Fig Q3 shows a uniform cantilever beam of length L which is loadedby a linearly varying load:w(x)= wowhere w is the load per unit length at the fixed end (x =0).w(x)Fig Q3: A uniform cantilever beam(a) Using Ritz method, derive a two-term polynomial function toapproximate the transverse displacement (u) of the beam.Total potential energy (TPE) for a beam under bending load is:TPE=EI du2 dr²-w(x)udxwhere E is Young's modulus and I is second moment of area.

The image you sent depicts a cantilever beam of length L subjected to a linearly varying load w(x).…

Answered: Fig Q3 shows a uniform cantilever beam…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A rectangular tube of outer width w = 7.5 m, outer height h = 5 m and thickness t = 0.17 m experiences bending through the x axis. What is the moment of inertia of the cross-sectional area In? y -- X MATLAB input variables: format shortEng W = 7.5; h = 5; t = 0.17; moment of inertia I, = m4
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: (a) What is the dimension of an area moment of inertia? (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.
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A square domain is modeled using either one bilinear rectangular element or two linear triangular elements as shown below. a) Determine the system element matrix for the Laplace equation for each discretization. b) Determine the displacement at the center of the domain (0.5,0.5) in terms of the nodal displacement. Hint: You need to assemble the stiffness matrix for the system on the right to form a 4*4 matrix from the two 3*3 element matrices. 1.0 4. 1.0 3. X- 1.0 1.0 2. 2.
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