tions to the biharmonic equation in polar coordinates. In certain structural and mechanical engineering applications, curved beams are very common. The purpose of this exercise is to demonstrate that the solution methods we developed in class can be applied to such problems. (a) Determine the differential equation that results from using the Airy stress function, o(r, 0) = f(r) sin 0, in the biharmonic equation. (b) Using the differential equation from (a), make a substitution f(r) = rm to arrive at an equation for r and m. Your equation should have roots m = 1, m = 1, m = -1, m = 3. You may need to use a computer to simplify the equation. (c) Substitute these roots back into the Airy stress function (Note that for terms in f(r) containing multiple roots, the second such term should be multiplied by log r).

tions to the biharmonic equation in polar coordinates. In certain structural and mechanical engineering applications, curved beams are very common. The purpose of this exercise is to demonstrate that the solution methods we developed in class can be applied to such problems. (a) Determine the differential equation that results from using the Airy stress function, o(r, 0) = f(r) sin 0, in the biharmonic equation. (b) Using the differential equation from (a), make a substitution f(r) = rm to arrive at an equation for r and m. Your equation should have roots m = 1, m = 1, m = -1, m = 3. You may need to use a computer to simplify the equation. (c) Substitute these roots back into the Airy stress function (Note that for terms in f(r) containing multiple roots, the second such term should be multiplied by log r).

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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