Thermomechanical Response of Smart Magneto-Electro-Elastic FGM Nanosensor Beams with Intended Porosity

This study investigates the behavior of free vibrations in a variety of porous functionally graded nanobeams composed of ferroelectric barium-titanate (BaTiO₃) and magnetostrictive cobalt-ferrite (CoFe₂O₄). There are four different models of porous nanobeams: the uniform porosity model (UPM), the symmetric porosity model (SPM), the porosity concentrated in the bottom region model (BPM), and the porosity concentrated in the top region model (TPM). The nanobeam constitutive equation calculates strains based on various factors, including classical mechanical stress, thermal expansion, magnetostrictive and electroelastic properties, and nonlocal elasticity. The study investigated the effects of various factors on the free vibration of nanobeams, including thermal stress, thermo-magneto-electroelastic coupling, electric and magnetic field potential, nonlocal features, porosity models, and changes in porosity volume. The temperature-dependent mechanical properties of BaTiO₃ and CoFe₂O₄ have been recently explored in the literature for the first time. The dynamics of nanosensor beams are greatly influenced by temperature-dependent characteristics. As the ratios of CoFe₂O₄ and BaTiO₃ in the nanobeam decrease, the dimensionless frequencies decrease and increase, respectively, based on the material grading index. The dimensionless frequencies were influenced by the nonlocal parameter, external electric potential, and temperature, causing them to rise. On the other hand, the slenderness ratio and external magnetic potential caused the frequencies to drop. The porosity volume ratio has different effects on frequencies depending on the porosity model.