TY - EJOU
AU - Reutskiy, S.Yu.
TI - Vibration Analysis of Arbitrarily Shaped Membranes
T2 - Computer Modeling in Engineering \& Sciences
PY - 2009
VL - 51
IS - 2
SN - 1526-1506
AB - In this paper a new numerical technique for problems of free vibrations of arbitrary shaped non-homogeneous membranes:∇^{2}w + k^{2}q(x)w = 0, x∈ Ω⊂R^{2}, B[w] = 0, x∈∂Ω is presented. Homogeneous membranes of a complex form are considered as a particular case. The method is based on mathematically modeling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. Applying the method, one gets a sequence of boundary value problems (BVPs) depending on the spectral parameter *k*. The eigenvalues are sought as positions of the maxima of some norm of the solution. In the particular case of a homogeneous membrane the method of fundamental solutions (MFS) is proposed as an effective solver of such BVPs in domains of a complex geometry. For non-homogeneous membranes the combination of the finite difference method and conformal mapping is used as a solver of the BVPs. The results of the numerical experiments justifying the method are presented.
KW - Free vibration
KW - eigenvalue problem
KW - membrane
KW - irregular domain
KW - non-homogeneous membrane
KW - conformal mapping
KW - nonlinear eigenvalue problem
DO - 10.3970/cmes.2009.051.115