Pressure-Based and Potential-Based Differential Quadrature Procedures for Free Vibration of Circular Plates in Contact with Fluid

Abstract

The differential quadrature method (DQM) has been so far applied to a wide variety of fluid and/or structural problems. The results of many researchers reveal that the DQM is computationally efficient and is applicable to a large class of boundary value problems. However, there is little information about its applications to fluidstructure interaction problems. Therefore, the purpose of this paper is to provide some information in this area and to develop procedures based on the DQM for the numerical solution of fluidstructure interaction problems. First, the governing partial differential equations of motion of the structure and fluid are discretized separately using the DQM. Then, by applying the boundary condition at fluid-structure interface, the governing eigenvalue equations of the coupled system are obtained which can then be solved for the eigenvalues of the system. The applicability of the proposed procedures is shown herein through the free vibration analysis of thin circular plates in contact with a cylindrical fluid-filled cavity. Issues related to the implementation of the regularity conditions at the center of the circular plate and the central line of the cylindrical cavity are addressed. Two new regularity conditions are proposed for the circular cylindrical fluid domain. The accuracy and efficiency of the proposed procedures are demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate converged results can be obtained by the proposed procedures using a small number of grid points. Three new dimensionless parameters and variables are also introduced for the free vibration of the coupled system. The influences of these parameters on dynamic behavior of the system are studied.

Fluid-structure coupling of concentric double FGM shells with different lengths

“…The inviscid, incompressible and irrotational fluid permits the introduction of a velocity potential for the fluid motion (Eftekhari 2016). The liquid velocity potential can be expressed as…”

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

“…However, these regularity conditions were only given for the vibration problem of dry circular plates. For the case of wet circular plates (i.e., fluid-loaded circular plates), the stiffness matrix of the fluid may also become singular [43]. In this case, it is necessary to implement some other regularity conditions for the fluid domain.…”

“…In the most recent paper on this subject, Eftekhari [43] developed two different procedures based on the DQM (i.e., pressure-based and potential-based DQMs) for numerical solution of circular plate-fluid interaction problems. Although the results of the two procedures were found to be identical, the potential-based procedure was found to be better than the pressure-based procedure due to its well-conditioning of the resulting eigenvalue equation.…”

Nonlinear vibration analysis of a circular plate–cavity system

“…The experiments and numerical simulations were used by Escaler and De La Torre [32] to quantify the changes in the modes of vibration of a circular Chladni plate completely submerged in a water tank. Two general procedures based on differential quadrature method, i.e., the pressure-based and potentialbased DQMs, were proposed by Eftekhari [33] to study the free vibration of thin circular plates in contact with a bounded compressible fluid. The transient vibroacoustic response suppression of a piezo-coupled sandwich circular plate backed by a rigid-walled cylindrical acoustic enclosure was investigated by Hasheminejad and Shakeri [34].…”