Dynamic stability and instability of a double-beam system subjected to random forces

On the basis of the Bernoulli–Euler beam theory, the stability and instability of a double-beam system subjected to compressive axial loading is investigated. It is assumed that the two beams of the system are simply supported and continuously joined by a Winkler elastic layer. Each pair of axial forces consists of a constant part and a time-dependent stochastic function. By using the direct Lyapunov method, bounds of the almost sure stability and instability and uniform stochastic stability of a double-beam system as a function of viscous damping coefficient, bending stiffness, stiffness modulus of the Winkler layer, variances of the stochastic forces, and intensity of the deterministic components of axial loading are obtained. When the almost sure stability and instability are investigated, numerical calculations are performed for the Gaussian process with a zero mean as well as a harmonic process with random phase. When axial forces are white noise processes, conditions for uniform stochastic stability are determined.

► The stability and instability of a double-beam system is studied using the direct Lyapunov method.
► Regions of uncertainty are obtained as a result of the used method.
► Stability regions are larger for the Gaussian than the harmonic process.
► Boundaries of stability, uncertainty and instability regions when the system is loaded at one or both beams are established.
► Regions of uniform stochastic stability have a similar form as regions of almost sure stability.