article · Smart Materials and Structures
Mathematical equations of motion describe the behaviour of a sandwich nanoplate consisting of a nano core and two piezo-magnetic face-sheets. Formulated using sinusoidal shear deformation plate theory and Hamilton's principle, the model accounts for three-dimensional electric and magnetic potentials alongside nonlocal piezo-magneto-elastic relations in a thermal environment. The system produces seven governing equations of motion incorporating mid-surface deformation, shear components, and electromagnetic potentials. Analysis of natural frequencies and parameter variations reveals that increasing the applied electric potential reduces the dimensionless deflection while raising peak electric and magnetic potentials. Conversely, applying higher magnetic potential increases structural deflection and substantially reduces these electromagnetic potentials. Consequently, structural deformation and internal stress across the nanostructure can be tuned directly through adjustments to applied electric and magnetic fields.
Understanding how nanoscale composite materials react to combined thermal, electrical, and magnetic environments is critical for developing responsive smart materials. By establishing exact mathematical relationships between applied fields and structural movement, this work demonstrates how mechanical deformation and stress can be actively controlled in tiny sandwich structures, providing foundational principles for designing micro and nanoscale devices.
This work represents early-stage theoretical and numerical research. While it establishes that electric and magnetic potentials can actively regulate stress and deflection in sandwich nanoplates, the abstract does not describe physical prototyping, specific real-world applications, target end-users, or commercial implementation pathways. Any practical utilisation in functional smart devices or sensors remains at a foundational stage requiring physical validation.
AI-generated from the published abstract. Always read the original work before citing.
In this paper, based on the sinusoidal shear deformation plate theory, equations of motion for a sandwich nanoplate containing a nano core and two integrated piezo-magnetic face-sheets are derived. The piezo-magnetic face-sheets are subjected to three dimensional electric and magnetic potentials. Nonlocal piezo-magneto-elastic relations are derived in a thermal environment. Hamilton's principle is used to derive seven equations of motion in terms of three deformation components of mid-surface, two shear components and electric and magnetic potentials. Natural frequencies of the sandwich nanoplate are derived in terms of nonlocal parameter. After finding solutions to the governing equations of motion, the effect of important parameters of the nanoplate are investigated on the mechanical, electrical and magnetic components of the nanoplate. Based on the present study, with increasing applied electric potential, dimensionless deflection is decreased and maximum electric and magnetic potentials are increased. Furthermore, with increasing applied magnetic potential, deflection is increased and maximum electric and magnetic potentials are decreased significantly. The numerical results of this problem indicate that one can control deformation or stress in the nano structure by changing the applied electric and magnetic potentials.
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DOI: 10.1088/0964-1726/25/11/115040
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