Free Vibration Analysis of Non-Homogeneous Rectangular Membranes Using a Hybrid Method

A new method for studying the vibration of non-homogeneous membranes

“…Our first example is taken from [1] and later studied by different authors [2,3,4]; these authors have considered the Helmholtz equation over a rectangle of sides a and b, and with a density…”

“…To allow a comparison with the results of ref. [1,2,3,4] a calculation of the fundamental frequency of the rectangular membrane for different sizes of the membrane and different density profile is reported in Table 2. The numerical results have been obtained working with N = 12.…”

“…[2], of Table 1 of ref. [3] and of Table 10 of ref. [4] (in the last two references only the case α = 0.1 is studied).…”

“…Table 2 Results for the fundamental frequency of a rectangular membrane with density ρ(x) = 1 + α(x + 1/2) for α = 0.1 and α = 1, using N = 12. we compare our results (LSF) with the results of ref. [3], for different sizes of the membrane. Our results, obtained with a grid corresponding to N = 20, agree with those of ref.…”

“…This problem has been considered in the past by several authors, using different techniques: for example, Masad in [1] has studied the vibrations of a rectangular membrane with linearly varying density using a finite difference scheme and an approach based on perturbation theory; the same problem was also considered by Laura and collaborators in [2], using an optimized Galerkin-Kantorovich approach and by Ho and Chen, [3], who have used a hybrid method. Recently Reutskiy has put forward in [4] a new numerical technique to study the vibrations of inhomogeneous membranes, the method of external and internal excitation.…”