As we know, if a solid structure excited by a continues harmonic force (even with small amplitude) with a frequency about 80-90 percent of its first resonance mode, its deflection would be greater than relative to the static loading of a force with a higher amplitude. Physically it is expected that, this structure will fail after a long time because of its fatigue conditions.
Based on the above statements, can we suppose the internal energy of a solid structure reduced to a lower level before its fracture (relative to unloaded conditions)?
By internal energy, I think you mean the strain energy.
The strain energy is greater at resonance, but it is finite if the system is damped; it keeps increasing with time and will eventually become infinite if the system is undamped.
In a word, this internal energy does not reduce to a low level at resonance.
It can be reduced. But generally, the reason can be more fundamental than just a "resonance"
https://www.researchgate.net/publication/259874565_Energy_of_a_solid_sphere_under_nonstationary_oscillations?ev=prf_pub
Article Energy of a solid sphere under nonstationary oscillations
Thanks Dear Huajiang
I think all of materials save the history of works that are done over them, even if their stresses keep lower than its yield strength.
For example if a new rotating rod that support a pulley, rotates 200000 revolution, and the bending load was greater than its critical load, it will be break after the remained revolution. so it may be assumed that the later rod has a lower energy than the new one.
what is your opinion about this?
Dear Mahmoud:
What you said above is true but your initial question refers to resonance. So my answer addressed that.
A material under dynamic load undergoes continuous acculation of damage and as a result its strength decreases over time (like fatigue), showing a memory or historical effect. The energy required to fracture such material decreases.
The growth of cracks within the material (if that occurs) will release strain energy. However the excitation of the structure will also be adding energy. The level of internal energy inside the structure will depend on the balance of these two energy flows (and possibly other energy flows as well).
If one were to pause the excitation before final fracture, and there has been an accumulation of fatigue damage, one would expect the stiffness of the specimen to have been reduced. Thus, if one were to place a certain load on the specimen, the internal energy would be lower than that of an undamaged specimen under the same load. However during the actual excitation the situation is likely more complex.
Relative to unloaded conditions the internal energy will certainly be higher, because when you load a structure elastically you are performing work which will be converted to strain energy in the structure. The strain energy will just be lower than for an undamaged specimen at the same load.
What you are talking about sounds like "vibration stress relief" to me. A technique that has been used and debated in the industry for years. I tend to think it should work in a certain degree. The energy input may realign some grain boundary dislocations and reduce residual stresses.
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