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ME 351: Problem Set 2: Mechanical Systems For the systems shown below: a. Find the free...
Question 1 A plane frame is loaded as shown in the figure below. The global coordinate axes are shown in the figure...
Question 1 A plane frame is loaded as shown in the figure below. The global coordinate axes are shown in the figure. For both elements, E = 30000 ksi, I-1000 in4 and A-100 in2. Determine all nodal displacements, nodal rotations and member end forces (including moments) for both members. Label member end forces in a free body diagram 1000 lb/ft 40 ft 45 30 ft
Part 1: Translation mechanical systems: 2.5 (a) Draw a complete free-body diagram for all the elements...
Part 1: Translation mechanical systems: 2.5 (a) Draw a complete free-body diagram for all the elements of the system shown in Fig. P2.5. (c) Derive the differential equation relating the displacement xto the input force F1. Figure P2.5.
MEE456 Homework Consider the beam shown below: 550 Analyze this beam using a 3-node, 2-element model...
MEE456 Homework Consider the beam shown below: 550 Analyze this beam using a 3-node, 2-element model (hand calculations or E-200 G Pa and i=1 x 10" m'. Report on a summary page: a) Sketch a diagram of the beam showing the nodes, elements and loading (FE model). b) Present the displacements, rotations, reactions and, element forces and moments. c) Sketch a free body diagram of the beam showing the original loading and the reactions. d) Sketch a free body diagram...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
The system shown below is made up of one mass and two inertia's (M, I1, and...
The system shown below is made up of one mass and two inertia's (M, I1, and I2). Mass M is connected to Inertia I2 by a damper Ci that is pivoted at each end. The system outputs are y and 0, and the input is force F. At the equilibrium position shown all of the springs are unstretched. Therefore for this problem the initial spring forces are zero and may be neglected. Find the governing differential equations of motion in...
Three rigid bodies (Nodes 2, 3, and 4) are connected by five springs as shown below....
Three rigid bodies (Nodes 2, 3, and 4) are connected by five
springs as shown below. Assume that the
bodies can only undergo translation in the horizontal direction.
Horizontal force P2=1000 N and
P4=1500 N is applied to Elements 2 and 4, respectively. The spring
constants in (N/mm) are given as:
k1=400, k2=500, k3=600, k4=100, and k5=300. Nodes 1 and 5 are
fixed. Determine the nodal
displacements and reaction forces at the walls.
Problem 1. (3 points) Three rigid bodies...
Please answer the questions for Part 1 and Part 2 showing all steps, using the provided...
Please answer the questions for Part 1 and Part 2 showing all
steps, using the provided data values.
Many thanks.
M2 2 C2 2' 2 2 C2 2'2 Spring steel Mi k1 C1 2'2 1 C1 Base y(t) Base movement Figure 2 shows a shear building with base motion. This building is modelled as a 2 DOF dynamic system where the variables of ml-3.95 kg, m2- 0.65 kg, kl-1200 N/m, k2- 68 N/m, cl- 0.40 Ns/m, c2- 0.70Ns/m The base...
matlab INSTRUCTIONS Consider the spring-mass damper that can be used to model many dynamic systems Applying Newton...
matlab
INSTRUCTIONS Consider the spring-mass damper that can be used to model many dynamic systems Applying Newton's Second Law to a free-body diagram of the mass m yields the following ODE m습+8 +kx=F(t) (1) dt2 Where F() is a forcing function, Consider the case where the forcing function itself is a damped oscillation: Where F F(t)-Ae-Bt COS(wt) (2) For this activity we'll see how we can formulate this ODE for a solution using MATLAB that could be used to study...
Problem 3 (34%) The figure below shows a Free Body Diagram (FBD) of a structure. Determine...
Problem 3 (34%) The figure below shows a Free Body Diagram (FBD) of a structure. Determine the forces for the FBD using the information shown. Develop equations and leave answers in Ax-b, where x shall be [F1, F2, F3, V2, Va]T. Unit for all forces is kN. P is external force and both V2 and V3 are reaction force at the node. Show all steps. Do not solve. Equation sequence for matrix A shall be as follows Row 1: Node...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
Question 1 A plane frame is loaded as shown in the figure below. The global coordinate axes are shown in the figure. For both elements, E = 30000 ksi, I-1000 in4 and A-100 in2. Determine all nodal displacements, nodal rotations and member end forces (including moments) for both members. Label member end forces in a free body diagram 1000 lb/ft 40 ft 45 30 ft
Part 1: Translation mechanical systems: 2.5 (a) Draw a complete free-body diagram for all the elements of the system shown in Fig. P2.5. (c) Derive the differential equation relating the displacement xto the input force F1. Figure P2.5.
MEE456 Homework Consider the beam shown below: 550 Analyze this beam using a 3-node, 2-element model (hand calculations or E-200 G Pa and i=1 x 10" m'. Report on a summary page: a) Sketch a diagram of the beam showing the nodes, elements and loading (FE model). b) Present the displacements, rotations, reactions and, element forces and moments. c) Sketch a free body diagram of the beam showing the original loading and the reactions. d) Sketch a free body diagram...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
The system shown below is made up of one mass and two inertia's (M, I1, and I2). Mass M is connected to Inertia I2 by a damper Ci that is pivoted at each end. The system outputs are y and 0, and the input is force F. At the equilibrium position shown all of the springs are unstretched. Therefore for this problem the initial spring forces are zero and may be neglected. Find the governing differential equations of motion in...
Three rigid bodies (Nodes 2, 3, and 4) are connected by five
springs as shown below. Assume that the
bodies can only undergo translation in the horizontal direction.
Horizontal force P2=1000 N and
P4=1500 N is applied to Elements 2 and 4, respectively. The spring
constants in (N/mm) are given as:
k1=400, k2=500, k3=600, k4=100, and k5=300. Nodes 1 and 5 are
fixed. Determine the nodal
displacements and reaction forces at the walls.
Problem 1. (3 points) Three rigid bodies...
Please answer the questions for Part 1 and Part 2 showing all
steps, using the provided data values.
Many thanks.
M2 2 C2 2' 2 2 C2 2'2 Spring steel Mi k1 C1 2'2 1 C1 Base y(t) Base movement Figure 2 shows a shear building with base motion. This building is modelled as a 2 DOF dynamic system where the variables of ml-3.95 kg, m2- 0.65 kg, kl-1200 N/m, k2- 68 N/m, cl- 0.40 Ns/m, c2- 0.70Ns/m The base...
matlab
INSTRUCTIONS Consider the spring-mass damper that can be used to model many dynamic systems Applying Newton's Second Law to a free-body diagram of the mass m yields the following ODE m습+8 +kx=F(t) (1) dt2 Where F() is a forcing function, Consider the case where the forcing function itself is a damped oscillation: Where F F(t)-Ae-Bt COS(wt) (2) For this activity we'll see how we can formulate this ODE for a solution using MATLAB that could be used to study...
Problem 3 (34%) The figure below shows a Free Body Diagram (FBD) of a structure. Determine the forces for the FBD using the information shown. Develop equations and leave answers in Ax-b, where x shall be [F1, F2, F3, V2, Va]T. Unit for all forces is kN. P is external force and both V2 and V3 are reaction force at the node. Show all steps. Do not solve. Equation sequence for matrix A shall be as follows Row 1: Node...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
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