Differential transformation method for vibration of membranes

• Main Authors: Kamonpad Mansilp, Jaipong Kasemsuwan
• Format: Article
• Language: English
• Published: Prince of Songkla University 2019-08-01
• Series: Songklanakarin Journal of Science and Technology (SJST)
• Subjects: vibration of membrane; differential transformation method; analytical solution; approximate solution
• Online Access: https://rdo.psu.ac.th/sjstweb/journal/41-4/1.pdf

The purpose of this research is to apply the three-dimensional differential transform method to estimate solutions to the equation of motion for vibration in a membrane with certain types of boundary conditions. The analytical solutions without external force or damping under specific initial and boundary conditions are presented. We found by comparison that the analytical solution and the estimated solution are in good agreement, in case there is no damping or external forces. Furthermore, the differential transform method can be used to find approximate solutions taking into account both external forces and damping. This cannot be achieved via an analytical solution.