Free vibration of membrane/bounded incompressible fluid

A differential quadrature procedure for free vibration of circular membranes backed by a cylindrical fluid-filled cavity

“…In Table 1, the numerical results for natural frequencies of the coupled system are compared with the approximate analytical solutions of Tariverdilo et al [16]. The present results are obtained using both approaches I and II.…”

“…To validate the present formulation for the free vibration analysis of fluid-membranes interaction systems, application is first made to a numerical example given by Tariverdilo et al [16]. Tariverdilo et al [16] proposed two analytical approaches, i.e., the Rayleigh quotient method and the variational method, for asymmetric free vibration of circular membranes in contact with a bounded incompressible fluid. The parameters used in their study are as follows:…”

“…2. The solutions based of variational formulation of Tariverdilo et al [16] are also shown for comparison. Figure 2a illustrates the convergence behavior of solutions with respect to the number of z-direction grid points (M).…”

“…Zhang et al [15] studied the dynamic behavior of membrane-type acoustic metamaterials and showed that better acoustic properties of the system can be achieved by attaching a concentrated mass to the membrane. Recently, Tariverdilo et al [16] developed two analytical approaches for asymmetric free vibration of circular membranes in contact with a bounded incompressible fluid. Most recently, Tarazaga et al [17] studied the dynamic behavior of coupled membrane-cavity systems experimentally.…”

Acoustic Influence on the Vibration of a Cylindrical Membrane Drum Filled with a Compressible Fluid

“…Shabani et al [2013] studied the hydroelastic vibration of a circular diaphragm in the fluid chamber of a reciprocating micro pump. Tariverdilo et al [2012Tariverdilo et al [ , 2013 considered the free vibration of a circular plate or membrane situated on the bottom of a cylindrical container filled with an incompressible and non-viscous fluid, for which it applies a variational approach taking into account the deformation of the plate and the velocity potential function for the fluid including also its boundary conditions. Kyeong et al [2005] analyzed the hydro-elastic vibration of a circular plate clamped at an off center location of a rigid cylindrical container with the fluid bisected by the plate in the container; for this the fluid was considered non-viscous and compressible and an analytical method was developed by the Rayleigh-Ritz method based on the Fourier-Bessel series expansion.…”