Mechanical vibrations problem
A machine of mass m= 500 kg is mounted on a simple supported steel beam of length l=2 m having a rectangular cross section (depth = 0.1 m, width = 1.2m) andyoung's modulus E = 2.06 * 10^11 N/m^2. To reduce the vertical deflection of the beam, a spring of stiffness k is attached at mid-spam, as shown in fig. Determinethe value of k needed to reduce the deflection of the beam by A) 25% of its original value. B) 50% of its original value. C) 75% of its original value.
Assume that the mass of the beam is negligible.
Homework Answers
Vibration Engineering Figure Q5(b) shows a motor having mass of 50 kg is mounted on the...
Vibration Engineering
Figure Q5(b) shows a motor having mass of 50 kg is mounted on the cantilever beam of length l = 0.3 m. The motor is supported by two springs of stiffness k = 2 kN/m each. The cantilever is made of steel (stiffness, k = 3E1 Young's modulus E = 209 MPa, moment of inertia, I = 1.5 x 10 kg.m²). i) Determine total stiffness of the system. 7 marks) ii) Determine the natural frequency of the system....
A rectangular cross section at a location along a beam in bending is
(a). A rectangular cross section at a location along a beam in bending is acted upon by a bending moment and a shear force. The cross section is \(120 \mathrm{~mm}\) wide, \(300 \mathrm{~mm}\) deep and is orientated such that it is in bending about its major axis of bending. The magnitudes of the bending moment and shear force are \(315 \mathrm{kNm}\) and \(240 \mathrm{kN}\) respectively. Determine the maximum bending and shear stresses on the cross section. Plot the bending and...
solve in detail Problem Statement Consider a simply supported beam with length L=1m, width w=25mm and...
solve in detail
Problem Statement Consider a simply supported beam with length L=1m, width w=25mm and height h. The beam has a mass m=10kg hanging from it as shown in Figure 1. The mass is located at the midpoint of the beam. Figure 1 Schematic of a simply supported beam with mass m attached to it at the midpoint. The deflection of the beam at the midpoint is given by the equation below: dmg/? 48E1 where g=9.81 m/s? is the...
Consider the two-beam system below. The beams are pin jointed at B and simply supported at...
Consider the two-beam system below. The beams are pin jointed at B and simply supported at their other ends at the base of the system). A spring of stiffness, k, connects the two beams to prevent the system collapsing. The unloaded length of the spring is h/2. A load of magnitude Pis applied at point B. } a. Using the method of virtual work, find the value of that keeps the system in equilibrium with the given geometry shown in...
Solve the two problems below using the finite element method with Euler-Bernoulli beam element. 2...
Solve the two problems below using the finite element method with Euler-Bernoulli beam element. 2) Assume a simply supported beam of length 1 m subjected to a uniformly distributed load along its length of 100 N/cm. The modulus of elasticity is 207 GPa. The beam is of rectangular cross-section with a width equal to 0.01 m and a depth equal to 0.02 m. Using only one beam element, determine the deflection and maximum stress at midspan.
Solve the two problems...
Problem 1.1 Consider the beam bending problem below 2 Po Consider the beam to be homogenous...
Problem 1.1 Consider the beam bending problem below 2 Po Consider the beam to be homogenous and linearly elastic, with length L, stiffness E, and moment of inertia I. The beam is cantilevered at x = 0 an d is supported by a linear spring of stiffness k at x-L. A uniformly distributed transverse load po (N/m) is applied to the upper surface a) Write and solve the GDE to obtain the exact solution for the deflection w(x) of this...
And please explain what difference does the roller support at B make. Question 1: Stiffness method...
And please explain what
difference does the roller support at B make.
Question 1: Stiffness method Figure Q1 shows a steel beam with length 1 m (The modulus of elasticity is E 210GPa) The beam is fixed at A. Joint B is a rigid roller that can only move up and down but not rotate. Furthermore, Joint B is supported by a vertical spring. (a) Compute the stiffness coefficient associated with the vertical displacement at Joint B. (b) Compute the...
PROBLEM: A simply supported beam is subjected to a harmonic load F(t)-Fo sin ณ at mid-span as a result of the operation of a mechanical system that rotates at a constant speed n rev/min. The beam is...
