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Consider a fixed-fixed uniform beam resting on an elastic foundation, with a foundation modulus k N/m....
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...
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 cross sectional area for the bar is A, mass density per unit length p, modulus of elasticity E and second moment of area I. For the longitudinal vibration: S Set the necessary coordinate system, governing equation of motion and boundary conditions a. b. Derive the general solution. Explain how you can obtain the natural frequencies...
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)...
2. Consider a cantilevered beam with length L = 3 m, uniform E = 180 GPa,...
2. Consider a cantilevered beam with length L = 3 m, uniform E = 180 GPa, Iz- 5.375 × 10-8 m. and ρ 3.0 kg/m. (a) (20 points) Compute, by hand, the first 5 (lowest) natural frequencies for this beam. Note, unlike for the simply-supported beam problem, you will not be able to solve, analytically, the transcendental equation obtained from the application of the boundary conditions to the general free vibration solution. So, use Matlab roots of this equation numerically
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....
A Semi-infinite beam is loaded by force P at distance a from its end, as shown...
A Semi-infinite beam is loaded by force P at distance a from its
end, as shown in figure. (a) Obtain formulas for deflection, slope,
moment, and shear force, Using the results from part (a), consider
a 2-m-long steel bar (E = 210 GPa) of 75mm´75mm square cross
section that rests with a side on a rubber foundation with a
modulus of k = 24 MPa. If a concentrated load P = 100 kN is applied
at the distance of a...
ans all parts please 15) (10 Points) Consider a horizontal beam of length L. with uniform...
ans all parts please
15) (10 Points) Consider a horizontal beam of length L. with uniform cross-section and made out of uniform material. It is resting on the x-axis, with one end at the origin. It is acted upon by a vertical force it's own weight in this simple version). The deflection of the beam at any point x,for 0 <=<L.is given by Ely) = w, where E, I, ware constants. E is the Young's modulus of elasticity of the...
Problem 2. The ball with mass m is attached to two elastic cords each of length...
Problem 2. The ball with mass m is attached to two elastic cords each of length L. The ball is constrained to move on a horizontal, frictionless plain. The cords are stretched to a tension T When t 0, your intrepid instructor gives the ball a very small horizontal displacement x (a) Derive the equation of motion and find expressions for the natural circular frequency, the frequency, and the period of vibration. (b) For m - 2 kg, L 3...
The two uniform bars are identical. The mass and length of each bar are m= 30...
The two uniform bars are identical. The mass and length of each bar are m= 30 kg and L=1.6 m. The top bar rotates around point A, coordinate , locates the bar, and force F(t) = 500 sin 60t (in N) is being applied to the end of the bar. A spring with k = 10000 N/m connects the top bar to a fixed point. The bottom bar rotates around its center at point B and coordinate 0g locates this...
in copyable matlab code The basic differential equation of the elastic curve for a cantilever beam as shown is given as: dx2 where E = the modulus of elasticity and I = the moment of inertia. Show...
in
copyable matlab code
The basic differential equation of the elastic curve for a cantilever beam as shown is given as: dx2 where E = the modulus of elasticity and I = the moment of inertia. Show how to use MATLAB ODE solvers to find the deflection of the beam. The following parameter values apply (make sure to do the conversion and use in as the Unit of Length in all calculations): E 30,000 ksi, 1 800 in4, P kips,...
The equation of the elastic curve (deflection) for a simply supported beam under uniform load is...
The equation of the elastic curve (deflection) for a simply supported beam under uniform load is given by y= 1.7 * 10^-5 x^2 (160 - x^2 + x^3), in which, x is the distance from the left support of the beam to any point on the beam, and y is the deflection, both in meters. Find the rate of change of the deflection of the elastic curve at x m = 2
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 cross sectional area for the bar is A, mass density per unit length p, modulus of elasticity E and second moment of area I. For the longitudinal vibration: S Set the necessary coordinate system, governing equation of motion and boundary conditions a. b. Derive the general solution. Explain how you can obtain the natural frequencies...
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)...
2. Consider a cantilevered beam with length L = 3 m, uniform E = 180 GPa, Iz- 5.375 × 10-8 m. and ρ 3.0 kg/m. (a) (20 points) Compute, by hand, the first 5 (lowest) natural frequencies for this beam. Note, unlike for the simply-supported beam problem, you will not be able to solve, analytically, the transcendental equation obtained from the application of the boundary conditions to the general free vibration solution. So, use Matlab roots of this equation numerically
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....
A Semi-infinite beam is loaded by force P at distance a from its
end, as shown in figure. (a) Obtain formulas for deflection, slope,
moment, and shear force, Using the results from part (a), consider
a 2-m-long steel bar (E = 210 GPa) of 75mm´75mm square cross
section that rests with a side on a rubber foundation with a
modulus of k = 24 MPa. If a concentrated load P = 100 kN is applied
at the distance of a...
ans all parts please
15) (10 Points) Consider a horizontal beam of length L. with uniform cross-section and made out of uniform material. It is resting on the x-axis, with one end at the origin. It is acted upon by a vertical force it's own weight in this simple version). The deflection of the beam at any point x,for 0 <=<L.is given by Ely) = w, where E, I, ware constants. E is the Young's modulus of elasticity of the...
Problem 2. The ball with mass m is attached to two elastic cords each of length L. The ball is constrained to move on a horizontal, frictionless plain. The cords are stretched to a tension T When t 0, your intrepid instructor gives the ball a very small horizontal displacement x (a) Derive the equation of motion and find expressions for the natural circular frequency, the frequency, and the period of vibration. (b) For m - 2 kg, L 3...
The two uniform bars are identical. The mass and length of each bar are m= 30 kg and L=1.6 m. The top bar rotates around point A, coordinate , locates the bar, and force F(t) = 500 sin 60t (in N) is being applied to the end of the bar. A spring with k = 10000 N/m connects the top bar to a fixed point. The bottom bar rotates around its center at point B and coordinate 0g locates this...
in
copyable matlab code
The basic differential equation of the elastic curve for a cantilever beam as shown is given as: dx2 where E = the modulus of elasticity and I = the moment of inertia. Show how to use MATLAB ODE solvers to find the deflection of the beam. The following parameter values apply (make sure to do the conversion and use in as the Unit of Length in all calculations): E 30,000 ksi, 1 800 in4, P kips,...
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