Abstract
In this work the governing temporal equations of motions with complex coefficients have been derived for a three-layered unsymmetric sandwich beam with nonconductive skins and magnetorheological elastomer (MRE) embedded soft-viscoelastic core subjected to periodic axial loads using higher order sandwich beam theory, extended Hamilton's principle, and generalized Galerkin's method. The parametric instability regions for principal parametric and combination parametric resonances for first three modes have been determined for various end conditions with different shear modulus, core loss factors, number of MRE patches and different skin thickness. This work will find application in the design and application of sandwich structures for active and passive vibration control using soft core and MRE patches.
Highlights
For light weight and suppression of vibration sandwich beams are very popular in aeronautical, space, automobile, structural and under-water applications
The stiffness of the system can be actively changed by applying suitable magnetic field as the sandwich beams with magnetorheological elastomer (MRE) core possess field-controllable flexural rigidities due to the field-dependent shear modulus of the MRE core
The parametric instability region of the sandwich beams with MRE embedded viscoelastic core and alulight [25] skins have been plotted for various boundary conditions viz., supported, clamped-guided and clamped-free boundary conditions
Summary
For light weight and suppression of vibration sandwich beams are very popular in aeronautical, space, automobile, structural and under-water applications. For example Ray and Kar [20,21,22] considered parametrically excited sandwich beams and studied the dynamic instability of various types of sandwich structures subjected to periodic axial loads. In such cases, the core layer was assumed to be rigid and classical theory was used to develop the governing equation of motion. For soft cored sandwich beams, considering transverse flexibility in the core layer, Dwivedy et al [23] used higher order theory to obtain the governing equation of motions of symmetric sandwich beams and determined the parametric instability regions of these systems for various boundary conditions. Area of cross section of top bottom and core layer respectively Width of the beam Magnetic field strength Thickness of core layer Thickness of top and bottom skin layers respectively Young’s modulus of elasticity for top, bottom and core layer respectively Shear modulus of the core material Shear modulus of the MRE material Moment of Inertia of top and bottom skin with respect to their own neutral axis Length of the beam Mass per unit length of the top, bottom and core layer respectively Mass of MRE layer per unit length Density of the core layer Longitudinal displacement of top and bottom skins (along X axis) Transverse displacement of the top and bottom skin (along Z axis) Derivative with respect to time Derivative with respect to x Nondimensional parameter corresponding to ( )
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