Nonlinear vibration analyses of a sandwich beam made of a magnetorheological fluid core and functionally graded material face layers, based on differential quadratic method

Background Magneto-rheological fluids (MRF) are considered smart materials with the principal characteristic being enhanced viscosity in the presence of magnetic fields. Sandwich MRF beams are able to minimize the effect of external vibrations by changing the structural hardness and damping properties in the presence of magnetic fields. Despite its importance in mechanical engineering, the behavior of such sandwich beams has not been investigated in response to free nonlinear vibration. Methods We investigated the behavior of a sandwich beam made of an MRF core and two functionally graded face layers exposed to free nonlinear vibration. Specifically, we examined the magnetic field intensity, power law components, the thickness of the fluid core and boundary layers, and the beam’s length versus the natural frequency and damping coefficient. Our analysis of the natural frequency and loss factor considered the Hamilton's principle, and Euler-Bernoulli (E-B) and Timoshenko (TS) beam theories, based on a generalized differential quadratic method. Finally, the findings were validated by comparison to reputable research publications. Results The structure’s natural frequency rose with increases in the beam’s maximal deflection, power law components, and the thickness of MRF core. Conversely, increases in the magnetic field intensity and the beam length reduced the beam behavior, while the effect of magnetic field intensity on the natural frequency and Loss factor was insignificant. Conclusions Increases in the maximal rise of the beam and natural frequency were greater based on the TS beam theory than on the E-B theory. Also, the maximal and minimal beam’s natural frequencies were observed based on simple and clamped support models of TS and E-B beam theories, respectively. The opposite was true with respect to the beam’s loss factor.