Stochastic vibrations of the Euler–Bernoulli beam based on various versions of the gradient nonlocal elasticity theory

We study and compare two models of vibration of the Euler–Bernoulli beam under stochastic excitation based on two different gradient versions of the non-local theory of elasticity, namely: the Eringen’s model, in which the strain is a function of gradient stresses, and a nonlocal model in which the stress is a function of gradient strains. We give the covariance functions for the transverse displacement of the Euler–Bernoulli beam based on the...