Parametric resonance of graphene platelet-reinforced metal foam beams under external excitation and boundary constraints

This paper investigates the parametric resonance of graphene-platelet reinforced metal foam (GPLRMF) beams under three typical boundary conditions. The Halpin-Tsai model and rule of mixture are employed to characterize the GPLRMF material properties, while the governing equations are established based on Euler-Bernoulli beam theory. Numerical results demonstrate that increased external excitation leads to significant amplification of vibration amplitudes. The modified variable amplitude method is adopted to ensure accurate prediction of system response across the entire frequency range, with validation against existing literature. Detailed parametric studies examine the effects of: (1) foam distributions (including Foam-I pattern), (2) porosity coefficients, (3) GPL dispersion patterns (Type-A to Type-X), and (4) GPL weight fractions. Furthermore, the influences of boundary constraints, thermal environments, external stimuli, and damping ratios on parametric resonance are systematically analyzed. Key findings indicate that Foam-I distribution with Type-A GPL arrangement exhibits negligible dynamic response, suggesting superior anti-vibration capacity. Both clamped boundaries and reduced temperature are shown to effectively shift resonance positions while enhancing beam stiffness.