The theoretical model of a simply supported magnetorheological material-based adaptive beam under an axial harmonic load is modified based on the DiTaranto sandwich beam theory for a symmetric three-layer beam. A differential equation for extensional motion of a freely vibrating beam is derived. This study considers an axially forced vibration of asymmetric magnetorheological materialbased beam and derives a sixth-order equation for transverse motion. The derived governing equation of motion is then simplified using Galerkin's method to yield the Mathieu equation. The formulae for buckling load, natural frequency, and loss factor of a simply supported adaptive beam are developed. Numerical results demonstrated from the formulae are highly consistent with the published results. The incremental harmonic balance (IHB) method is utilized to study the regions of dynamic instability, which are demonstrated graphically. The dynamic responses of the adaptive beam are assessed via the fourth-order Runge-Kutta method. The effects of magnetic field, core thickness ratio and beam length on the buckling load, natural frequency, loss factor, and dynamic instability are also presented. The influence of the static load parameter factor on natural frequency, loss factor, and dynamic instability is considered.KEY WORDS: magnetorheological, adaptive beam, dynamic instability, incremental harmonic balance method.

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This work analyses the overall stress/strain characteristic of flexible encapsulations with organic light-emitting diode (OLED) devices. A robust methodology composed of a mechanical model of multi-thin film under bending loads and related stress simulations based on nonlinear finite element analysis (FEA) is proposed, and validated to be more reliable compared with related experimental data. With various geometrical combinations of cover plate, stacked thin films and plastic substrate, the position of the neutral axis (NA) plate, which is regarded as a key design parameter to minimize stress impact for the concerned OLED devices, is acquired using the present methodology. The results point out that both the thickness and mechanical properties of the cover plate help in determining the NA location. In addition, several concave and convex radii are applied to examine the reliable mechanical tolerance and to provide an insight into the estimated reliability of foldable OLED encapsulations.