PROBLEM: A simply supported beam is subjected to a harmonic load F(t)-Fo sin ณ at mid-span as a result of the operation of a mechanical system that rotates at a constant speed n rev/min. The beam is made from steel with an elasticity modulus E 29x103 ksi and specific weight 490 lb/ft3. The beam has a cross-sectional area A = 1.59 in, a moment of inertia 1 = 3.85 in, and an approximate viscous damping factor 0.05. The length between...
k Problem 2 (30 pts) Blocks A and B are released from rest when the spring...
k Problem 2 (30 pts) Blocks A and B are released from rest when the spring is unstretched. Block A has a mass my=3kg, and the linear spring has stiffness k=8N/m. If all sources of friction are negligible, determine the mass of block B such that it has a speed vp=1.5m/s after moving 1.2m downward, assuming that A never leaves the horizontal surface shown and the cord connecting A and B is inextensible. Use the work-energy principle. A B
Question 2 Parta: A cantilever AB of length 800mm is made of steel and has a...
Question 2 Parta: A cantilever AB of length 800mm is made of steel and has a square cross section with sides of length c. The cantilever is fixed at B and carries a concentrated load of 5kN at A. Calculate the minimum length of side (c) necessary to limit the maximum deflection to 10mm. [E = 200GN/m²]. Determine also the slope in degrees at A. [6] Fig 2a N.B. The weight of the beam to be neglected. Fig 2b1 Part...
Vibration Engineering
Figure Q5(b) shows a motor having mass of 50 kg is mounted on the cantilever beam of length l = 0.3 m. The motor is supported by two springs of stiffness k = 2 kN/m each. The cantilever is made of steel (stiffness, k = 3E1 Young's modulus E = 209 MPa, moment of inertia, I = 1.5 x 10 kg.m²). i) Determine total stiffness of the system. 7 marks) ii) Determine the natural frequency of the system....
solve in detail
Problem Statement Consider a simply supported beam with length L=1m, width w=25mm and height h. The beam has a mass m=10kg hanging from it as shown in Figure 1. The mass is located at the midpoint of the beam. Figure 1 Schematic of a simply supported beam with mass m attached to it at the midpoint. The deflection of the beam at the midpoint is given by the equation below: dmg/? 48E1 where g=9.81 m/s? is the...
Consider the two-beam system below. The beams are pin jointed at B and simply supported at their other ends at the base of the system). A spring of stiffness, k, connects the two beams to prevent the system collapsing. The unloaded length of the spring is h/2. A load of magnitude Pis applied at point B. } a. Using the method of virtual work, find the value of that keeps the system in equilibrium with the given geometry shown in...
Solve the two problems below using the finite element method with Euler-Bernoulli beam element. 2) Assume a simply supported beam of length 1 m subjected to a uniformly distributed load along its length of 100 N/cm. The modulus of elasticity is 207 GPa. The beam is of rectangular cross-section with a width equal to 0.01 m and a depth equal to 0.02 m. Using only one beam element, determine the deflection and maximum stress at midspan.
Solve the two problems...
Problem 1.1 Consider the beam bending problem below 2 Po Consider the beam to be homogenous and linearly elastic, with length L, stiffness E, and moment of inertia I. The beam is cantilevered at x = 0 an d is supported by a linear spring of stiffness k at x-L. A uniformly distributed transverse load po (N/m) is applied to the upper surface a) Write and solve the GDE to obtain the exact solution for the deflection w(x) of this...
And please explain what
difference does the roller support at B make.
Question 1: Stiffness method Figure Q1 shows a steel beam with length 1 m (The modulus of elasticity is E 210GPa) The beam is fixed at A. Joint B is a rigid roller that can only move up and down but not rotate. Furthermore, Joint B is supported by a vertical spring. (a) Compute the stiffness coefficient associated with the vertical displacement at Joint B. (b) Compute the...
PROBLEM: A simply supported beam is subjected to a harmonic load F(t)-Fo sin ณ at mid-span as a result of the operation of a mechanical system that rotates at a constant speed n rev/min. The beam is made from steel with an elasticity modulus E 29x103 ksi and specific weight 490 lb/ft3. The beam has a cross-sectional area A = 1.59 in, a moment of inertia 1 = 3.85 in, and an approximate viscous damping factor 0.05. The length between...
k Problem 2 (30 pts) Blocks A and B are released from rest when the spring is unstretched. Block A has a mass my=3kg, and the linear spring has stiffness k=8N/m. If all sources of friction are negligible, determine the mass of block B such that it has a speed vp=1.5m/s after moving 1.2m downward, assuming that A never leaves the horizontal surface shown and the cord connecting A and B is inextensible. Use the work-energy principle. A B
Question 2 Parta: A cantilever AB of length 800mm is made of steel and has a square cross section with sides of length c. The cantilever is fixed at B and carries a concentrated load of 5kN at A. Calculate the minimum length of side (c) necessary to limit the maximum deflection to 10mm. [E = 200GN/m²]. Determine also the slope in degrees at A. [6] Fig 2a N.B. The weight of the beam to be neglected. Fig 2b1 Part...
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