Comments on “free transverse vibrations of uniform circular plates and membranes with eccentric holes”

Dynamics of a circular membrane with an eccentric circular areal constraint: Analysis and accurate simulations

“…This problem was considered in the literature [6,14,16] and the results were summarized by Singh et al [17]. We compare these results with those obtained using our algorithm, implemented with k max = 10a and Dk = k max .…”

“…For simulation of the dynamics of a constrained membrane, it is necessary to accurately compute many frequencies and mode shapes; this is difficult to compute using existing methods due to singularity. For example, Nagaya [14], Singh and Kothari [16], and Singh et al [17] proposed to combine the two equations for symmetric modes in Eq. (13) into the following single equation…”

“…(16) derived by Lin [15] was revised by Singh et al [17]; they expanded the inner summation and used the property of Bessel functions…”

“…(11) and (12) were investigated by several researchers [14][15][16][17] and the eigenfrequencies were determined for the even (symmetric) and the odd (antisymmetric) modes.…”

“…Lin [15] missed a term in the final expression, which affected the results of calculation. The missing term was identified by Singh and Kothari [16] and Singh et al [17], who used Nagaya's approach together with Graf's addition theorem. Later, Nagaya and Hai [18] studied composite membranes with arbitrarily shaped inner and outer boundaries.…”