Advanced Engineering Mathematics

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Advanced Engineering Mathematics

• LAPLACE TRANSFORM

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Laplace Transform
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Laplace Transform
Problem 1
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Linear Transform
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Laplace Transform
Problem 2
Evaluate Lt
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Transformation Laplace
Problem 3
Evaluate Le-3t
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Transformation Laplace
Problem 4
Evaluate Lsin2 t
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Transformation Laplace
Problem 2
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Inverse Transform
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Linear Transform
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Inverse Transform
Problem 1
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Inverse Transform
Problem 2
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Inverse Transform
Problem 3
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Applications
Deflection of Beams
Beam is assumed as a homogeneous, and has uniform
cross sections along its length Deflection curve
can be derived from differential equation based
on elasticity concept.
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Applications
Deflection of Beams
Elasticity theory bending moment M(x) at a point
x along the beam is related to the load per unit
length w(x)
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Applications
Deflection of Beams
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Applications
Deflection of Beams

• y(0) 0 at embedded end.
• y(0) 0 (deflection curve is tangent to the
  x-axis at embedded end)
• y(L) 0, bending moment at free end is zer0.
• y(L) 0, shear force is zero at a free end.
  EIy dM/dx is the shear force.

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Applications
Determining deflection of a Beam using Laplace
Transform
x
A beam of length L is embedded at both ends. In
this case the deflection y(x) must satisfy
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Applications
Determining deflection of a Beam using Laplace
Transform
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Applications
Determining deflection of a Beam using Laplace
Transform