I am trying to mathematically model the derivative of the Dirac delta function for the Euler-Bernoulli beam equation using the finite difference method. I have tried using the Gauss and Lorentz delta sequence kernel, but neither could model the Dirac delta accurately for the piezo-beam equation. Any advice would be appreciated.
Rapidly changing functions are incompatible with the finite difference method. It is much better to use numerical integration methods with automatic division of the integration step.
Then the delta-function is replaced by its continuous analog:
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a = 500;
Delta = a/Pi/(1 + (a*z)^2);
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Here is an example on Wolfram Mathematica.
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Obviously, the continuous analogue of the delta function admits differentiation. This feature can be used to simulate the moment load.
Sincerely, Sorokin
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