Design aspects of nonlinear vibration analysis of rectangular orthotropic membranes

The natural frequencies of a specially orthotropic rectangular membrane are examined with respect to its design parameters. A method is presented for inferring the initial tensions from measured vibration frequencies and the sensitivity of the tensions with respect to imprecision in the measured frequencies is demonstrated. A sensitivity analysis is used to define the key design parameters, where relatively small changes in those parameters lead to large changes in the natural frequency. This analysis is useful in two senses: It permits the design to be rapidly changed in an efficient manner, and it indicates the physical parameters that must be closely controlled in order to achieve the desired frequency. The results of the theoretical analysis were compared with a finite element simulation using Abaqus for validation. The comparison showed that results were in close agreement up to an initial displacement magnitude-to-membrane thickness ratio (T₀/h) value of about 25 for the given values of design parameters. This shows the limit of applicability of the analytical solution since the finite element (FE) simulation is fully updated at each time step with precision not available from the analytical solution.