Size-dependent and microinertia effects on statics and dynamics based on the modified couple stress theory with arbitrary boundary conditions

In this work, we discuss size-dependent and microinertia effects on the static and dynamic performances of a microscale model based on the microinertia-based modified couple stress theory, a non-classical continuum theory capable of capturing the behavior of size dependence and frequency dispersion characteristics. In the framework of the variational statement, a microscale structure model is developed and the governing equations of equilibrium as well as all boundary conditions for statics and dynamics are reformulated. The developed theory is imposed to tackle microstructure-dependent Timoshenko beam model in two distinct scale parameters: the material length scale parameter is utilized to determine the size dependence and the microinertia length scale parameter is employed to describe the higher-order microrotation relation. The generally valid closed-form analytic expressions are obtained and suitable for various formats of boundaries and mechanical loads. As case studies, the predicted trends agree with those observed within the framework of the modified couple stress theory. Results indicate that the material microlength scale parameter strengthens the static deformations, while the microinertia length scale parameter weakens the dynamic frequencies. In addition, boundary conditions are also an important aspect in statics and dynamics as well as the mechanical response predicted by non-classical continuum theories.