# Advanced Engineering Mathematics - PowerPoint PPT Presentation

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### Advanced Engineering Mathematics LAPLACE TRANSFORM ... Transform Inverse Transform Inverse Transform Inverse Transform Applications Applications ... – PowerPoint PPT presentation

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1
• LAPLACE TRANSFORM

2
Laplace Transform
3
Laplace Transform
Problem 1
4
Linear Transform
5
Laplace Transform
Problem 2
Evaluate Lt
6
Transformation Laplace
Problem 3
Evaluate Le-3t
7
Transformation Laplace
Problem 4
Evaluate Lsin2 t
8
Transformation Laplace
Problem 2
9
Inverse Transform
10
Linear Transform
11
Inverse Transform
Problem 1
12
Inverse Transform
Problem 2
13
Inverse Transform
Problem 3
14
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.
15
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)
16
Applications
Deflection of Beams
17
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.

18
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
19
Applications
Determining deflection of a Beam using Laplace
Transform
20
Applications
Determining deflection of a Beam using Laplace
Transform