F. Giménez-Palomares, J.F. Giménez-Luján, J.A. Monsoriu-Serra

Universitat Politècnica de Valencia (SPAIN)
Vibrations of membranes and plates are of interest in many branches of Engineering and Physics. The study of vibrational movements in flexible, thin and homogeneous membranes under certain simplifications is modeled by two-dimensional wave equation. If the method of separation of variables is used the part that is not time dependent satisfies the Helmholtz equation, whose solutions for given boundary conditions are the normal modes of vibration of the membrane (resonances). Only in a few cases (rectangular or circulars domains and others) it is possible to obtain the exact solution. The problem is compounded greatly in the case of more complex domains. In this paper we present a virtual laboratory implemented as a graphical user interface (GUI) of Matlab to visualize the membrane vibration modes for arbitrary Dirichlet, Neumann or mixed conditions. To solve Helmholtz’s equation has used the method of finite differences. The program can determine the nodal lines of the resonances (regions where no transversal displacement occurs). The GUI that we have developed has very useful applications from a educational point of view.