Question

The compressor weighs 2,060 lb, and operates at 1,800 rpm. At this operating speed, undesirable vibration occurs when the compressor is attached directly to the floor of a small building in a manufacturing plant. To reduce the annoying, and potentially damaging, vibration of the concrete floor that is resting on a silty-clay soil, it is proposed to isolate the compressor by mounting it on a square concrete block separated from the rest of the concrete floor as shown. The density of the concrete block has been measured as 23,563 N/m3, and the vertical compression coefficient ke of the silty-clay soil has been experimentally determined to be ke-20.36(10)° N/n3. The geometry of the compressor leads to choosing a block 2 by 2 m. Determine the depth h of the block that will yield a 75% reduction in the force transmitted by the compressor-block system to the supporting soil m Compressor Asphalt filler Floor Fo sin co Conerete block ^ k (soil)

Answer 1

0 Gfven -that op eia speed - \, 8oospm -The densty of the Concrete block c93,5 63NIm3 u9n rm U9 188 495 188.50 ad|sec cohexe > 1s Sptng costant m S displacement

som equation Slom equation e Centfug due-to-the unbalance of -the Com fore SSA we need to 9(educe -the face-tranm,tted b - the f8ee txnAmTt ted -to-the goound 0.35-1 25 at 5

V5 Bidstkutb 188-50 xedlsec n -the above euation ove ejuatron) 188.50) (9n 84, 30 Had/sec = Natural frequency of sell/h--Unl-Q rm cahese m Combtned mass of compoxe$ Concrete block 84 30 203% xio'x4 กา m-114596 k (mg) Cordo, ele blocks lo525.19F Volume of Concmete block mg concslete

93563 Nm Concset e 9401.936 V- 4.389G m3 .: Volume of the ConCaete y): Ath 4. 381% hec concstete biock depth musl be 09649m p the tonsmitted te -the ound -to be telared by 75-1 5/.