TY - JOUR
T1 - Dynamic characteristics of vertically irregular structures with random fields of different probability distributions based on stochastic homotopy method
AU - Zhang, Heng
AU - Liu, Yuhao
AU - Huang, Bin
AU - Wu, Xianfeng
AU - Wu, Zhifeng
AU - Faber, Michael Havbro
N1 - Publisher Copyright:
© 2024
PY - 2024/11/1
Y1 - 2024/11/1
N2 - 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.
AB - 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.
KW - Different probability distributions
KW - Modal shape
KW - Natural frequency
KW - Nonlinear functional relationship
KW - Vertically irregular structures
UR - http://www.scopus.com/inward/record.url?scp=85196404199&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2024.111638
DO - 10.1016/j.ymssp.2024.111638
M3 - Journal article
AN - SCOPUS:85196404199
SN - 0888-3270
VL - 220
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
M1 - 111638
ER -