Vibration Analysis of Magneto-electro-elastic Nanobeams on Elastic Foundation using Integrodifferential Equations model

During the past decade researchers have investigated vibrations of piezoelectric and piezomagnetic nanobeams. In addition to displacement fields, usually the electromagnetic fields are also considered one dimensional because the small ratio of height to length of the beam geometry. This makes the implication of electromagnetic boundary conditions on the upper and lower faces of the beam rigorous. In this study free vibration of Timoshenko beam having Magneto-Electro-Elastic properties laying on Elastic foundation has been studied considering one dimensional displacement fields and two dimensional electromagnetic fields. State equations which are a Integro-Differential couple has been discretized using a modified radial point interpolation function. Frequency response and the mode shapes have been queried for Dirichlet and Neumman boundary conditions with two conditions open circuit and closed circuit.. Obtained frequencies have been compared with results of the corresponding fully one dimensional problem.