Discrete singular convolution–polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams

This article enhances the discrete singular convolution method for free vibration analysis of non-uniform thin beams with variability in their geometrical and material properties such as thickness, specific volume (inverse density) Young’s modulus. The solves differential equation motion a structure high accuracy using small number discretisation points. uses polynomial chaos expansion to express these variabilities simulating uncertainty closed form. Non-uniformity is locally provided by changing cross section modulus beam along its length. In this context, firstly natural frequencies deterministic uniform are predicted via convolution. These results compared finite element calculations analytical solutions (if available) purpose verification. Next, because modelled global manner predict probability distribution functions frequencies. Monte Carlo simulations then performed validation purpose. Results show that proposed algorithm very accurate also efficient, regarding computation cost, handling having variabilities. Therefore, it promises can be reliably applied more complex structures uncertain parameters.