This paper presents the dynamic response of cantilever beam on
fractional-order nonlinear viscoelastic foundation subjected to Gaussian
white noise. The control equations of the cantilever beam on
viscoelastic foundation are established using Hamilton's principle. The
problem is solved using the shifted Chebyshev polynomial algorithm, and
the control equations are transformed into a system of nonlinear
algebraic equations. Numerical examples analyse the correction error and
the second norm error, confirming the effectiveness and accuracy of the
algorithm in solving such problems. Furthermore, the algorithm's
robustness was verified by comparing the responses of Gaussian white
noise and non-Gaussian white noise cantilever beam on the viscoelastic
foundation. The study examined the impact of various loads and
parameters on the cantilever beam, as well as the effect of different
harmonic loads on its stress. The research results are in line with the
existing literature. These studies offer valuable guidance for practical
engineering and enhance comprehension of the dynamic response of
cantilevers on foundation in complex environments.