Uncertain material properties on wave dispersion behaviors of smart magneto-electro-elastic nanobeams

Uncertainties in material properties caused by the small-scale length effect are serious for nanostructures, which may affect their mechanical responses accordingly. This paper devotes to studying the effect of uncertain material properties on wave propagation characteristics of magneto-electro-elastic nanobeams subjected to external electric and magnetic fields. Based on the nonlocal Euler-Bernoulli beam theory, the governing differential equations of motion are derived by using the Hamilton's principle. Considering limited experimental data, uncertain-but-bounded parameters are employed to quantify the uncertain material properties including elastic constants, mass density, piezoelectric, piezomagnetic, dielectric, magnetoelectric and magnetic constants. A high precision interval analysis method is presented to evaluate the upper and lower bounds of the wave dispersion curves. Meanwhile, the presented method is validated with Monte-Carlo simulation, and its validation is also demonstrated by comparing with probabilistic method. Numerical results suggest the effect of uncertainties in material properties is significant in understanding the wave dispersion behaviors of magneto-electro-elastic nanobeams. The presented method can serve as an effective tool to quantify the dynamic response of nanosensors and nanoactuators with uncertain material properties.