A Comparative Study of Differential Quadrature Methods for METE Nanobeam Vibrations

This study investigates the use of three different quadrature schemes, as well as an iterative quadrature methodology, to analyze vibrations in magneto-electro-thermo-elastic nanobeams. Individual MATLAB programs for each method are developed with the goal of minimizing errors in comparison to accurate findings, as well as determining the execution time for each strategy. This study shows that the Discrete Singular-Convolution Differential Quadrature Method with a Regularized Shannon Kernel (DSCDQM-RSK) and specified parameters produces the best accurate and efficient results for this particular situation. A subsequent parametric study is carried out to determine the effect of various factors on the vibrated nanobeam, including boundary conditions, material types, linear and nonlinear elastic foundation properties, nonlocal parameters, length-to-thickness ratios, external electric and magnetic potentials, axial forces, and temperature variations. Important discoveries include insights into the relationship between fundamental frequency, linear elastic foundation features, axial loads, external magnetic fields, temperature fluctuations, and material types. According to this study, these findings could be critical in the development of sophisticated nanostructures made from magneto-electro-thermo-elastic materials for use in a variety of electromechanical applications. This would entail utilizing nanobeams’ unique properties in applications such as sensors, resonators, and transducers for nanoelectronics and biology.