On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model

We study a time-dependent thermoelastic coupling within free vibrations of piezomagnetic (PM) microbeams considering the flexomagnetic (FM) phenomenon. The flexomagneticity relates to a magnetic field with a gradient of strains. Here, we use the generalized thermoelasticity theory of Lord–Shulman to analyze the interaction between elastic deformation and thermal conductivity. The uniform magnetic field is permeated in line with the transverse axis. Using the strain gradient approach, the beam yields microstructural properties. The analytical solving process has been gotten via applying sine Fourier technique on displacements. Graphical illustrations are assigned to shape numerical examples concerning variations in essential physical quantities. It was observed that the flexomagnetic effect could be extraordinary if the thermal conductivity of the material is higher or the thermal relaxation time of the heat source is lesser. This theoretical study will provide the way of starting studies on magneto-thermoelastic small-scale piezo-flexomagnetic structures based on the heat conduction models.