Vibration Engineering Mechanical Engineering
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Vibration Engineering
![-)A JEEPNEY CARRYING A 124 ka/m MASS OF
PASSENGERS ON A LONG CHAIR HANING
5m LENGTH HAS A LEAF SPRING SUP-
PORT HAVING THE DIMENSIONS 4 2"0.5
(L-wat), 2 FULL LENGTH LEA VES AND
4GRADUATED LEAVES. FIND THE DEF-
LECTION IN m AND FLEXURAL S TRESS
IN GPa. [ 3.8066/s]
Flexural Stress =
GPa
Deflection](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feff5a29e-0d2b-41d5-ad8a-10b0526993b6%2Ffc2cbc86-d53b-494d-af2c-a460f93f1aa5%2Fvmmgns8_processed.jpeg&w=3840&q=75)
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- A stepped shaft ABC consisting of two solid, circular segments is subjected to uniformly distributed torque t1acting aver segment 1 and concentrated torque t2applied at C, as shown in the figure. Segment 1 of the shaft has a diameter of d1= 57 mm and length of L1= 0.75 m; segment 2 has a diameter d2— 44 mm and length L2= 0.5 m. Torque intensity /,"= 3100 N . m/m and T2= 1100 N. m. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: .x = L1/2 and at .x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams.Solve the preceding problem for the following data: diameter LO m, thickness 48 mm, pressure 22 MPa, modulus 210 GPa. and Poisson's ratio 0.29Solve the preceding problem for the following data: b = 6 in., b = 10 in, L = 110 ft, tan a = 1/3, and q = 325 lb/ft.
- Repeat the preceding problem using sx= 5.5 MPa. ??y= 4 MPa. and txy= 3.2 MPa.In the given fig shows the suspension system of a freight truck with a parallel-spring arrangement. Find the equivalent spring constant of the suspension if each of the three helical springs is made of steel with a shear modulus G = 120GPaand has five effective turns, mean coil diameter D = 50 cm, and wire diameter d = 5 cmA shaft having length equal to 10 m and diameter equal to (50+ 01) mm is simply supported at both ends. The shatt carries four masses (150 + 01) kg, (200 + 01) kg, (250 +01) kg and (300 + 01) kg. These masses are located at a distance of 1.5m, 2.5 m, 5.5 mand 7.5 m from the left hand side support, respectively. The modulus of elasticity, E, for the material of the shaft is 200 GN/m? and mass density for the shaft material is 7500 kg/m?3. Determine critical speed of the shaft in revolutions per minute for the following two cases: 1. Effect of the mass of the shaft is neglected. 2. Effect of the mass of the shaft is considered. What is the usefulness of the answers determined in this problem?
- 3) The force, FT = 1 kN, and moment, MT = 0.5 kN-m, at the tip are caused by a wing tip vortexand a winglet, not shown. L = 12 m and the spar has an elastic modulus of E = 70 GPa and aPoisson’s ratio of n = 0.33. The mass of the wing is 4000 kg, and the weight of the engine is 107kN. Use 9.8 m/s 2 for the acceleration due to gravity.Consider the cross-section shown (you can look these up). Pay attention to the coordinate systemgiven in the drawing.d) where is the centroid?e) what is the area?f) Calculate the shear modulus3) The force, FT = 1 kN, and moment, MT = 0.5 kN-m, at the tip are caused by a wing tip vortexand a winglet, not shown. L = 12 m and the spar has an elastic modulus of E = 70 GPa and aPoisson’s ratio of n = 0.33. The mass of the wing is 4000 kg, and the weight of the engine is 107kN. Use 9.8 m/s 2 for the acceleration due to gravity.Consider the cross-section shown (you can look these up). Pay attention to the coordinate systemgiven in the drawing.g) Compute each of these moments of inertia with the values b = 0.4 m, d =0.5 m , t =0.1 m.3) The force, FT = 1 kN, and moment, MT = 0.5 kN-m, at the tip are caused by a wing tip vortexand a winglet, not shown. L = 12 m and the spar has an elastic modulus of E = 70 GPa and aPoisson’s ratio of n = 0.33. The mass of the wing is 4000 kg, and the weight of the engine is 107kN. Use 9.8 m/s 2 for the acceleration due to gravity.Consider the cross-section shown (you can look these up). Pay attention to the coordinate systemgiven in the drawing.a) what is the moment of inertia about y-axis in terms of the symbolic dimensions shown?b) what is the moment of inertia about z-axis in terms of the symbolic dimensions shown?c) what is the polar moment of inertia in terms of the symbolic dimensions shown (i.e.about the x-axis)?d) where is the centroid?e) what is the area?f) Calculate the shear modulusg) Compute each of these moments of inertia with the values b = 0.4 m, d =0.5 m , t =0.1 m.
- A vertical shaft 20 mm in dia and 100 cm long is mounted in long bearings and carries a rotor of mass 10 kg midway between bearings. The center of rotor is 0.5 mm away from axis of shaft. Neglect the weight ofshaft and take E-200 GPa forshaft material. Determing whirling speed of shaft and bending stress induced in it when it is rotating at 2000 rpm.A three-dimensional elastic body with dimensions b=2m, h=60cm and a=80cm was subjected to forces of Fx = 960kN and Fy = 4800kN. Since E=210GPa, V=0.3, find the length changes and volume changes in the x, y, z axes.A vertical shaft 25 mm diameter and 0.75 m long is mounted in long bearings and carries a pulleyof mass 10 kg midway between the bearings. The centre of pulley is 0.5 mm from the axis of theshaft. Find (a) the whirling speed, and (b) the bending stress in the shaft, when it is rotating at 1700r.p.m. Neglect the mass of the shaft and E = 200 GN/m2.