Flutter analysis of laminated fiber-reinforced magnetorheological elastomer sandwich plate resting on an elastic foundation using an improved first-order shear deformation theory

Magnetorheological elastomers (MREs) are polymers with viscoelastic properties that can be adjusted by manipulating the magnetic field. When MREs are combined with reinforcing fabrics, a new category of materials known as MRE composites (MRECs) can be created, which not only possess the characteristics of MREs but also enhance their rigidity. This study focuses on investigating the supersonic aeroelastic instability of a rectangular sandwich plate with a laminated MREC core layer and functionally graded materials with porosities as face layers. Additionally, the sandwich plate is supported by an elastic foundation and subjected to supersonic airflow. This investigation presents an improved first-order shear deformation theory, postulating a parabolic distribution of shear stresses. Consequently, the transverse shear stresses are rendered as zero at the surface of every individual layer; thus, the requirement for shear correction in this theory is eliminated. In addition, 8-node elements are implemented to circumvent the necessity for distinct handling of shear-locking. The aeroelastic pressure acting on the structure is considered using first-order piston theory. Micromechanical approaches, such as Halpin-Tsai and rule of mixture approaches, are employed to determine the effective mechanical properties of the core and face layers. The dynamic equations of the structure are derived using Hamilton's principle and the finite element method. The study also examines the impact of different magnetic fields, fiber volume fraction, elastic foundation factors, layering angles, geometry, and boundary conditions on flutter frequency.