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A cantilever beam of length L is embedded at its right end, and a horizontal tensile force of P pounds is applied to its free left end. When the origin is taken at its free end, as shown in the figure below, the deflection y(x) of the beam can be shown to satisfy the differential equation Ely" = Py-w(x) P y(x) = y4 wox Find the general solution of the given differential equation if w(x) = xwo Wo w EI x- cash (Vải ) t exinh((Vải + 2p+ p² D X Find the deflection of the cantilever beam if w(x) = wox, 0 < x < L, and y(0) = 0, y'(L) = 0. WEI p2 cosh√x+ ΕΙ + PWEI √ L- El p² P El cosh sinh√P ΕΙ P ΕΙ L w L P [P -sinh√ EX+ EI Wo 2p+² + WEI

A cantilever beam of length L is embedded at its right end, and a horizontal tensile force of P pounds is applied to its free left end. When the origin is taken at its free end, as shown in the figure below, the deflection y(x) of the beam can be shown to satisfy the differential equation Ely" = Py-w(x) P y(x) = y4 wox Find the general solution of the given differential equation if w(x) = xwo Wo w EI x- cash (Vải ) t exinh((Vải + 2p+ p² D X Find the deflection of the cantilever beam if w(x) = wox, 0 < x < L, and y(0) = 0, y'(L) = 0. WEI p2 cosh√x+ ΕΙ + PWEI √ L- El p² P El cosh sinh√P ΕΙ P ΕΙ L w L P [P -sinh√ EX+ EI Wo 2p+² + WEI

Advanced Engineering Mathematics
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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A cantilever beam of length L is embedded at its right end, and a horizontal tensile force of P pounds is applied to its free left end. When the origin is taken at its free end, as shown in the figure below, the deflection y(x) of the beam can be shown to satisfy the differential equation Ely" = Py - w(x). y y(x) = wox Find the general solution of the given differential equation if w(x) = xw. W y = C₁cosh c.cohl((V£a \r\+ csinh((VẺ } + x + P 02 ΕΙ X ΕΙ 2px² X Find the deflection of the cantilever beam if w(x) WO EI cosh₁ p² P x + ΕΙ P WEI ΕΙ p² P = ΕΙ L sinhy P ΕΙ X Wox, 0 < x < L, and y(0) = 0, y'(L) = 0. cosh P ΕΙ w EI L w L P p² sinh√ √ W P wo 2 x+ ΕΙ 2px² + W EI p² X X
Transcribed Image Text:A cantilever beam of length L is embedded at its right end, and a horizontal tensile force of P pounds is applied to its free left end. When the origin is taken at its free end, as shown in the figure below, the deflection y(x) of the beam can be shown to satisfy the differential equation Ely" = Py - w(x). y y(x) = wox Find the general solution of the given differential equation if w(x) = xw. W y = C₁cosh c.cohl((V£a \r\+ csinh((VẺ } + x + P 02 ΕΙ X ΕΙ 2px² X Find the deflection of the cantilever beam if w(x) WO EI cosh₁ p² P x + ΕΙ P WEI ΕΙ p² P = ΕΙ L sinhy P ΕΙ X Wox, 0 < x < L, and y(0) = 0, y'(L) = 0. cosh P ΕΙ w EI L w L P p² sinh√ √ W P wo 2 x+ ΕΙ 2px² + W EI p² X X
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