critical frequency of shaft

intoduction:
this assignment is about the vibration analyasis on a shaft with rotating disk,the resonant frequencies of various vibrations are found using this analysis and the stress distribution on the material is been visualized,with this analysis we can design a roating material by avoiding the resonant frequencies,or else testing would reqire lots of time ,energy and equipments.in automobiles this design can be used to create the crank shaft, propeller shaft etc where the there will be vibration on the shaft so by using proper analysis method we can design the right kind of dimensions and material ,theoriticaly the resonant frequency of an vibrating material is soley dependent on its stiffness and mass of the material .which is given by the formula

but there theoritical values is not absolute so we often do experimental testing for some material as well for critical analysis .so the analysis that is been carried out must have a mathematical model which is close to natural phenomenon .but desing that kind of a model would reqire lots of time and effort .but cumilatively its worth it ,cause it saves a lot of time in experiments .nowadays people have started to design their own sofware to do this kind of simulations instead of testing.with each sofware having its own advanages and drawback .so the user must be smart enough to find out which type of software should be used fo these kind of testing.so it is importannt to understand the black box process which is happening behind the sofware to use them
expalnation:
this study was executed on the shaft which is 6cm in dia and the circular disc which is mounted on center of the shaft is 30cm dia made out of alloy steel material and, at the end of the shaft there is a shoulder to mount the roller ball bearing to it which is in 3 cm in dia .so after designing the material the simulated option is chosen and under this frequency study is chosen at the two shoulder joints two roller ball bearing is placed so that the software recioginizes the condition which has to be simulated then a torque value is given to the shaft (5NM) was given in this case then mesh is done on the solid model the mesh size is choosen corresponding to accurasy of the value that we need.the result is calulated the results shows diffrent resonant frequencies for different types of vibration
the result of the various types of vibrbartion are compared and been studied
vibration1
in this type of the vibration the shaft is been rotated at resonant frequency of 104hz in this frequency the shaft oscillates due the offset of the center of gravity and center of mass thus experinces centrifugal force which causes the tremendous amplitudes at this frequency
vibration 2
in this type vibration the shaft is acted by a bending force and this force changes in direction periodically or the once bending force is given and the shaft starts oscillating due to strain energy stored within it
vibration 3 and vibration 4
in this type the circular disc at the center of the shaft is acted upon by a twisting force which causes the vibtation in the shaft

results :

resonant frequencies

vibration 1=104.19hz

vibration2=93.033hz

vibration3=443.76hz

vibration4=451.76hz