Dynamic characteristics of vertically irregular structures with random fields of different probability distributions based on stochastic homotopy method

Considering the uncertainty of elastic modulus in different materials as well as the strong nonlinearity between the structural frequency and elastic modulus, it is a great challenge for computing the dynamic characteristics of vertically irregular structures. In this research, a new stochastic homotopy approach is presented to compute the basic dynamic characteristics of the vertically irregular structures, where the elastic modulus of different materials are assumed as the random fields with different probability distributions. To obtain the dynamic characteristics of the vertically irregular structures, a stochastic eigenvalue equation is established firstly. Then the stochastic eigenvalue and eigenvector are represented by the homotopy series, and the stochastic residual error in relation to the stochastic eigenvalue equation is minimized to obtain the coefficients of the homotopy series. Afterwards, the basic dynamic characteristics, including stochastic natural frequencies and modal shapes, of the vertically irregular structures are obtained. In comparison to the sampling-based stochastic surrogate model methods like the Kriging and non-intrusive arbitrary polynomial chaos methods, the presented approach can efficiently yield more stable statistical moments of the natural frequencies. Meanwhile the proposed method can generate the statistical moments of the modal shapes, which is difficult to achieve with the stochastic surrogate model methods. Finally, the effectiveness of the suggested method is testified through two examples of a reinforced concrete-steel column and a realistic reinforced concrete-steel frame structure.