Welcome to Dr. Layer Exercises. This page is designed
to provide a simple overview of the concepts of wave propagation in layer
media through the use of DrLayer. Each exercise or lesson introduces a
variety of concepts related to wave propagation using simple visual experiments
performed in real time. Simple step by step procedures are described for
each problem followed by some recommendations or questions to expand the
knowledge. Virtually all the functionality of the program DrLayer is presented
in the accompanying exercises, and since the exercises present the program
features in the context of the underlying concepts and principles, they
provide the recommended way to be introduced to the program.
Basic
Concepts
An introduction to basic concepts of 1D wave
propagation in layer media. The concepts of wave speed and wave length
are visually introduced and possible analytical formulations are analyzed
(.pdf).
Loading
Emphasizes different loading conditions used
in the application. Exercises that display graphical representations of
the layer structure with each load type are carried out.
Boundary
Conditions
This exercise emphasizes the effect of various
boundary conditions on the propagation of waves in layered media. Fixed
supports at the base and a free support at the ends and vice versa could
suffice. A practical understanding of these concepts is he focus of this
exercise. (.pdf).
Impedance
Mismatch
Describes specific impedance as a measure of
density and wave velocity of a material. Impedance ratio is introduced
as a relationship that quantifies the relative differences in material
properties at boundaries. The attached exercise relates boundary conditions
to impedance ratios. (.pdf).
Damping
Effects
Damping is shown to be a process of steadily
diminishing the amplitude of free vibration. The exercises attached to
this section attempts to ascribe a visual representation to the different
damping types we have. (.pdf).
Natural
Modes of Vibration
Describes the period of vibration of a system as the
time required to complete one cycle of free vibration (.pdf).
Transfer
Function
Transfer functions are introduced as filters
that are applied to an incoming signal to produce an output signal. The
amplification function is also explained. The exercises attached to this
section describe how both functions can be obtained using DrLayer(.pdf).
Frequency
Response
Describes natural period of vibration of a system
as the time required to complete one cycle of free vibration. The effects
of varying the input frequency of the loading on the output earthquake
loading are complicated with motions that span a broad range of frequencies.
The exercises in this section accomplish the different effects obtained
by varying frequency characteristics. The idea of resonance is further
investigated. (.pdf).
Time
Stepping
This exercise describes a variation on the computational
side. It involves varying time step, i.e. the time it takes the numerical
tool to repeat each iteration process. The exercises also displays the
limiting value of time step above which analysis becomes unstable(.pdf).
Material
Behavior
Yielding of materials is the focus of discussion
in this section. The type of models employed for the analyses are explained.
The differences between different models are highlighted. (.pdf).
