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Welcome to
Dr. Layer Theory. This section is designed to provide an overview
of basic theoretical concepts on 1-D wave propagation. The material is
organized in six thematic lessons each one covering specific concepts
on wave propagation. The lessons complement the exercises section and
have been selected to help the reader understand the fundamental concepts
that are explored in the exercises. The lessons cover the following topics:
Basic
Concepts
Introduces the concepts of mechanical waves,
wave speed, and wave number.
Harmonic
Loading
Introduces the concept of traveling waves,
complex representation of motion, standing waves, and modes of vibration.
Impedance
Ratio
Introduces the concepts of reflection and refraction
at an interface, defines the concept of impedance ratio coefficients,
and addresses some important issues associated with impedance ratio phenomena.
Transfer
Function
In this lesson, transfer functions are derived
for a series of successively more complicated geotechnical conditions.
Three simple cases are used to illustrate some of the important effects
of soil deposits on ground motion characteristics without undue mathematical
complexity.
Numerical
Solution
This lesson introduces basic numerical time-stepping
solution methods that can be used for the numerical solution of the wave
equation.
Fourier
Analysis
This lesson introduces the basic ingredients required
to perform an analysis in the frequency domain. The FFT concept is investigated
and some illustrated examples are used to illustrate its significance
and applicability.
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