would call it.

Then type in one value for one initial positions and its negation for the
other, then click start. This is the "out of synch" mode - the 'anti' mode.

Then watch what happens when you type in two different values: when one is
0, and when neither is 0.


Have fun and learn


Tom Davidson
Richmond, VA