Transfer
Function

Dr. Layer 1.0 Lesson 7  Transfer Function 
Introduction  
BackgroundA transfer function is somewhat like a filter that is applied to an incoming wave to produce an output signal. It determines how each frequency in the input motion is amplified or suppressed, by the medium of wave travel. Considering a springmass system with an excitation motion at input from the foundation connected to the spring and the corresponding response motion of the connected mass in the inertial system. The response motion of the mass will be a composite factor of the elastic and the viscous damping forces which are inherently embedded in the transfer function that determines the output motion we will obtain. In our wave propagation study we also employ transfer functions as a tool to explain the factors that make our input wave motion different from our output wave obtained. Evaluating the transfer function mathematically involves converting our known input motion to a Fourier series. Each term of the Fourier series is multiplied by the transfer function to obtain the Fourier series of the output response. Resonance is a physical phenomenon that occurs when the natural frequency of vibration of particles in a body (in our case the layers) matches the frequency of the forcing function (our input motion). It is experienced as an infinite amplification of the model. BACK TO TOPObjectiveAfter this exercise you should be able to understand and obtain different transfer functions using Dr. Layer.Things to Do
The relationship below for the transfer function is applicable to only standing waves, which are produced by the constructive interference of two waves travelling in opposite directions. The transfer function between two points on the top and bottom of a soil layer is given by
Where
BACK TO TOPObservationThe transfer function is different for each combination of parameters employed and is seen to show a general trend consistent with the damping and stiffness characteristics of the medium of travel.On Your Own
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