The present invention discloses a
fast algorithm for wind-induced response of long-span roof structures considering the quasi-
static response of high-order
modes, comprising the following steps: Step S11, establishing a finite
element model of the long-span roof structure and determining the
modal damping ratio of the long-span roof structure according to the design conditions to obtain the structural dynamic characteristics of the long-span roof structure; Step S12, determining the random wind load acting on the long-span roof structure through a wind tunnel test and calculating the
Fourier transform function of the wind load corresponding to the truncation function of the random wind load; Step S13, calculating by using the
modal acceleration method according to the structural dynamic characteristics and the
Fourier transform function of the wind load to obtain the
Fourier transform function of the structural displacement response; Step S14, performing power
spectral density estimation by using the
periodogram method according to the Fourier transform function of the structural displacement response to obtain the power
spectral density matrix of the structural displacement response, and integrating the power
spectral density matrix of the structural displacement response to obtain the
root mean square of the displacement response of the long-span roof structure. In the present invention, the quasi-
static response of high-order
modes is taken into account, which has better convergence than the traditional method, and under the condition of the same accuracy, the calculation time and memory occupation of the present invention are relatively small.