- 3 A Fire Sprinkler Pump Is Installed On The Basement Floor Of A Building Which Can Be Modeled As A Rigid Rectangular Pl 1 (31.4 KiB) Viewed 36 times
3 A fire sprinkler pump is installed on the basement floor of a building, which can be modeled as a rigid rectangular plate resting on four clastic columns as shown in Figure Q3. The equivalent mass of the sprinkler pump is m1 of 150×Pkg and it is observed to vibrate badly at a frequency of 10 Hz. The vibration is caused by the application of a harmonic force, F of 100×Q N to the pump. A hypothesis was made by a mechanical engineer that the excessive vibration is due to the frequency of the harmonic force which coincides with the natural frequency of the sprinkler pump. (b) If the sprinkler pump can be modeled as a single degree of freedom spring-mass system, calculate the stiffness, k for each elastic column possessed. Give the final answer in the unit of kN/m.
c) Analyze the mass and stiffness of the attached device that would eliminate vibrations of the sprinkler pump at a frequency of 10 Hz, if given the amplitude motion of the device mass, Xa at 10 Hz is observed to be 0.01×Rm. d) Detemnine the new natural frequencies of the system after the device is attached to the sprinkler pump. Give the final answer in the unit of Hz. Note: The values of P,Q and R depend on the 4th ,5th and 6th digits of your matric number, respectively as shown in Table Q3. For example, if your matrix number is DD 170130, it gives the value of m1=150 kg,F=1000 N and Xα=0.1 m.
Table Q3