Mp3002 Cheat Sheet
|Free Vibration |Rotating Unbalance (Harmonic Excitation) |Principal of Virtual Work |
|[pic]rad/s & [pic]Hz (cps) & [pic]sec |M = mass of system, m = mass of unbalance mass |[pic] |
|[pic] ncycle = t fn t = 1/f |Equ of Motion: [pic] | |
|(because[pic]where[pic]is pure stretching due to mass in static |Amplitude,[pic], |Principal of Virtual Complementary Work |
|equilibrium ) |phase angle, [pic]rad |[pic] |
| |Or Non-dimensional Amplitude, (MR) | |
|General Solution for Free Vibration: [pic] |[pic], |Unit Load Method |
|Principal of Conservation of Energy, KE = PE ([pic] |phase angle, [pic]rad |[pic] |
|Principal of Conservation of Momentum: |Lowest critical speed = 1st whirling speed | |
|[pic](If mass 1 & 2 is perfect collision) |= 1st wn = [pic] |[pic] |
| |Note: critical speed, Vcr occur and natural freq, ωn | |
|To find meff ( [pic] = Total K.E |
|[pic]rad/s & [pic]Hz (cps) & [pic]sec |M = mass of system, m = mass of unbalance mass |[pic] |
|[pic] ncycle = t fn t = 1/f |Equ of Motion: [pic] | |
|(because[pic]where[pic]is pure stretching due to mass in static |Amplitude,[pic], |Principal of Virtual Complementary Work |
|equilibrium ) |phase angle, [pic]rad |[pic] |
| |Or Non-dimensional Amplitude, (MR) | |
|General Solution for Free Vibration: [pic] |[pic], |Unit Load Method |
|Principal of Conservation of Energy, KE = PE ([pic] |phase angle, [pic]rad |[pic] |
|Principal of Conservation of Momentum: |Lowest critical speed = 1st whirling speed | |
|[pic](If mass 1 & 2 is perfect collision) |= 1st wn = [pic] |[pic] |
| |Note: critical speed, Vcr occur and natural freq, ωn | |
|To find meff ( [pic] = Total K.E |