New modal identification method under the non-stationary Gaussian ambient excitation

Based on the multivariate continuous time autoregressive （CAR） model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian random excitation. The method can identify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into a continuous time autoregressive model （CAR） of order 3. Second, based on the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short period of time and on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Two special situations are discussed. Finally, by virtue of the Girsanov theorem, we introduce a likelihood function, which is just a con- ditional density function. Maximizing the likelihood function gives the exact maximum likelihood estimators of model parameters. Numerical results show that the method has high precision and the computation is efficient.

Indecomposable Decomposations of R-Quasi-continuous Modules

It is shown that if M is an R-quasi-continuous left R-module and R satisfies ACC on left ideals of the form l(m), m ∈ M, then M is a direct sum of uniform sub-modules.

Study of Modules over 3 × 3 Formal Triangular Matrix Rings

In this paper we carry out a study of modules over a 3 × 3 formal triangular matrix ringГ=（T 0 0 M U 0 N×UM N V）where T, U, V are rings, M, N are U-T, V-U bimodules, respectively. Using the alternative description of left Г-module as quintuple （A, B, C; f, g） with A ∈ mod T, B ∈ mod U and C ∈ mod V, f ： M ×T A →B ∈ mod U, g ： N ×U B → C ∈ mod V, we shall characterize uniform, hollow and finitely embedded modules over F, respectively. Also the radical as well as the socle of r （A ＋ B ＋ C） is determined.

Effects of non-stationary wind velocity models on buffeting performance of closed-box girder suspension bridges

Non-stationary characteristic in nature wind has a great effect on buffeting performance of long-span bridges.The influence of key parameters in non-stationary wind velocity models on nonlinear buffeting responses of a super long-span suspension bridge was investigated in this paper.Firstly,four non-stationary wind velocity models are established by combing the time-varying average wind velocity with an exponential function and the fluctuating wind velocity with four modulation functions,respectively.These non-stationary wind velocity models have obvious non-stationary characteristics and then are validated by the classical power spectrum densities.Finally,three displacement responses of the bridge deck under four different independent variables ofβin the exponential function and four modulation functions were compared,respectively.Results show that the turbulence intensities using two non-uniform modulation functions(NMF)are larger than those using uniform modulation functions(uMF).Moreover,the root mean square(RMS)values of three displacement responses increase with the decrease ofβ.Besides,the RMS values of three displacement under two NMFs are larger than those under two uMFs,and their RMS values under the second uMF are the smallest.