ANALYSIS OF FREE VIBRATIONS OF A CONTINUOUS BEAM CONSIDERING THE RANDOM STIFFNESS OF THE SUPPORTS AND THE TWO-DIMENSIONAL RANDOM MATERIAL PROPERTIES USING MONTE CARLO SIMULATION - N. D. Diem; T. D. Hien; D. N. Tien (Journal of Mechanics of Continua and Mathematical Sciences, 2025)
This paper presents a Monte Carlo simulation for analyzing the random vibration of continuous beams with random spring stiffness and 2D random material properties. The spectral modeling approach is utilized to model the 2D stochastic field of material properties and generate realizations. The stiffness of elastic springs is assumed to follow a normal distribution. By applying the standard finite element method to beam structures with random input parameters, including realizations of a 2D random field and joint stiffness, the statistical characteristics of the natural frequencies can be quantified through analysis of the resulting frequency data. Results demonstrate the influence of 2D random material properties and the variability of spring stiffness on the statistical distribution of natural frequencies. The coefficient of variation (COV) of natural frequencies exhibits an upward trend as the standard deviation of either the 2D stochastic field representing material properties or the joint stiffness increases. Notably, the stochastic variations in the 2D random field exert a significantly greater influence than those in spring stiffness. Additionally, at small correlation lengths, the COV increases significantly with increasing correlation length Conversely, at large correlation lengths, the COV remains on an increasing trend, yet at a much more gradual rate.