In case of cantilever made of uniform material(not bimaterial) should the natural frequency go up or drop down with the function of temperature? Any comment!
As far as Modulus of Elasticity, E, usually drops with temperature, and natural frecuencies are proportional to E, they definitively should drop too.
Hi Roberto,
Thanks for your answer. That's what usual perception is. However, we are seeing an unusual response of a hollow channel cantilever. It is a microcantilever of 200 um length dimension. 4 and 3 um is width and thickness. Its response with temperature is quite different. With increasing temperature, frequency goes up. Though the increment is
Which material is the cantiever made of? How big is temperature increase?
Hi Ankur, Natural frequency depends on mass and stiffness. Mass being constant here, but stiffness changes with temperature. Now stiffness is a function of Material property (E or G) and cross section and Moment of inertia. Although E reduces with temperature, but there is a possibility that the cross section may increase due to expansion, thereby increasing the Area moment of inertia also. Increase in area moment of inertia will lead to increased stiffness and hence frequency too. Maybe the increase of inertia is overcompensating the effect of decreased E value with temperature..
Additional stress caused by the thermal effect may increase the natural frequency of your cantilever beam.
In general natural frequency (w) is a inherent parameter of structure and it's dependent to stiffness (k) and mass (m) of structure. So, If with change of temperature we assume that mass is constant, stiffness will be changed. Coefficients of Stiffness matrix are elastic modulus (E) and moment of inertia (I). But, vital hint is about to the different behavior of E and I with change of temperature. It seems that with increase of temperature, I go up and E drop down. Thus, this function is complex and for different material not same. But, certainly natural frequency is a dynamic parameter dependent to temperature (may be go up and or may be drop down).
- Badges
- Science topic