一种诊断复合材料层合板损伤的频响方法

本文首先选取对故障比较敏感,又能反映结构动力学特性的频响函数作为诊断故障的参数。通过计算无损板在给定模态下各单元的模态能量,求得每个单元对该阶模态下全板能量的贡献,并由模态实验得到损伤前后频响函数在各阶共振峰处的变化。分析发现两者之间存在内在联系,从而得到一种分析小损伤位置和范围的新方法。     

随机激励的耗散的哈密尔顿系统的平稳解

本文首先为一般的随机激励的耗散的哈密尔顿系统得到精确的平稳解,然后在此基础上为类似而更为一般的系统发展了等效非线性系统法     

高速移动荷载下黏弹性半空间体的动力响应

分别以移动荷载和黏弹性半空间体模拟运动列车荷载和地基,分析了地基在运动列车作用下的动力响应.首先采用Green函数法求解黏弹性半空间体在各种移动荷载模式作用下的动力响应的解析解,包括恒常和简谐移动点源、线源和面源荷载.然后采用IFFT算法和自适应数值积分算法计算解析解中的二维积分,得到了包括低音速、跨音速和超音速移动荷载作用下位移的数值结果.最后分析了速度对位移的分布和最大值的影响,发现当速度大于Rayleigh波速时,位移发生显著变化.     

Advanced response surface method for mechanical reliability analysis

Based on the classical response surface method (RSM), a novel RSM using improved experimental points (EPs) is presented for reliability analysis. Two novel points are included in the presented method. One is the use of linear interpolation, from which the total EPs for determining the RS are selected to be closer to the actual failure surface; the other is the application of sequential linear interpolation to control the distance between the surrounding EPs and the center EP, by which the presented method can ensure that the RS fits the actual failure surface in the region of maximum likelihood as the center EPs converge to the actual most probable point (MPP). Since the fitting precision of the RS to the actual failure surface in the vicinity of the MPP, which has significant contribution to the probability of the failure surface being exceeded, is increased by the presented method, the precision of the failure probability calculated by RS is increased as well. Numerical examples illustrate the accuracy and efficiency of the presented method.     

Studies on structural safety in stochastically excited Duffing oscillator with double potential wells

The effects of the Gaussian white noise excitation on structural safety due to erosion of safe basin in Duffing oscillator with double potential wells are studied in the present paper. By employing the well-developed stochastic Melnikov condition and Monte–Carlo method, various eroded basins are simulated in deterministic and stochastic cases of the system, and the ratio of safe initial points (RSIP) is presented in some given limited domain defined by the system’s Hamiltonian for various parameters or first-passage times. It is shown that structural safety control becomes more difficult when the noise excitation is imposed on the system, and the fractal basin boundary may also appear when the system is excited by Gaussian white noise only. From the RSIP results in given limited domain, sudden discontinuous descents in RSIP curves may occur when the system is excited by harmonic or stochastic forces, which are different from the customary continuous ones in view of the first-passage problems. In addition, it is interesting to find that RSIP values can even increase with increasing driving amplitude of the external harmonic excitation when the Gaussian white noise is also present in the system. The project supported by the National Natural Science Foundation of China (10302025 and 10672140). The English text was polished by Yunming Chen.     

A new stochastic method of reconstructing porous media

We present a new stochastic method of reconstructing porous medium from limited morphological information obtained from two-dimensional micro- images of real porous medium. The method is similar to simulated annealing method in the capability of reconstructing both isotropic and anisotropic structures of multi-phase but differs from the latter in that voxels for exchange are not selected completely randomly as their neighborhood will also be checked and this new method is much simpler to implement and program. We applied it to reconstruct real sandstone utilizing morphological information contained in porosity, two-point probability function and linear-path function. Good agreement of those references verifies our developed method’s powerful capability. The existing isolated regions of both pore phase and matrix phase do quite minor harm to their good connectivity. The lattice Boltzmann method (LBM) is used to compute the permeability of the reconstructed system and the results show its good isotropy and conductivity. However, due to the disadvantage of this method that the connectivity of the reconstructed system’s pore space will decrease when porosity becomes small, we suggest the porosity of the system to be reconstructed be no less than 0.2 to ensure its connectivity and conductivity.     

