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Statement of question: A centrifugal pump having a mass of m, having an unbalance of me, is supported on a rigid foundation of mass m2 through isolator springs of stiffness k1 as shown in Figure Q1. The centrifugal pump on a rigid foundation can be modeled for vibration analysis in the x direction as Two-degree-of-freedom system. The mass of the pump m, and the foundation, m2 can be approximated as 360 kg and 900 kg respectively. Whereas, the the soil stiffness k2 is 175 kN/m. The soil damping c1 is 35 kN.s/m. The mass m and eccentricity e of umbalence are 0.23 kg and and 0.15 m respectively. Discuss the system response for the pump speed of 1200 rpm using modal analysis for isolator spring stiffness of 300 kN, 350 kN and 400 kN, The total vertical component of the exciting force on the centrifugal pump is given by F(t) = mew? sin wt. F(t) = mew sin wt Centrifugal pump (mass, m) Isolator springs (stiffness, k) Foundation m2 (mass, m2) Soil k2 (stiffness, k; damping, cz) A schematic of centrifugal pump on a rigid foundation. Model for forced vibration in two degrees of freedom Figure Q1 1. Draw the free body diagram of each mass and use Newton methods to develop the equations of motion for the system. 2. Rewrite the coupled equations of motion in matrix form. 3. Suggest the suitable values of isolator spring stiffness between pump and foundation. 4. Use modal analysis and find the natural frequencies wi and wa for undamped system. 5. Determine model force vector

Statement of question: A centrifugal pump having a mass of m, having an unbalance of me, is supported on a rigid foundation of mass m2 through isolator springs of stiffness k1 as shown in Figure Q1. The centrifugal pump on a rigid foundation can be modeled for vibration analysis in the x direction as Two-degree-of-freedom system. The mass of the pump m, and the foundation, m2 can be approximated as 360 kg and 900 kg respectively. Whereas, the the soil stiffness k2 is 175 kN/m. The soil damping c1 is 35 kN.s/m. The mass m and eccentricity e of umbalence are 0.23 kg and and 0.15 m respectively. Discuss the system response for the pump speed of 1200 rpm using modal analysis for isolator spring stiffness of 300 kN, 350 kN and 400 kN, The total vertical component of the exciting force on the centrifugal pump is given by F(t) = mew? sin wt. F(t) = mew sin wt Centrifugal pump (mass, m) Isolator springs (stiffness, k) Foundation m2 (mass, m2) Soil k2 (stiffness, k; damping, cz) A schematic of centrifugal pump on a rigid foundation. Model for forced vibration in two degrees of freedom Figure Q1 1. Draw the free body diagram of each mass and use Newton methods to develop the equations of motion for the system. 2. Rewrite the coupled equations of motion in matrix form. 3. Suggest the suitable values of isolator spring stiffness between pump and foundation. 4. Use modal analysis and find the natural frequencies wi and wa for undamped system. 5. Determine model force vector

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Statement of question: A centrifugal pump having a mass of m1, having an unbalance of me, is supported on a rigid foundation of mass m2 through isolator springs of stiffness k1 as shown in Figure Q1. The centrifugal pump on a rigid foundation can be modeled for vibration analysis in the x direction as Two-degree-of-freedom system. The mass of the pump m, and the foundation, m2 can be approximated as 360 kg and 900 kg respectively. Whereas, the the soil stiffness k2 is 175 kN/m. The soil damping c1 is 35 kN.s/m. The mass m and eccentricity e of umbalence are 0.23 kg and and 0.15 m respectively. Discuss the system response for the pump speed of 1200 rpm using modal analysis for isolator spring stiffness of 300 kN, 350 kN and 400 kN. The total vertical component of the exciting force on the centrifugal pump is given by F(t) = mew² sin wt. F(t) = mew sin wt Centrifugal pump (mass, m1) m1 Isolator springs (stiffness, k1) Foundation m2 (mass, m2) k2 Soil (stiffness, k; damping, c2) A schematic of centrifugal pump on a rigid foundation. Model for forced vibration in two degrees of freedom Figure Q1 1. Draw the free body diagram of each mass and use Newton methods to develop the equations of motion for the system. 2. Rewrite the coupled equations of motion in matrix form. 3. Suggest the suitable values of isolator spring stiffness between pump and foundation. 4. Use modal analysis and find the natural frequencies w1 and wz for undamped system. 5. Determine model force vector
Transcribed Image Text:Statement of question: A centrifugal pump having a mass of m1, having an unbalance of me, is supported on a rigid foundation of mass m2 through isolator springs of stiffness k1 as shown in Figure Q1. The centrifugal pump on a rigid foundation can be modeled for vibration analysis in the x direction as Two-degree-of-freedom system. The mass of the pump m, and the foundation, m2 can be approximated as 360 kg and 900 kg respectively. Whereas, the the soil stiffness k2 is 175 kN/m. The soil damping c1 is 35 kN.s/m. The mass m and eccentricity e of umbalence are 0.23 kg and and 0.15 m respectively. Discuss the system response for the pump speed of 1200 rpm using modal analysis for isolator spring stiffness of 300 kN, 350 kN and 400 kN. The total vertical component of the exciting force on the centrifugal pump is given by F(t) = mew² sin wt. F(t) = mew sin wt Centrifugal pump (mass, m1) m1 Isolator springs (stiffness, k1) Foundation m2 (mass, m2) k2 Soil (stiffness, k; damping, c2) A schematic of centrifugal pump on a rigid foundation. Model for forced vibration in two degrees of freedom Figure Q1 1. Draw the free body diagram of each mass and use Newton methods to develop the equations of motion for the system. 2. Rewrite the coupled equations of motion in matrix form. 3. Suggest the suitable values of isolator spring stiffness between pump and foundation. 4. Use modal analysis and find the natural frequencies w1 and wz for undamped system. 5. Determine model force vector
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