On the Internal Resonances of Size-Dependent Clamped–Hinged Microbeams: Continuum Modeling and Numerical Simulations

The nonlinear forced vibrations of size-dependent clamped–hinged microbeams to fundamental excitations of respectively the first mode and second mode in the presence of three-to-one internal resonance are investigated both analytically and numerically for the first time. Equation of motion incorporating large deflection, along with the symmetric part of couple stress is derived by virtue of Hamilton’s principle. Utilizing Galerkin discretization...