Consider a beam with clamped ends at x = 0 and x = L. A concentrated load P is applied at the point x = L/3. The differential equation describing the deflection y is given as: d*y P =8 (x -). y(0) = 0, y'(0) = 0, y(L) = 0, y'(L) = 0 dx4 EI 3. where 8 is the Dirac delta function. Find the deflection of the beam, y(x), subject to the point load. Hints: P (i) assume y"(0) = C, and y""(0) = C2, and obtain the solution form of y in terms of C, and C2 using Laplace transform. (ii) find the constants C, and C2 by boundary conditions at x = L, and hence determine the final form of y. L
Consider a beam with clamped ends at x = 0 and x = L. A concentrated load P is applied at the point x = L/3. The differential equation describing the deflection y is given as: d*y P =8 (x -). y(0) = 0, y'(0) = 0, y(L) = 0, y'(L) = 0 dx4 EI 3. where 8 is the Dirac delta function. Find the deflection of the beam, y(x), subject to the point load. Hints: P (i) assume y"(0) = C, and y""(0) = C2, and obtain the solution form of y in terms of C, and C2 using Laplace transform. (ii) find the constants C, and C2 by boundary conditions at x = L, and hence determine the final form of y. L
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider a beam with clamped ends at x = 0 and x = L. A concentrated load P is applied at the
point x = L/3. The differential equation describing the deflection y is given as:
d*y
P
=8 (x -). y(0) = 0, y'(0) = 0, y(L) = 0, y'(L) = 0
dx4
EI
3.
where 8 is the Dirac delta function. Find the deflection of the beam, y(x), subject to the point load.
Hints:
P
(i) assume y"(0) = C, and y""(0) = C2, and obtain the solution
form of y in terms of C, and C2 using Laplace transform.
(ii) find the constants C, and C2 by boundary conditions at x = L,
and hence determine the final form of y.
L
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