Spectral stochastic analysis of structures with uncertain parameters

We present a probabilistic analysis of a structure with uncertain parameters subject to arbitrary stochastic excitations in a frequency domain. The problem of stochastic dynamic analysis of a linear system in a frequency domain is formulated by taking into consideration the uncertainty of structural parameters. The solution is based on the idea of a random frequency response vector for stationary input excitation and a transient random frequency response vector for nonstationary one which are used in the context of spectral analysis in order to determine the influence of structural uncertainty on the random response of structure. The numerical spectral analysis of the building structure under wind and earthquake excitation is provided to demonstrate the described algorithms in the context of computer implementation.     

Heating of a body in a bounded volume of well mixed fluid

The problem of the nonstationary heating of an arbitrary body of finite dimensions in a bounded fluid volume is solved for an arbitrary volume heat source and an arbitrary initial-temperature distribution.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 19, No. 3, pp. 401–405, September, 1970.     

Quality indices of nonparametric sequential detector-meters of signals in a noisy background and a stream of errors with arbitrary distribution laws

Methodology and results of calculating quality characteristics of rank and sign sequential signal detectors under noisy conditions and a stream of nonstationary interference with arbitrary distribution laws are presented. A comparative analysis of noise-stability of nonparametric sequential detectors under these conditions is provided. An approximation to an equivalent increment of the threshold signal/noise ratio is obtained under the action of nonstationary interferences with arbitrary distribution laws. Moscow. Translated from Izmeritel'naya Tekhnika, No. 8, pp. 19–23, August, 1997.     

Two dimension-reduction probabilistic models for simulating nonstationary turbulent wind fields

The reasonable modeling of a nonstationary stochastic turbulent wind field is an important basis and premise for the analysis of the wind-induced response and reliability of engineering structures. In the present study, two dimension-reduction probabilistic models are established for simulating the multi-dimensional and multi-variable nonstationary turbulent wind fields based on the double proper orthogonal decomposition (DPOD) and the double spectral representation method (DSRM). Among them, the DPOD, originally used to simulate a stationary turbulent wind field, is extended to a nonstationary one, and the DSRM is a newly proposed method for a nonstationary turbulent wind field with a large number of simulation points. In essence, the DPOD is a discrete method with explicit physical significance and flexible spatial location of simulation points, while the DSRM is a continuous method, of which the simulation efficiency is theoretically independent of the number of simulation points. Furthermore, by introducing the dimension-reduction methods based on random function and POD-FFT (Fast Fourier transform) technique into the DPOD and the DSRM, the nonstationary stochastic turbulent wind field can be effectively described with merely three elementary random variables. Numerical examples of the nonstationary stochastic turbulent wind fields acting on a long-span bridge and a communication tower fully verify the effectiveness and superiority of the proposed methods.     

Calculation of the nonstationary thermoelastic stresses in a plane wall

An approximate method is proposed for calculating the nonstationary thermoelastic stresses in a plane wall for an arbitrary law of variation of fluid temperature with time.     

高斯白噪声激励的阻尼耦合的两个杜芬-范德波振子的近似瞬态响应

研究受高斯白噪声作用下的非线性阻尼耦合的两个杜芬-范德波振子响应的近似瞬态概率密度。应用基于广义谐和函数的随机平均法,并将幅值的瞬态概率密度的近似解表示为拉盖尔正交基函数的级数和,其中系数是随时间变化的,用Galerkin法可得到幅值的近似瞬态概率密度,从而得到状态变量响应的近似瞬态概率密度,数值模拟结果表明该方法有很好的适用性及精度。     

On diffusion in the critical domain

An approach permitting the construction of approximate solutions of problems for the non-linear nonstationary critical diffusion equation in a space domain of arbitrary geometry is proposed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 1, pp. 121–128, July, 1973.     

Heating of a half-space by a heat source in the shape of a rectangular frame

A solution is presented for the inverse nonstationary spatial coefficient problem of heat conduction for a half-space heated through a domain in the shape of a rectangular frame on its surface by an arbitrary heat source with respect to time.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 2, pp. 322–326, August, 1989.     

Theory of the interaction of a pulsed electromagnetic field with two-wire transmission lines in nonuniform media

Equations are obtained which describe the interaction between a nonstationary electromagnetic field and a measuring transducer consisting of two linear parallel conductors separated by a dielectric layer. The system of equations obtained holds for an arbitrary orientation of the Poynting vector and different angles of polarization.Translated from IzmeritePnaya Tekhnika, No. 9, pp. 44–47, September, 1993.     

Measurement of nonstationary heat fluxes by “auxiliary wall” sensors

Computational dependences are obtained to determine the nonstationary heat flux by using sensors executing the method of an auxiliary wall. The dependences are valid for an arbitrary relationship between the thermophysical properties of the sensor and the object on which it is located.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 1, pp. 99–103, July, 1979.     

Nonstationary equivalent linearization of nonlinear continuous systems

This paper presents a technique for obtaining the nonstationary stochastic response of a nonlinear continuous system. The method of equivalent linearization is generalized to continuous systems subjected to nonstationary random excitation. This technique allows replacement of the original nonlinear system with a time-varying linear continuous system. A numerical implementation is also described. In this procedure, the linear replacement system is discretized by the finite element method. Application to systems satisfying the one-dimensional wave equation with a constitutive nonlinearity is discussed. Results are presented for nonlinear stress-strain laws of a strain-hardening type.     

