Reduce Differential Transformation Method for Vibration of Membranes
Keywords:
Differential Transformation Method, Reduced Differential Transformation Method, The equation of motion of a membraneAbstract
This research demonstrates the calculation of an estimated solution for the membrane motion equation with given initial and boundary conditions using the 3D reduced differential transformation method (RDTM) obtained from the normal differential transformation (DTM). By comparing the analytical solution and the approximate solution obtained from RDTM, it is found that the approximate error is considerably small. Therefore, the RDTM is effective in solving the equation of membrane motion. In addition, adding a damping term, an external force term as well as both damping and external force terms result in a decrease in the approximate solution amplitude for each time. In conclusion, the RDTM is the method with less complexity compared to the analytical method, so that it is possible to find an approximate solution in terms of the polynomials of t conveniently.
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