Analytic Method Of Random Wind-Induced Extremal Response To General Linear Viscoelastic Energy-Dissipation Structure

In order to explore random response of linear viscoelastic energy-dissipation structure subjected to wind load, theory of random vibration are adopted and random wind-induced extremal response of viscoelastic energy dissipation structure are studied based on Davenport spectrum and Baskin spectrum, by using the most general integral constitutive model of linear viscoelastic damper.First of all, as a primer, random wind-induced response of SDOF (single degree of freedom) structure with general Maxwell damper is analyzed. Then, analytical expression of structural response is obtained directly, by using transfer function method. The variance of structural response based on Daven-port spectrum is decomposed precisely into linear combination of displacement response variance and velocity response variance of the first standard order oscillator and second standard order oscillator. Analytic solution of wind-induced response of the first standard order oscillator based on Davenport spectrum is deduced in this paper. By applying present analytic solution of wind-induced response of the second standard order oscillator based on Daven-port spectrum and that of the first standard order oscillator deduced in this paper, the extremal response of structure is obtained.Secondly, the displacement vector is expanded by the first mode of the structure, and the analytic expression of the structural response is obtained by the transfer function method. On the one hand, adopting the random vibration theory, analytic solution of the variance of structural response based on Baskin spectrum is aquired directly without decompose the variance. On the other hand, the variance of structural response and structural extremal response are obtained, after decomposing the variance of structural response into that of the first and second order standard oscillator, based on Davenport spectrum.Thirdly, the analytic solution of wind-induced response of general linear viscoelastic dissipation structure based on Davenport spectrum, after adopting transfer matrix method to get the exact analytic expression of structural response under arbitrary load vector. The analytic solution acquired is an exact solution of non-orthogonal mode superposition of structure and can be regarded as existing classical superposed exact solution of orthogonal vibration modes of structure with proportional viscous dampers and viscoelastic dampers, in the promotion of frequency stationary dissipation structure with general linear viscoelastic dampers, and thus can exactly discover the vibration characteristics of dissipation structure, that is:the response analysis of dissipation structure with general linear viscoelastic dampers can be attributed to the analysis of structural free vibration characteristics (including structural eigenvalue, eigenvectors); Although the vibration modes of energy-dissipation structure are not orthogonal, the dynamic equations cannot be decoupled by using traditional modal analysis method, the response of energy-dissipation structure can be decomposed exactly into the combination of each structural vibration mode.Finally, as to the SDOF structure and structure whose displacement vector is expanded by the first mode, equivalent wind vibration force of structure under the action of fluctuating wind is calculated, by applying the IWL method adopted by Load Standard of China, according to the extremal displacement response of structure subjected to wind load, which is acquired in this paper. Then take the interaction of mean wind and fluctuating wind into consideration, equivalent static wind load is obtained. When it comes to structure that must consider several vibration modes, as the vibration mode of the general linear viscoelastic energy dissipation structure is not orthogonal in general, the tradi-tional method of calculating the equivalent wind load by using the linear combi-nation of several vibration modes is invalid. At this point, the extreme value of interlaminar shear is calculated, according to the relationship between inter-laminar shear and interlaminar displacement, which can supply references for engineering design.