Magnetostrictive materials exhibit unique properties that make them highly suitable for applications involving sensors, actuators, and energy harvesting devices. These materials can change their shape or dimensions in response to an applied magnetic field, making them attractive for use in composite structures, where the mechanical and magnetic responses can be precisely controlled. One area of interest in magnetostrictive materials is their application in cantilever resonators, which are widely used in various engineering fields, including vibration sensing, force measurement, and micro-electromechanical systems (MEMS). The vibration characteristics of magnetostrictive composite cantilever resonators have been extensively studied; however, many existing models fail to account for the nonlocal effects, which can significantly influence the resonator's behavior, especially at the micro- and nano-scales. In the traditional theory of elasticity, the material is assumed to have a local response to external forces, meaning that the stress at any point within the material is influenced only by the strain at that same point.
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