plS answer faster A fire sprinkler pump is installed on the basement floor of a building, which can be modeled as a rigi
Posted: Thu Jul 14, 2022 2:53 pm
plS answer faster
A fire sprinkler pump is installed on the basement floor of abuilding, which can be modeled as a rigid rectangular plate restingon four elastic columns as shown in Figure Q3. The equivalent massof the sprinkler pump is 𝑚1 of 1500 kg and it is observed tovibrate badly at a frequency of 10 Hz. The vibration is caused bythe application of a harmonic force, 𝐹 of 1000 N to the pump.A hypothesis was made by a mechanical engineer that the excessivevibration is due to the frequency of the harmonic force whichcoincides with the natural frequency of the sprinkler pump.
1.If the sprinkler pump can be modeled as a single degree offreedom spring-mass system, calculate the stiffness, 𝑘 for eachelastic column possessed. Give the final answer in the unit ofkN/m.
2.Analyze the mass and stiffness of the attached device thatwould eliminate vibrations of the sprinkler pump at a frequency of10 Hz, if given the amplitude motion of the device mass, 𝑋𝑎 at 10Hz is observed to be 0.07 m.
3.Determine the new natural frequencies of the system after thedevice is attached to the sprinkler pump. Give the final answer inthe unit of Hz.
Figure Q3
A fire sprinkler pump is installed on the basement floor of abuilding, which can be modeled as a rigid rectangular plate restingon four elastic columns as shown in Figure Q3. The equivalent massof the sprinkler pump is 𝑚1 of 1500 kg and it is observed tovibrate badly at a frequency of 10 Hz. The vibration is caused bythe application of a harmonic force, 𝐹 of 1000 N to the pump.A hypothesis was made by a mechanical engineer that the excessivevibration is due to the frequency of the harmonic force whichcoincides with the natural frequency of the sprinkler pump.
1.If the sprinkler pump can be modeled as a single degree offreedom spring-mass system, calculate the stiffness, 𝑘 for eachelastic column possessed. Give the final answer in the unit ofkN/m.
2.Analyze the mass and stiffness of the attached device thatwould eliminate vibrations of the sprinkler pump at a frequency of10 Hz, if given the amplitude motion of the device mass, 𝑋𝑎 at 10Hz is observed to be 0.07 m.
3.Determine the new natural frequencies of the system after thedevice is attached to the sprinkler pump. Give the final answer inthe unit of Hz.
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