On the dynamics of nanoscale structures upon a novel mixture model of elasticity: buckling analysis, vibration analysis, and wave propagation

Abstract

In this study, a novel mixture model of elasticity, that can cover all size-dependent theories together with simultaneously taking of soft- ening and stiffening impacts, is regarded as mathematical modeling and dynamic analysis of Timoshenko nanobeams. Since the mix- ture model is the combination of Eringen’s two-phase theory with two-phase stress-driven theory, therefore, there are four parameters containing two various types of nonlocal parameters and two addi- tional local phase fraction factors. In this work, after introducing the mixture model together with essential assumptions and relations, the integral form of relations with an equivalent differential form of ones is illustrated. Next, essential conditions are considered and satisfied to match the integral relations with differential relations without any conflict of restrictions are obtained. Finally, through some examples, the essential relations together with compatibility boundary conditions are derived to analyze the buckling, vibration, and wave propagation of Timoshenko nanobeams. Utilizing an effi- cient numerical solution, the results are achieved, and the validity as well as integrity of the constitutive differential relations are examined through some validation studies. The output results disclose that the previous results in the field of contemporary continuum theories are the particular state of dynamic response of the nanobeams.