A two-dimensional analysis based on the linear theory of elasticity in conjunction with the classical structural damping model involving frequency-dependent complex material moduli is formulated for investigating the sound insulation characteristics of an arbitrarily thick smart sandwich plate with a tunable magnetorheological elastomeric (MRE) core. The effect of applied magnetic field strength (0-0.8T) on controlling the transmission loss of the adaptive panel is determined for two different kinds of magneto-sensitive rubber core materials constrained by either soft or stiff skin layers in the audible frequency range of 100-1000Hz for all angles of incidence. Also, the sound transmission loss for a perfectly diffuse sound field with a Gaussian directional distribution of energy is calculated. The numerical results reveal that, while application of the magnetic field has no appreciable effect on sound transmission in the low frequency range (f < 300Hz), it can lead to notable improvements (up to 15dB) at intermediate to high frequencies, depending on the angle of incidence, the skin/core type and core thickness. Moreover, it is demonstrated that, for moderate and high applied magnetic field strengths, there is an optimum intermediate value of core thickness parameter associated with the silicon-rubber-based MRE material which leads to enhanced acoustic insulation performance, especially at intermediate and high incident wave frequencies. Limiting cases are considered and good agreement with the solutions available in the literature is obtained.
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