A unified higher-order shear deformable model for direct piezo-flexomagnetic nanobeams with strain gradient effect

A unified higher-order shear deformable model has been developed to analyze the direct transduction effect in flexomagnetic nanobeams. Our model incorporates the second-order strain gradient parameter for capturing the size-effect and a function that facilitates switching among the established shear theories, thus avoiding multiple derivations for comparative analysis. The governing equations of motion are derived using Hamilton’s principle, while Navier’s solution technique is used for bending, buckling, and free vibration analyses. The model is satisfactorily verified by comparing the present results with the established ones. The strain gradient parameter results in a stiffness enhancement for all the beam models considered in this study. Interestingly, the magnetic potential differences obtained for Euler-Bernoulli and Timoshenko beams are found to be similar in this framework, despite their considerable differences in mechanical behavior. Consequently, the use of higher-order shear deformable beam models is recommended for studying the direct transduction of low-aspect-ratio flexomagnetic nanostructures.