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Problem 4 (20%) Figure 5 shows a uniform elastic bar fixed at one end and attached to a mass M at the other end. The cr...
3. 2090] Consider a uniform bar of Young's modulus E, cross-sectional area A, moment of inertia d...
3. 2090] Consider a uniform bar of Young's modulus E, cross-sectional area A, moment of inertia density p, length L, with an attached end mass, m, connected to a rigid wall via a linear spring of spring constant, k, see Figure. Let the longitudinal vibration of the bar be Wa.f). (a) [4] Write down the boundary conditions. m E, p Boundary condition at x 0 Boundary condition at x L (b) [81 Derive the equation for the natural frequency (c)...
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?...
2. An elastic string of m attached to it at a distance ' The other end...
2. An elastic string of m attached to it at a distance ' The other end of the string is fixed to a point B so that the string is just unstretched t held at B (by stretching the length a of the string) and then released. Show thatit will oscillate to andfto natural length (a + b) where a s b and modulus of elasticity y has a particle of mass a from one end, which is fixed to...
Figure II.2 shows a truncated conical bar of length L and end radii (R. R) is fixed as a fixed boundary at the restrained end (4) while loaded transversely by a uniform shear: at the free end (B). In...
Figure II.2 shows a truncated conical bar of length L and end radii (R. R) is fixed as a fixed boundary at the restrained end (4) while loaded transversely by a uniform shear: at the free end (B). In the figure the τ =Ότ r-axis is through the centroidal axis (C.A.) of the bar, which is made of a linearly elastic material of Young's modulus E and Poisson's ratio v. R1 / T. FIGURE II.2 A truncated conical bar loaded...
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has been derived as (1) Find...
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x (0) 0, x, (0) 0.001 m 2k E 2m Figure 4
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www
Problem 5 (20%) For the system shown in Figure...
A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L-0.5m and the mass of attached bob m-2kg, the stiffness coefficient of the...
A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L-0.5m and the mass of attached bob m-2kg, the stiffness coefficient of the connecting spring is k-80Ns/m. 02 Figure A2. a) Using the free-body diagram method derive the following governing equations for the coupled pendulum system which are given below in matrix form b) Using the characteristic equation method or transformation to principal coordinates find out two...
An elastic string of negligible mass has one end fixed to a ceiling at point A....
An elastic string of negligible mass has one end fixed to a
ceiling at point A. The other end, point B, which is attached to a
particle of mass 3 kg, is in a position such that it is vertically
below point A, with the distance AB equal to 0.7 m. The mass is
released from rest. If the modulus of elasticity of the string is
35 N and its natural length is 1.3m find i) The distance of the...
The figure shows the mass m at the end of a bar of length / is...
The figure shows the mass m at the end of a bar of length / is restrained by a spring and dashpot. The mass is initially at rest and vibrates in the vertical plane under the action of the force F(1). Determine the equation of motion, natural frequency, and damping ratio of the system when m = 45 kg, k = 9700 N/m, c = 950 N.s/m, a - 0.8 m, and I = 2 m. Neglect the mass of...
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...
3. 2090] Consider a uniform bar of Young's modulus E, cross-sectional area A, moment of inertia density p, length L, with an attached end mass, m, connected to a rigid wall via a linear spring of spring constant, k, see Figure. Let the longitudinal vibration of the bar be Wa.f). (a) [4] Write down the boundary conditions. m E, p Boundary condition at x 0 Boundary condition at x L (b) [81 Derive the equation for the natural frequency (c)...
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?...
2. An elastic string of m attached to it at a distance ' The other end of the string is fixed to a point B so that the string is just unstretched t held at B (by stretching the length a of the string) and then released. Show thatit will oscillate to andfto natural length (a + b) where a s b and modulus of elasticity y has a particle of mass a from one end, which is fixed to...
Figure II.2 shows a truncated conical bar of length L and end radii (R. R) is fixed as a fixed boundary at the restrained end (4) while loaded transversely by a uniform shear: at the free end (B). In the figure the τ =Ότ r-axis is through the centroidal axis (C.A.) of the bar, which is made of a linearly elastic material of Young's modulus E and Poisson's ratio v. R1 / T. FIGURE II.2 A truncated conical bar loaded...
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x (0) 0, x, (0) 0.001 m 2k E 2m Figure 4
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www
Problem 5 (20%) For the system shown in Figure...
A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L-0.5m and the mass of attached bob m-2kg, the stiffness coefficient of the connecting spring is k-80Ns/m. 02 Figure A2. a) Using the free-body diagram method derive the following governing equations for the coupled pendulum system which are given below in matrix form b) Using the characteristic equation method or transformation to principal coordinates find out two...
An elastic string of negligible mass has one end fixed to a
ceiling at point A. The other end, point B, which is attached to a
particle of mass 3 kg, is in a position such that it is vertically
below point A, with the distance AB equal to 0.7 m. The mass is
released from rest. If the modulus of elasticity of the string is
35 N and its natural length is 1.3m find i) The distance of the...
The figure shows the mass m at the end of a bar of length / is restrained by a spring and dashpot. The mass is initially at rest and vibrates in the vertical plane under the action of the force F(1). Determine the equation of motion, natural frequency, and damping ratio of the system when m = 45 kg, k = 9700 N/m, c = 950 N.s/m, a - 0.8 m, and I = 2 m. Neglect the mass of...
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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