A Study Of Stochastic Finite Element For Linear Vibration

The vibration of the equipment or structures is a widespread phenomenon. Under most conditions, the vibration is harmful. Finite element method is not only a common method of calculating static problem, but also a powerful tool to calculate vibration of structure. In order to enhance computational accuracy, the influence of the random factors must be considered and it is called stochastic finite element.Due to spatial variability of material property, Young's modulus is assumed to be a stochastic process. This paper proposes a new method of calculating stochastic field, which includes the information of nodes and the midpoint, not only is high accuracy, butalso it is easy to program. It is an improvement of the midpoint method of stochastic field.Material properties, geometry parameters and applied loads are assumed to be stochastic; the vibration equation of structure is transformed to static problem using Newmark method. The Taylor expansion stochastic finite element method (TSFEM) is extended for the structure vibration analysis. In order to develop computational efficiency and save storage, the Conjugate Gradient method (CG) is employed, which is a valid method that solves the large system of linear equations and belongs to method of iteration that converges quickly and the accuracy is high. An example that analyzes vibration of ten storey space frame made up the concrete is given respectively.Material properties, geometry parameters and applied loads are assumed to be stochastic, mechanical vibration is studied by TSFEM. A method of dynamic sensitivity analysis for stochastic finite element is presented. Simulating random variables, a lot of samples are generated. The CG (PCG) is adopted to study mechanical vibration. Examples that analyze vibration of cantilever and four-bar linkage are given respectively.Using DSFEM, TSFEM and CG (PCG), examples are given respectively and calculated results are compared to validate the proposed methods.