Stochastic finite element analysis of the free vibration of non-uniform beams with uncertain material

Abstract

This paper deal with the stochastic finite element method for investigating the eigenvalues of free vibration of non-uniform beams due to a random field of elastic modulus. The formulation of stochastic analysis of the non-uniform beam is established using perturbation method in conjunction with finite element method. Monte Carlo simulation (MCS) used for validation with stochastic finite element approach. The spectral representation was used to generate a random field to employ the Monte Carlo simulation. The performance of results of the uncertain eigenvalue problem of non-uniform beams with random field of elastic modulus by comparing the first-order perturbation technique with the same moments evaluated from the Monte Carlo simulation. The numerical results show that the response of coefficient of variation of eigenvalue increases when the ratio of correlation distance of random field increases.

Keywords

• non-uniform beam
• free vibration
• stochastic fem
• spectral representation, random field