EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 27, Problem 9P
Repeat Example 27.6, but for five interior points
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Solve the following problem.
D.I 3.4-5. Use the graphical method to solve this problem:
Minimize z = 15x, + 20x2,
subject to
x1 + 2x, 2 10
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and
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The natural frequency (f) of a piezoelectric cantilever beam is described by the following equation:, where E = Modulus of elasticity, I = Area moment of inertia, L = Length of the cantilever beam, and m = Mass of proof mass (or end mass). The area moment of inertia for an arbitrary shape R with respect to an arbitrary axis (for example, x-axis) is related by:
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(b) If the thickness of a piezoelectric cantilever beam increases, does the natural frequency increase or decrease?
(c) Both the thickness and width of a piezoelectric cantilever beam can change the natural frequency. Which parameter (thickness or width) will lead to the natural frequency change more significantly? Briefly explain your answer.
Chapter 27 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 27 - A steady-state heat balance for a rod can be...Ch. 27 - 27.2 Use the shooting method to solve Prob. 27.1....Ch. 27 - 27.3 Use the finite-difference approach with to...Ch. 27 - 27.4 Use the shooting method to solve
Ch. 27 - Solve Prob. 27.4 with the finite-difference...Ch. 27 - 27.7 Differential equations like the one solved...Ch. 27 - 27.8 Repeat Example 27.4 but for three masses....Ch. 27 - 27.9 Repeat Example 27.6, but for five interior...Ch. 27 - Use minors to expand the determinant of...Ch. 27 - 27.11 Use the power method to determine the...
Ch. 27 - 27.12 Use the power method to determine the...Ch. 27 - Develop a user-friendly computer program to...Ch. 27 - Use the program developed in Prob. 27.13 to solve...Ch. 27 - 27.15 Develop a user-friendly computer program to...Ch. 27 - Use the program developed in Prob. 27.15 to solve...Ch. 27 - 27.17 Develop a user-friendly program to solve...Ch. 27 - Develop a user-friendly program to solve for the...Ch. 27 - 27.19 Use the Excel Solver to directly solve...Ch. 27 - Use MATLAB to integrate the following pair of ODEs...Ch. 27 - The following differential equation can be used to...Ch. 27 - 27.22 Use MATLAB or Mathcad to...Ch. 27 - 27.23 Use finite differences to solve the...Ch. 27 - Solve the nondimensionalized ODE using finite...Ch. 27 - 27.25 Derive the set of differential equations for...Ch. 27 - 27.26 Consider the mass-spring system in Fig....Ch. 27 - 27.27 The following nonlinear, parasitic ODE was...Ch. 27 - A heated rod with a uniform heat source can be...Ch. 27 - 27.29 Repeat Prob. 27.28, but for the following...Ch. 27 - 27.30 Suppose that the position of a falling...Ch. 27 - Repeat Example 27.3, but insulate the left end of...
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