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Vibration Engineering
Figure Q5(b) shows a motor having mass of 50 kg is mounted on the...
Figure Q5(a) shows a plane truss supported by a horizontal spring at the top node. The...
Figure Q5(a) shows a plane truss supported by a horizontal spring at the top node. The truss members are of a solid circular cross section having a diameter of 20 mm and an elastic modulus (E) of 80 GPa (10° N/m2). The spring has a stiffness constant of k-2000 kN/m. A point load of 15 kN is applied at the top node. The direction of the load is indicated in the figure. The code numbers for elements, nodes, DOFS, and...
Q5. The cantilever beam, AC, is subjected to the load case shown in Figure 5. For the loading shown, do the following: [10 Marks] a) Calculate the magnitude and direction of the reactions at A b) Usi...
Q5. The cantilever beam, AC, is subjected to the load case shown in Figure 5. For the loading shown, do the following: [10 Marks] a) Calculate the magnitude and direction of the reactions at A b) Using the Macaulay function, determine the displacement in y of the point B of the beam (x 2.4 m from the support at A) [10 Marks] c) Determine the slope at B. [5 Marks] The beam has a Young's modulus of E-200 GPa and...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two springs of stiffnesses ki - 100 N/m and k2 120 N/m. Its natra frequency is evaluated by means of a cantilever sensor, which is attached to the point mass. Knowing the cantilever has a constant circular cross section, a length 1 0.08 m, the cantilever's Young's modulus is E -200 GPa, and mass density is p 7600 kg/m3, determine its diameter d, such that...
QUESTION 2 Consider an electrical motor with mass M = 901.8129 kg located at the middle...
QUESTION 2
Consider an electrical motor with mass M = 901.8129 kg
located at the middle of pinned-pinned beam, as shown in the figure
below. Assume that the Young’s modulus of the beam E =
8.5470x1010 Pa, moment of inertia I =
8.3375x104 mm4 , length of the beam
L = 0.2859 m and zero initial conditions. If there is an
unbalance mass of m0 = 2.3714 kg in the
rotating part of the motor, eccentricity is e = 4.1473...
*Vibration A shaft carrying two rotating disks of masses m Figure Q5(a). Assume that the deflections...
*Vibration
A shaft carrying two rotating disks of masses m Figure Q5(a). Assume that the deflections of the bearings and gyroscopic effect of the disks are negligible. Take E 209 x 109 N/m2. 20 kg and m2 35 kg as shown in Find the flexibility influence coefficients of the system. i) (5 marks) Determine the natural frequency of the system using Dunkerley's method. ii) (5 marks) 20 mm dia 35 kg 20 kg 150 mm 150 mm 600 mm DIK...
The figure below shows a uniform slender bar supported by cantilevers at A and C. At B a linear spring with stiffness K' is connected to an additional point mass 'm'. Note the physical pr...
The figure below shows a uniform slender bar supported by cantilevers at A and C. At B a linear spring with stiffness K' is connected to an additional point mass 'm'. Note the physical properties of the bar include cross sectional area A, Young's modulus E, second moment of area I, and, density ρ, and length AB-BC-L. 1. 2. Develop the matrix equation of motion for the FEM system in the model How many natural frequencies are in the system?...
The mass of the uniform slender steel rod, shown in Figure 2, is 3 kg. The...
The mass of the uniform slender steel rod, shown in Figure 2, is 3 kg. The system is set in motion with small oscillations about the horizontal equilibrium position shown. (i) Determine the position x for the slider such that the system period is 1 s. (ii) When the pivot is replaced by a built-in support that restricts any rotation at O and the spring is moved to the right-hand end with the 1.2 kg mass removed, calculate the frequency...
b) Figure Q5(b) shows a frame ABCDE that is supported by a hinge at A and...
b) Figure Q5(b) shows a frame ABCDE that is supported by a hinge at A and E )Construct the free body diagram for the entire structure, the disc and member DBE i) By applying equation of equilibrium, determine the horizontal and vertical components of the force that is acting on the hinge of member DBE li) If the weight of the cylinder is increased to 60 N and all the reaction forces are remain unchanged, evaluate the new radius of...
The figure shows a trolley of mass M, which runs on a frictionless horizontal plane. A...
The figure shows a trolley of mass M, which runs on a frictionless horizontal plane. A t O the trolley carries a simple pendulum of length I with a body of mass m at its end. Two equal springs, each of stiffness k, are attached to the trolley and to the fixed walls. By using the independent co-ordinates x and ? as shown in the figure, determine, for the small free oscillations, the equations of motion. If M-100 kg, m-10...
