Consider the second mode of a cantilever beam for instance, where a piezoelectric actuator is attached at the place as the node of this mode (about 0.78*L from the clamped end). Is a harmonic input at the frequency of second mode excite the structure?
How different is going to be the vibration amplitude compared to placing it at the peak of this mode (about 0.48*L)?
For an ideal beam structure, I think a force at the node of a mode surelly can not excite any response of this specific mode. Actually this is just what I considered as the theorical basis of system dynamics design, such as trying to place a motor or engine near the node location of a structure to minimize vibration.
I do not look into the formula to check this point theoretically. But I hope this is right.
For the first question: sure, you need a forced vibration with single harmonic content at the damped resonant frequency of the mode of your interest. be aware that placing a sensor/actuator you are changing your system from the more theoretical one.
For the input location, only when you have absolutely no motion in a point you face infinite stiffness and you can burn your shaker; but as soon as you have a minimal displacement, your structure in your input becomes more flexible and you can try to excite the mode, always keeping in mind that nodes and quasi-nodes deserve much more energy than extrema in the displacement field of that resonant modeshape.
Be also aware of possible complex-valued modes, in which case absolute nodes might be more difficult to locate (e.g. travelling waves) and you might find no fixed point, so that more places are useful for your task.
Hoping this helps,
my regards,
Alessandro
Actually if you get a SENSR CX1 accelerometer (I have no stake in the company) and you put it on the bridge and you randomly jump up and down the FFT signal when contoured in time will tell you all you need to know. Masonry International has an article on this in the last two years.
Cheap - simple and it works.
John
As already stated by other answers, from an ideal point of view you cannot excite a mode applying a force in a node of that mode. Anyway, in practice, you will always get a little excitation, since you cannot locate the node in a mathematically perfect way. Moreover, your actuator has a finite dimension, while the node is a single point.
For the case of the piezoelectric patch, pay attention to another thing: the patch works on the deformation and the position of a deformation node of a clamped beam is different from the position of the displacement node. For the second mode the displacement node is around 0.78 L, while the deformation node is closer to the clamp.
An actuator placed at the node (zero deflection point) of a mode will not excite that mode, whether the excitation is harmonic or not. This is the theoretical answer.
In practice, one may not know the location of a node exactly, or, as one of the previous answers noted, the location of the node may change due to the addition of actuator hardware, so there likely will be some small amount of excitation on that mode.
It is always preferable to stay away from resonance. If you cannot, then place the actuator on (or very near to) a node of the mode whose natural frequency is close to the excitation frequency.
Good answer - Haim is correct - there is no way to know the node point exactly.
John: The nodal line (say 2nd mode) of a cantilever beam can be experimentally obtained by sprinkling small number of sand particles in actual situation. I observed this to be a straight line and not a point. Therefore, placing a needle shaped actuator right on the mid-span can be done though theoretically only. In my opinion, the answer to this question comes from the expansion theorem and in the ideal case the beam will have some reponse.
Based ion what mathematics calculations one can not excite a particular mode at its node where the displacement is zero. This is also possible in practical world if you were lucky to exactly locate that node . In addition different modes can be excited from many different locations.
Read this paper
Vibration Health Monitoring for Tensegrity Structures
section 3.2. which is about Sensor and excitation locations
Hang on a minute, if I place a load at a stationary point in the second mode and load the structure, I will get displacement for the other modes most likely, which will likely carry over into the other modes including by default the second. Any excitation gets carried through the stiffness matrix into the structure, you have to dissipate the energy.
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