OICC Press Journal of Solid Mechanics 2008-7683 12 5 2020 12 30 Vibration Analysis of the Sandwich Beam with Electro-Rheological Fluid Core Embedded Within Two FG Nanocomposite Faces Resting on Pasternak Foundation 729 743 EN A.H Ghorbanpour-Arani School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran A Rastgoo School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Journal Article 2020 12 30 This investigation deals with the vibration analysis of the sandwich beam with electro-rheological (ER) core embedded within two functionally graded (FG) carbon nanotubes (CNTs) reinforced composite (FG-CNTRC) layers. In this regard, the governing equations are extracted by the Hamilton principle and the rule of mixture is employed to calculate the effective mechanical and physical properties of the CNTRCs face-sheets. Don and Yalcintas shear modulus models are applied to simulate shear modules of the ER core of the beam. The elastic medium is simulated by Winkler-Pasternak model and then, the governing equations are analytically solved. Finally, a parametric study is carried out in details and the effects of some main designing parameters such as applied voltage, Winkler coefficient, Pasternak coefficient, core to face-sheets thickness ratios and the different pattern of the CNTs along the face-sheets and loss factors are examined on the natural frequency. Based on the obtained results, volume fraction of CNTs in face-sheets have significant influence on the natural frequency in which by increasing the volume fractions the flexural rigidity of the sandwich beam increases as well as natural frequency.