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QUESTION 1:(15 points) Determine the natural frequency of the system corsisting of a cantilever beam and...
Problem 5 (10 points) Assuming the beam to be massless, the system shown below has a...
Problem 5 (10 points) Assuming the beam to be massless, the system shown below has a single dynamic DOF defined as the vertical deflection under the weight w. Derive the vertical period of vibration of the beam by using static condensation in terms of w, EI and L. Evaluate the period of vibration by assuming w=100KN, E=200KN/mm², I =50.100mmº and L=10 m. Ellw H /3— 20/3—
Determine the natural frequencies and eigenvectors of a beam system with negligible mass shown below, and EI is the flexural rigidity of the beam.
Determine the natural frequencies and eigenvectors of a beam system with negligible mass shown below, and EI is the flexural rigidity of the beam.
Consider a cantilever beam under a concentrated force and moment as shown below. The deflections ofthe...
Consider a cantilever beam under a concentrated force and moment as shown below. The deflections ofthe beam under the force F (y) and moment M (y) are given by: 2. y' Mo L-x) , and y2 Me , where EI is the beam's flexural rigidity. The slope of the beam, 0, is the derivative of the deflection. Write a program that asks the user to input beam's length L, flexural rigidity EI (you may consider this as a single parameter,...
Problem-1 (15 points) A cantilever beam ACB supports a concentrated load P and a couple moment Mo, as shown in the figure below. (a) Determine the total strain energy of the beam, (b) Determine t...
Problem-1 (15 points) A cantilever beam ACB supports a concentrated load P and a couple moment Mo, as shown in the figure below. (a) Determine the total strain energy of the beam, (b) Determine the deflections δ and δ8 at points C and B respectively. (c) Determine the angle of rotations 0 and θι, at points C and B respectively. Use the Castigliano's theorem(s). Assume that the beam's flexural rigidity is EI Mo
Problem-1 (15 points) A cantilever beam ACB...
Question 1(10 Marks) Design a strain gage-transducer to measure the deflection of the cantilever beam (Fig.1) if the fo...
Question 1(10 Marks) Design a strain gage-transducer to measure the deflection of the cantilever beam (Fig.1) if the force P is applied at the end of the beam. Consider the length of the beam is L
Question 1(10 Marks) Design a strain gage-transducer to measure the deflection of the cantilever beam (Fig.1) if the force P is applied at the end of the beam. Consider the length of the beam is L
Problem 2: Cantilever beam In class we derived the spring constant of a beam of length...
Problem 2: Cantilever beam In class we derived the spring constant of a beam of length L and constant bending stiffness El clamped at x=0 and subject to a vertical force Fat x= L. Let's study a few different variations of that problem. Let's replace the vertical force F by a counter clockwise bending moement Mo applied at x = L. Recom- pute the equivalent spring constant. Note that in the class we computed spring constant with force and displacement....
Vibration solve 1.2 by using numbers (values) from 1.1 1.1 Determine the natural period for the...
Vibration
solve 1.2 by using numbers (values) from 1.1
1.1 Determine the natural period for the system in Fig. P1.1. Assume that the beam and springs supporting the weight Ware massless. Fig. P1.1 1.2 The following numerical values are given in Problem 1.1: L = 100 in, EI - 10% (b.in), W=3000 lb, and k = 2000 lb/in. If the weight W has an ini- tial displacement of yo = 1.0 in and an initial velocity Vo = 20 in/sec,...
Problem 1. The natural frequencies wn of free vibration of a cantilever beam are determined from...
Problem 1. The natural frequencies wn of free vibration of a cantilever beam are determined from the roots of the equation: ET Cantilever beam Wn = (k~L)2 VPALA in which E = 2.0 x 1011 N/m is the elastic modulus, L = 0.45 m is the beam length, 1 = 4.5 x 10-11 m is the moment of inertia, A = 6.0 x 10-5 mº is the cross-sectional area, and p = 6850 kg/m' is the density per unit length....
EMT 101- Engineering Programming Homework 3 Deflection of an I-Beam(100 %) You are to develop a program that calculates and plots the vertical deflection of a beam subjected to a force acting on it...