FEEDBACK CONTROL OPTIMIZATION FOR SEISMICALLY EXCITED BUILDINGS

A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the partially observable control problem of the structure under horizontal ground acceleration excitation is converted into a completely observable control problem. Then the It6 stochastic differential equations of the system are derived based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stationary solution to the Fokker-Plank-Kolmogorov （FPK） equation associated with the It6 equations is obtained. The performance index in terms of the mean system energy and mean square control force is established and the optimal control force is obtained by minimizing the performance index. Finally, the numerical results for a three-story building structure model under E1 Centro, Hachinohe, Northridge and Kobe earthquake excitations are given to illustrate the application and the effectiveness of the proposed method.     

Non-linear vibrations and frequency response analysis of piezoelectrically driven microcantilevers

Microcantilevers have recently received widespread attentions due to their extreme applicability and versatility in both biological and non-biological applications. Along this line, this paper undertakes the non-linear vibrations of a piezoelectrically driven microcantilever beam as a common configuration in many scanning probe microscopy and nanomechanical cantilever biosensor systems. A part of the microcantilever beam surface is covered by a piezoelectric layer (typically ZnO), which acts both as an actuator and sensor. The bending vibrations of the microcantilever beam are studied considering the inextensibility condition and the coupling between electrical and mechanical properties in the piezoelectric materials. The non-linear terms appear in the form of quadratic expression due to presence of piezoelectric layer, and cubic form due to geometrical non-linearities. The Galerkin approximation is then utilized to discretize the equations of motion. In addition, the method of multiple scales is applied to arrive at the closed form solution for the fundamental natural frequency of the system. An experimental setup consisting of a commercial piezoelectric microcantilever attached on the stand of a state-of-the-art microsystem analyzer for non-contact vibration measurement is utilized to verify the theoretical developments. It is found that the experimental results and theoretical findings are in good agreement, which demonstrates that the non-linear modeling framework could provide a better dynamic representation of the microcantilever than the previous linear models. Due to microscale nature of the system, excitation amplitude plays an important role since even a small change in the amplitude of excitation can lead to significant vibrations and frequency shift.     

On the effects of non-linear elements in the reliability-based optimal design of stochastic dynamical systems

The aim of the present paper is to study the effects of non-linear devices on the reliability-based optimal design of structural systems subject to stochastic excitation. One-dimensional hysteretic devices are used for modelling the non-linear system behavior while non-stationary filtered white noise processes are utilized to represent the stochastic excitation. The reliability-based optimization problem is formulated as the minimization of the expected cost of the structure for a specified failure probability. Failure is assumed to occur when any one of the output states of interest exceeds in magnitude some specified threshold level within a given time duration. Failure probabilities are approximated locally in terms of the design variables during the optimization process in a parallel computing environment. The approximations are based on a local interpolation scheme and on an efficient simulation technique. Specifically, a subset simulation scheme is adopted and integrated into the proposed optimization process. The local approximations are then used to define a series of explicit approximate optimization problems. A sensitivity analysis is performed at the final design in order to evaluate its robustness with respect to design and system parameters. Numerical examples are presented in order to illustrate the effects of hysteretic devices on the design of two structural systems subject to earthquake excitation. The obtained results indicate that the non-linear devices have a significant effect on the reliability and global performance of the structural systems.     

RESPONSE ANALYSIS OF PIEZOELECTRIC SHELLS IN PLANE STRAIN UNDER RANDOM EXCITATIONS

The random response of a piezoelectric thick shell in plane strain state under boundary random excitations is studied and illustrated with a piezoelectric cylindrical shell. The differential equation for electric potential is integrated radially to obtain the electric potential as a function of displacement. The random stress boundary conditions are converted into homogeneous ones by transformation,which yields the electrical and mechanical coupling differential equation for displacement under random excitations. Then this partial differential equation is converted into ordinary differential equations using the Galerkin method and the Legendre polynomials,which represent a random multi-degree-of-freedom system with asymmetric stiffness matrix due to the electrical and mechanical coupling and the transformed boundary conditions. The frequency-response function matrix and response power spectral density matrix of the system are derived based on the theory of random vibration. The mean-square displacement and electric potential of the piezoelectric shell are finally obtained,and the frequency-response characteristics and the electrical and mechanical coupling properties are explored.