Stochastic beam equations under random dynamic loads

A numerical solution for a stochastic beam equation exhibiting purely viscous behavior

“…Here $${G}_{1}(x,t)=4\beta {e}^{-0.1t}\sin \pi x$$ and $${G}_{2}(x,t)=4\sigma {e}^{-0.1t}\sin \pi x$$. Here the expressions for the notations involved in the above equation can be found in 25 . We use the values of the notations involved in the above PDE as available in 25 .…”

“…$$c=\frac{C}{\rho A}$$, $$G(x,t;\omega )=\frac{F(x,t;\omega )}{\rho A}$$, $${\alpha }^{2}=\frac{EI}{\rho A}$$, $$S=\frac{\hat{N}}{\rho A}$$, the above equation takes the form $$${\alpha }^{2}\frac{{\partial }^{4}u(x,t)}{\partial {x}^{4}}+\frac{{\partial }^{2}u(x,t)}{\partial {t}^{2}}+c\frac{\partial u(x,t)}{\partial t}-S\frac{{\partial }^{2}u(x,t)}{\partial {x}^{2}}={G}_{1}(x,t)+{G}_{2}(x,t)\dot{B}(t).$$$ One can refer to Galal et al 25 for the expansions of the notations involved in the above equation. Applying the following boundary and initial conditions for the simply supported beam of length $$l$$, $$$u(0,t)=0,$$$ …”

“…The motivation for this paper comes from the work of Galal et al In Galal et al, 25 the author has considered a general fourth‐order stochastic partial differential equation, namely, the beam equation. It is solved analytically in a general closed‐form expression depending on the governing parameters and under stochastically perturbed loads.…”

Stochastic elastic equation driven by multiplicative multi-parameter fractional noise

“…2. Stochastic elastic equation driven by Brownian motion has been studied by many authors, see [5,7,13,25,38]. However, there were few papers consider stochastic elastic equation driven by fractional Brownian motion.…”

Response variability due to randomness in Poisson’s ratio for plane-strain and plane-stress states

“…In the category of perturbation method, new tries had been made to overcome the drawbacks in that method (Elishakoff et al, 1997;Falsone and Impollonia, 2002;Kaminski, 2001). Some research works are dedicated to determine the bounds in response variability (Deodatis and Shinozuka, 1989;Deodatis et al, 2003;Papadopoulos et al, 2005) and to the dynamic and non-linear problems (Adhikari and Manohar, 1999;Anders and Hori, 1999;Galal et al, 2002;Liu et al, 1986;Li et al, 1999). In addition to the material parameters, some researchers put their focus on the evaluation of response variability due to randomness in geometrical parameters such as the thickness of plate structures and section of beams (Altus and Totry, 2003;Noh, 1996, 2000;Lawrence, 1987), due to temporal uncertainties in applied loads (Chiostrini and Facchini, 1999;Galal et al, 2002;To, 1986) and due to random temperature (Liu et al, 2001) in concrete structures.…”