Application of hyperbolic differential quadrature method for vibration responses of the electrorheological disk

The Electrorheological (ER) disk is a widely used smart material in various engineering applications due to its ability to change its mechanical properties in response to electric fields. The vibration analysis of such a disk is essential for understanding its dynamic behavior and designing efficient control strategies. In this paper, the hyperbolic differential quadrature method (HDQM) is applied to investigate the vibration responses of the ER disk. Both first and higher-order shear deformation theories are incorporated for modeling displacement fields in sandwich disks. In the interface of the layers’ compatibility conditions are applied. The HDQM is a numerical technique based on the differential quadrature method that can handle problems with hyperbolic partial differential equations. The validity and accuracy of the proposed method are confirmed by comparing the results with those obtained by previous studies. Finally, the effects of disk geometry, and boundary conditions on the natural frequencies and mode shapes of the ER disk are investigated. The results demonstrate the effectiveness of the HDQM in solving the vibration problems of the ER disk and provide valuable insights for designing ER-based devices.