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Boundary Conditions

Impedance Mismatch

Damping Effects

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Transfer Function

Frequency Response

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Material Behavior

 

Dr. Layer 1.0
Exercise 3 - Boundary Conditions

Introduction

Introduction

Background

This exercise is related to the basic conditions of relative fixity at layer boundaries. A fixed support is one that prevents translations or rotations. A partially restrained support allows some minimal amount of rotation or translation. A free support allows displacements and rotations at its ends. Fixed supports at the base and a free support at the ends and vice versa could suffice for the demonstration that follows

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Objective

The relevance of the type of wave propagation obtained from different boundary conditions will be studied and related to the impedance ratio values (discussed in Lesson #2) of 0 and infinity and their physical meanings i.e. infinity value indicating travel of an incident wave to a fixed support, zero value indicating a free support.

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Things to Do

  1. Open the Dr. Layer program. By default we get twelve layers. The top six layers are hardwired into the system with a very fast velocity. The bottom six layers are hardwired with a very slow velocity. Using the Edit menu select All Layers and using the wave speed menu assign them a very slow speed.

  2. In its default configuration the top boundary is free and the bottom one is set fixed.

  3. Using the load pop-up window select a pulse load, and using the sliders assign the pulse a medium amplitude and frequency.

  4. Send a pulse wave through the layer and observe its charateristics as it reaches the top boundary (free end) and later the bottom boundary (fixed end). To check the displacement at these points use dispalcement plot-boxes (Figure 1.a).

  5. Using the Options menu select the Release base option. Reset the motion to zero and send again a wave through the layer (Figure 1.b). Observe the wave characteristics as it gets to the top and bottom ends of the layer. Do you observe any change?


    Figure 1.a FIxed base -------------Figure 1.b Free base
  6. To investigate the effect of relative fixity we can select the bottom eleven layers to have a medium wave speed and the top sublayer to have a very fast wave speed.

  7. Send a wave through the media with different load types and record your observation. Pay attention to the wave reflection and travel, (Figure 2.a).

  8. Change the top layer to medium wavespeed. Note what you observe about the wave, (Figure 2.b).

  9. Change the top layer to very slow wavespeed. Note what you observe about the wave, (Figure 2.c).

    Figure 2

  10. Repeat with another load type.

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Observation

The "stiffer" member on top was made to supply some degree of fixity to the support. Although perfect fixity was not attained with our method. A trend should be noticed showing the amount of reflection obtained is a function of how rigid the boundary layer is. Ideally the end member is still considered free.

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On Your Own

  1. Obtain motions along a string with
    • The string end fixed to a wall the other end held in the hands.

    • The string end free to move the other end held in the hands.

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 Last Updated:
 12/27/00

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