Heat transfer between a flat plate with a nonstationary surface temperature and a laminar flow of liquid around it

Analytical formulas are derived to describe the nonstationary heat transfer taking place when a laminar flow of liquid passes around a flat plate, the surface temperature being an arbitrary but specified function of time.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 3, pp. 499–505, September, 1969.     

An effective approach to the solution of two-dimensional heat-conduction problems for multiconnected composite bodies of complex shape

An algorithm to solve two-dimensional nonstationary heat-conduction problems for multiconnected bodies of complex shape, constructed on the basis of potential theory methods with preliminary application of the Rothe method in the time variable, is described. Results of computations are presented for a single- and multilayer strip with holes of arbitrary outline.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 1, pp. 152–159, January, 1976.     

Heat conduction with a temperature-dependent thermal conductivity coefficient

A variational method is employed to solve stationary and nonstationary heat conduction problems when the thermal conductivity coefficient is temperature-dependent and the heat generation function of the medium is arbitrary.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 19, No. 6, pp. 1070–1078, December, 1970.     

Stochastic sensitivity analysis of energy-dissipating structures with nonlinear viscous dampers by efficient equivalent linearization technique based on explicit time-domain method

Nonlinear fluid viscous dampers have been widely used in energy-dissipating structures due to their stable and high dissipation capacity and low maintenance cost. However, the literature on stochastic optimization of nonlinear viscous dampers under nonstationary excitations is limited. This paper is devoted to the stochastic response and sensitivity analysis of large-scale energy-dissipating structures equipped with nonlinear viscous dampers subjected to nonstationary seismic excitations. The analysis procedure is developed in the frame of the equivalent linearization method (ELM) in conjunction with the explicit time-domain method (ETDM). The equivalent linear system and the corresponding statistical moments of responses at a specific time instant are first obtained through a series of stochastic response analyses of the linearized systems. Then the sensitivities of the statistical moments of responses are determined via a series of stochastic sensitivity analyses of the equivalent linear system at the corresponding time instant. The above two iterative procedures are facilitated at high efficiency using ETDM with explicit formulations of the statistical moments of responses and the sensitivities of the statistical moments. This process is repeated for different time instants, and the time histories of the statistical moments and their sensitivities can be obtained. The stochastic response and sensitivity results are further utilized to conduct the stochastic optimal parametric design of the nonlinear viscous dampers. A one-storey building model equipped with a nonlinear viscous damper is analyzed to demonstrate the accuracy of the proposed method, and a suspension bridge with a main span of 1200 m equipped with 4 nonlinear viscous dampers is further investigated to illustrate the feasibility of the proposed method for stochastic optimal design of large-scale structures.     

一种分段平稳随机信号的参数识别方法

基于振动的结构健康监测的前提是从振动测试信号中提取结构模态参数。随机子空间方法是近年来发展起来的一种线性系统辨识方法，可以有效地从环境激励的结构响应信号中提取结构模态参数。随机子空间识别方法的应用前提是输人满足白噪声的假定，输出信号应当是平稳信号。论文对随机子空间方法的使用前提进行了拓展。将非平稳信号划分为分段平稳随机信号进行处理，为非平稳信号的研究提供一种新的分析方法。基本思想是将在现场采集的结构输出信号进行分段，各段信号应满足稳定的条件，即分段平稳。将各段信号用随机子空间结合稳定图进行识别，然后将所有各段所识别的模态参数再一次用稳定图方法进行分析，得出结构的模态参数。最后用-3跨连续梁的数值模型进行验证，结果表明用随机子空间方法结合两次稳定图可以有效地识别分段平稳的随机信号。     

Response analysis of nonlinear multi-degree-of-freedom systems with uncertain properties to non-Gaussian random excitations

The investigation reported in this paper is concerned with the development of an approach for response analysis of multi-degree-of-freedom (mdof) nonlinear systems with uncertain properties of large variations and under non-Gaussian nonstationary random excitations. The developed approach makes use of the stochastic central difference (SCD) method, time co-ordinate transformation (TCT), and adaptive time schemes (ATS). It is applicable to geometrically complicated systems idealized by the finite element method (FEM). For demonstration of its use and availability of results for direct comparison, a two-degree-of-freedom (tdof) nonlinear asymmetric system with uncertain natural frequencies and under Gaussian and non-Gaussian nonstationary random excitations is considered. Computed results obtained for the system with and without uncertain natural frequencies, and under Gaussian and non-Gaussian nonstationary random excitations are presented. It is concluded that the approach is relatively simple, accurate and efficient to apply.     

An efficient simulation approach for multivariate nonstationary process: Hybrid of wavelet and spectral representation method

Currently, the classical spectral representation method (SRM) for nonstationary process simulation is widely used in the engineering community. Although this scheme has the higher accuracy, the time-dependent spectra results in unavailability of fast Fourier transform (FFT) and thus the simulation efficiency is lower. On the other hand, the approach based on stochastic decomposition can apply FFT in the simulation. However, the algorithm including the fitting procedure is relatively complicated and thus limits its use in practice.In this paper, the hybrid efficient simulation method is proposed for the vector-valued nonstationary process, which contains the spectra decomposition via wavelets and SRM. This method can take advantage of FFT and is also straightforward to engineering application. Numerical examples are employed to evaluate the proposed method. Results show that the method performs fairly well for the scalar process and vector-valued process with real coherence function. In the case of complex coherence function, the majority of the phase in the coherence function cannot be remained in the simulation. In addition, the validity of proper orthogonal decomposition (POD) in nonstationary process simulation via the decomposition of the time-dependent nonstationary spectra is studied. Analysis shows that the direct use of POD in nonstationary spectra decomposition may not be useful in nonstationary process simulations.