Question Solved1 Answer In the figure below, the pipe carrying feed-water to a boiler in a thermal power plant "the pipe can be modeled as spring-mass system" has been found to vibrate violently at a pump speed of 427 rpm. If the operating speed range of the pump is between 360 rpm to 900 rpm. In order to reduce the vibration, an absorber consisting of a spring of stiffness k, and a trial mass of 10 kg is attached to the pipe and tuned to the 640.5 rpm speed, 1.c. tuning ratio of 1.5 This arrangement is found to give natural frequencies of the system at 342 rpm and 800 rpm Design the absorber to be attached to the pipe, le calculating its mass m and stiffness k, to satisfy the above-mentioned requirement (to keep the natural frequencies of the system outside the operating range) Pump hp Boiler 11 pipe

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Transcribed Image Text: In the figure below, the pipe carrying feed-water to a boiler in a thermal power plant "the pipe can be modeled as spring-mass system" has been found to vibrate violently at a pump speed of 427 rpm. If the operating speed range of the pump is between 360 rpm to 900 rpm. In order to reduce the vibration, an absorber consisting of a spring of stiffness k, and a trial mass of 10 kg is attached to the pipe and tuned to the 640.5 rpm speed, 1.c. tuning ratio of 1.5 This arrangement is found to give natural frequencies of the system at 342 rpm and 800 rpm Design the absorber to be attached to the pipe, le calculating its mass m and stiffness k, to satisfy the above-mentioned requirement (to keep the natural frequencies of the system outside the operating range) Pump hp Boiler 11 pipe
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Transcribed Image Text: In the figure below, the pipe carrying feed-water to a boiler in a thermal power plant "the pipe can be modeled as spring-mass system" has been found to vibrate violently at a pump speed of 427 rpm. If the operating speed range of the pump is between 360 rpm to 900 rpm. In order to reduce the vibration, an absorber consisting of a spring of stiffness k, and a trial mass of 10 kg is attached to the pipe and tuned to the 640.5 rpm speed, 1.c. tuning ratio of 1.5 This arrangement is found to give natural frequencies of the system at 342 rpm and 800 rpm Design the absorber to be attached to the pipe, le calculating its mass m and stiffness k, to satisfy the above-mentioned requirement (to keep the natural frequencies of the system outside the operating range) Pump hp Boiler 11 pipe
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Answer:- Given information pump speed of 820 rpm ud835udc58=130N/m Forcing frequency Wn 2N 60 27x820 60 Wn rad 85.87 sec ud835udc58=130N/m k .. Wn m 130 85.87 = m m = 0.0176 kg 21 - 800rpm T1 Ω1 N1 800 11 820 71 = 0.976 O2 = 840rpm Y2 Ω2 N1 12 840 820 T2 = 1.024 ri, r? = (1+) + u0f0d (1+g) + (1+ 2 – 1 for frac{w}{w_{n}}=1   Where u mi ** = (1+4) - 1 (1+5)*-1 1+ 5) -1=(1+)-u884c +1 -2- + 6+1)-1 - 6+1) + 2 2 +4+1= 2r} (1+2) +1 27 2 1+ 2 J = 2 ri+1 2r 2 (1+ri - 2 u = u = 1+(0.976) (0.976) 2 =0.00244 therefore m_{1}=frac{m}{mu } mi 0.0176 0.00244 mi 7.213 Kg Natural freq s ... See the full answer