EMT 101- Engineering Programming Homework 3 Deflection of an I-Beam(100 %) You are to develop a program that calculates and plots the vertical deflection of a beam subjected to a force acting on it as given in Figure 1. The I-Beam has length, L 2m with its left end fixed at the wall (no deflection at wall) The right end of the beam is applied with a vertical load force P with a vertical deflection function (3L -a) EI wherer...
Q1. For the system shown in Figure 1 where the beam with mass m and length...
Q1. For the system shown in Figure 1 where the beam with mass m and length L is connected to the fixed surfaces through three springs with same stiffness k, (i) Calculate the total kinetic energy and total potential energy of the system; (ii) Derive the equation of motion in terms of rotation angle 0; (iii) Find the natural frequency of the system; (iv) Calculate the natural period if the stiffness k of all springs is doubled; (v) If the...
Problem 5 (10 points) Assuming the beam to be massless, the system shown below has a single dynamic DOF defined as the vertical deflection under the weight w. Derive the vertical period of vibration of the beam by using static condensation in terms of w, EI and L. Evaluate the period of vibration by assuming w=100KN, E=200KN/mm², I =50.100mmº and L=10 m. Ellw H /3— 20/3—
Consider a cantilever beam under a concentrated force and moment as shown below. The deflections ofthe beam under the force F (y) and moment M (y) are given by: 2. y' Mo L-x) , and y2 Me , where EI is the beam's flexural rigidity. The slope of the beam, 0, is the derivative of the deflection. Write a program that asks the user to input beam's length L, flexural rigidity EI (you may consider this as a single parameter,...
Problem-1 (15 points) A cantilever beam ACB supports a concentrated load P and a couple moment Mo, as shown in the figure below. (a) Determine the total strain energy of the beam, (b) Determine the deflections δ and δ8 at points C and B respectively. (c) Determine the angle of rotations 0 and θι, at points C and B respectively. Use the Castigliano's theorem(s). Assume that the beam's flexural rigidity is EI Mo
Problem-1 (15 points) A cantilever beam ACB...
Question 1(10 Marks) Design a strain gage-transducer to measure the deflection of the cantilever beam (Fig.1) if the force P is applied at the end of the beam. Consider the length of the beam is L
Question 1(10 Marks) Design a strain gage-transducer to measure the deflection of the cantilever beam (Fig.1) if the force P is applied at the end of the beam. Consider the length of the beam is L
Problem 2: Cantilever beam In class we derived the spring constant of a beam of length L and constant bending stiffness El clamped at x=0 and subject to a vertical force Fat x= L. Let's study a few different variations of that problem. Let's replace the vertical force F by a counter clockwise bending moement Mo applied at x = L. Recom- pute the equivalent spring constant. Note that in the class we computed spring constant with force and displacement....
Vibration
solve 1.2 by using numbers (values) from 1.1
1.1 Determine the natural period for the system in Fig. P1.1. Assume that the beam and springs supporting the weight Ware massless. Fig. P1.1 1.2 The following numerical values are given in Problem 1.1: L = 100 in, EI - 10% (b.in), W=3000 lb, and k = 2000 lb/in. If the weight W has an ini- tial displacement of yo = 1.0 in and an initial velocity Vo = 20 in/sec,...
Problem 1. The natural frequencies wn of free vibration of a cantilever beam are determined from the roots of the equation: ET Cantilever beam Wn = (k~L)2 VPALA in which E = 2.0 x 1011 N/m is the elastic modulus, L = 0.45 m is the beam length, 1 = 4.5 x 10-11 m is the moment of inertia, A = 6.0 x 10-5 mº is the cross-sectional area, and p = 6850 kg/m' is the density per unit length....
EMT 101- Engineering Programming Homework 3 Deflection of an I-Beam(100 %) You are to develop a program that calculates and plots the vertical deflection of a beam subjected to a force acting on it as given in Figure 1. The I-Beam has length, L 2m with its left end fixed at the wall (no deflection at wall) The right end of the beam is applied with a vertical load force P with a vertical deflection function (3L -a) EI wherer...
Q1. For the system shown in Figure 1 where the beam with mass m and length L is connected to the fixed surfaces through three springs with same stiffness k, (i) Calculate the total kinetic energy and total potential energy of the system; (ii) Derive the equation of motion in terms of rotation angle 0; (iii) Find the natural frequency of the system; (iv) Calculate the natural period if the stiffness k of all springs is doubled; (v) If the...
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