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Concept explainers
(a)
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
(a)
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Answer to Problem 53AAP
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
Explanation of Solution
For plane
For plane
And for plane
Miller-Bravais Indices for Planes are shown in table.
Planer Intercepts | Reciprocals of Intercepts | Miller-Bravais Indices | |
Plane-a | |||
Plane-b | |||
Plane-c |
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
(b)
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
(b)

Answer to Problem 53AAP
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
Explanation of Solution
The coordinates of intercepts for plane-
For plane
For plane
And for plane
Conclusion:
Miller-Bravais Indices for Planes are shown in table below.
Planes | Planer Intercepts | Reciprocals of Intercepts | Miller-Bravais Indices |
Plane-a | |||
Plane-b | |||
Plane-c |
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
The Miller-Bravais indices of the hexagonal crystal plane,
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Chapter 3 Solutions
Foundations of Materials Science and Engineering
- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
- Understanding Motor ControlsMechanical EngineeringISBN:9781337798686Author:Stephen L. HermanPublisher:Delmar Cengage Learning
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