Question

Subject: Vibration

3. Answer the following question. It does not require numeical calculation. You must provide correct i reason(s) to carn credits (a) [5%] Consider theSDOF vibration x(t) contains only one frequency of oscillation? /) , undamped, mass-spring system under harmonic force : mx + kx-Focos (? /rn. In general, lhe vibration x(1) contains oscillations in both.co and ??. How can the ry'X) (b) 10%) Themachine surfaces own below is nown to exhibit sinusoidal vibration. To monitor the vibration of the machine surfacc, a mass-spring-damper system is put in between the machine and the rigid wall. The idea is to use the vibration signal z() xt) -() to characterize the vibration property of the machine surface. (bl) [7/10] Provide your reasons fi is the displacemen, velocity or acceleration that z can characterize. (b2) [3/10] In what frequency range can the quantity you answer in (bl) be best captured? rigid wall /n machine surfacc Asin

Answer 1

Solt Given eauation %, ven ue S Hachine surface 1 Asintiot) Abo from gen equation%, 2. lugn-us*)누 Iz? o.@n) LO Suyface here,z9s he displacement BY t base surface.

Accelezemeler adualy measures the accelevational amplttude bud heste e have deatved he cruation ampilude , noso deentale his cauation you uniu gol velocaky %, ampklude also amin different; amplitade exen fiale rate 10ll give the acceleraion The frequenor d ha system s natural fmequency hen Btesource happens and amplktude is large encugh ire, at 3.1 Btfrequeney must be nat to tesslve fneguenef or least evect