Figure 5 shows a pick-up truck of a total mass mi transporting a small cart of a mass m2. The sma...
Figure 5 shows a pick-up truck of a total mass mi transporting a small cart of a mass m2. The small cart is hitched through two springs of axial stiffness k each to the truck (b) body. Absolute displacement of the truck is xi while that of the cart is x2 (i) Find the relative motion (n-m) of the cart when the truck is subjected to a (7 marks) Find the natural frequencies and mode shapes of this two-degree-of-freedom harmonic...
Figure Q5(a) shows a plane truss supported by a horizontal spring at the top node. The truss members are of a solid circular cross section having a diameter of 20 mm and an elastic modulus (E) of 80 GPa (10° N/m2). The spring has a stiffness constant of k-2000 kN/m. A point load of 15 kN is applied at the top node. The direction of the load is indicated in the figure. The code numbers for elements, nodes, DOFS, and...
Q5. The cantilever beam, AC, is subjected to the load case shown in Figure 5. For the loading shown, do the following: [10 Marks] a) Calculate the magnitude and direction of the reactions at A b) Using the Macaulay function, determine the displacement in y of the point B of the beam (x 2.4 m from the support at A) [10 Marks] c) Determine the slope at B. [5 Marks] The beam has a Young's modulus of E-200 GPa and...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two springs of stiffnesses ki - 100 N/m and k2 120 N/m. Its natra frequency is evaluated by means of a cantilever sensor, which is attached to the point mass. Knowing the cantilever has a constant circular cross section, a length 1 0.08 m, the cantilever's Young's modulus is E -200 GPa, and mass density is p 7600 kg/m3, determine its diameter d, such that...
QUESTION 2
Consider an electrical motor with mass M = 901.8129 kg
located at the middle of pinned-pinned beam, as shown in the figure
below. Assume that the Young’s modulus of the beam E =
8.5470x1010 Pa, moment of inertia I =
8.3375x104 mm4 , length of the beam
L = 0.2859 m and zero initial conditions. If there is an
unbalance mass of m0 = 2.3714 kg in the
rotating part of the motor, eccentricity is e = 4.1473...
*Vibration
A shaft carrying two rotating disks of masses m Figure Q5(a). Assume that the deflections of the bearings and gyroscopic effect of the disks are negligible. Take E 209 x 109 N/m2. 20 kg and m2 35 kg as shown in Find the flexibility influence coefficients of the system. i) (5 marks) Determine the natural frequency of the system using Dunkerley's method. ii) (5 marks) 20 mm dia 35 kg 20 kg 150 mm 150 mm 600 mm DIK...
The figure below shows a uniform slender bar supported by cantilevers at A and C. At B a linear spring with stiffness K' is connected to an additional point mass 'm'. Note the physical properties of the bar include cross sectional area A, Young's modulus E, second moment of area I, and, density ρ, and length AB-BC-L. 1. 2. Develop the matrix equation of motion for the FEM system in the model How many natural frequencies are in the system?...
The mass of the uniform slender steel rod, shown in Figure 2, is 3 kg. The system is set in motion with small oscillations about the horizontal equilibrium position shown. (i) Determine the position x for the slider such that the system period is 1 s. (ii) When the pivot is replaced by a built-in support that restricts any rotation at O and the spring is moved to the right-hand end with the 1.2 kg mass removed, calculate the frequency...
b) Figure Q5(b) shows a frame ABCDE that is supported by a hinge at A and E )Construct the free body diagram for the entire structure, the disc and member DBE i) By applying equation of equilibrium, determine the horizontal and vertical components of the force that is acting on the hinge of member DBE li) If the weight of the cylinder is increased to 60 N and all the reaction forces are remain unchanged, evaluate the new radius of...
The figure shows a trolley of mass M, which runs on a frictionless horizontal plane. A t O the trolley carries a simple pendulum of length I with a body of mass m at its end. Two equal springs, each of stiffness k, are attached to the trolley and to the fixed walls. By using the independent co-ordinates x and ? as shown in the figure, determine, for the small free oscillations, the equations of motion. If M-100 kg, m-10...
Figure 5 shows a pick-up truck of a total mass mi transporting a small cart of a mass m2. The small cart is hitched through two springs of axial stiffness k each to the truck (b) body. Absolute displacement of the truck is xi while that of the cart is x2 (i) Find the relative motion (n-m) of the cart when the truck is subjected to a (7 marks) Find the natural frequencies and mode shapes of this two-degree-of-freedom harmonic...
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