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In this paper, the free vibration and low velocity impact response of a sandwich plate with a Magneto Rheological (MR) flexible core have been studied. The rectangular sandwich plate contains a Magneto Rheological (MR) flexible core and two constrained layers. The MR materials have different properties with respect to different magnetic field intensities. The governing equations of motion have been derived using Hamilton principles. The solution of these equations was obtained using Fourier series and analytical systematic procedure. Using the proposed solution method, the natural frequencies, structural loss factors, impact load and transverse deflection of the plate were calculated. Also, the contact force history was derived using a two degrees of freedom spring mass model analytically. The effects of variations of magnetic field intensity on the natural frequency, loss factors, contact force and deformations of the plate and impactor were investigated. In ordre to calculate the equivalent mass of the plate, the obtained fundamental natural frequency from solution of eigen value problem was used. The obtained equivalent mass of the plate was used in analytical spring mass model. The results show that with systematic variation of magnetic field, the magnitudes of transverse stiffness, structural loss factors and maximum contact force can be changed and controlled, respectively.

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In this article, the physical and Geometrical effective parameters on free vibration and Force impact a three-layer sandwich plate in the middle layer with magneto rheological (core) Under cross-shot with low speed is investigated. The first natural frequency and loss factor of comparable modal for the first four vibrative modes for Core thickness, magnetic fields and different sheet’s geometrical parameters, is founded. The MR material shows variations in the rheological properties when subjected to varying magnetic fields. These materials with fast response time (in milliseconds) Through a detailed with variation in Magnetic field can be controlled. The governing equations of motion were obtained using Hamilton̕s principle. The results were obtained by the systematic analytical solution. Using the two degrees of freedom mass-spring model, the contact force function can be obtained analytically. The obtained natural frequency from eigen value problem, was used for calculating of equivalent mass of the plate in spring mass model. The results show that with systematic variation of magnetic field and with increasing the ratio of core thickness to the layer thickness and also with increasing the ratio of length to the whole of sheet thickness, we can in order, the stiffness, structural loss factor coefficient and maximum contact force can be changed and controlled.

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Free vibration characteristics of rectangular composite plate with constrained layer damping and magneto-rheological fluid (MR) core are presented.. Hamilton principal is used to obtain the equation of motion of the sandwich plate. Based on the Navier method, a closed-form solution is presented for free vibration analysis of MR sandwich plate under simply supported boundary conditions. The governing equation of motion is derived on the base of classical lamination theory for the faceplates. Only shear strain energy density of the core is considered. Using displacement continuity conditions at the interface of the layers and core, shear strain of the core is expressed in terms of displacement components of the base and constraint layers. The complex shear modulus of the MR material in the pre-yield region was described by complex modulus approach as a function of magnetic field intensity. The validity of the developed formulation is demonstrated by comparing the results in terms of natural frequencies with those in the available literature. The effects of magnetic field intensity, plate aspect ratio, thicknesses of the MR core, base layer and constrained layer for three different stacking sequences of composite faceplates on the fundamental frequency and loss factor of the first mode are discussed. The results indicate significant effect of physical and geometrical parameters on the natural frequency and loss factor associated with the first mode.

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One of the common ways to reduce vibration in the structures is to add a thin viscoelastic material layer to the structure. By appropriate using of viscoelastic materials one may increase modal loss factor of the structure and reduce unfavorable structural vibration which is a main cause of fatigue and failure in the structures. In this paper, low velocity impact response of sandwich plate with magnetorheological fluid core is investigated. Hamilton principal is used to obtain the governing equation of motion for sandwich plate. Free vibration problem of the sandwich plate is solved using the Navier solution method. Classical lamination theory is used to analyze the mechanical behavior of the composite laminate in the facesheets. Only shear strain energy of the core is considered and viscoelastic behavior of the MR material was described by complex shear modulus approach as a function of magnetic field intensity. Furthermore, analytical solution for impact force is obtained by a two degree of freedom spring mass model. For three different stacking sequence of face layers, contact for history and variation of maximum impact force and it’s corresponding time by magnetic field intensity is investigated. The results show considerable effect of variation in magnetic field intensity on maximum impact force and it’s corresponding time.