Efficacy of Hilbert and Wavelet Transforms for Time-Frequency Analysis

Two independently emerging time-frequency transformations in Civil Engineering, namely, the wavelet transform and empirical mode decomposition with Hilbert transform (EMD+HT), are discussed in this study. Their application to a variety of nonstationary and nonlinear signals has achieved mixed results, with some comparative studies casting significant doubt on the wavelet’s suitability for such analyses. Therefore, this study shall revisit a number of applications of EMD+HT in the published literature, offering a different perspective to these commentaries and highlighting situations where the two approaches perform comparably and others where one offers an advantage. As this study demonstrates, much of the differing performance previously observed is attributable to EMD+HT representing nonlinear characteristics solely through the instantaneous frequency, with the wavelet relying on both this measure and the instantaneous bandwidth. Further, the resolutions utilized by the two approaches present a secondary factor influencing performance.     

Time‐Series Models for Nonlinear Systems

Discrete time‐series models can be used for the dynamic response prediction of linear structures. When structural nonlinearities are present, it may be possible to modify the form of the discrete time‐series model to account for the nonlinearities. One approach is to allow the model parameters to become functions of state. This paper explores some possible forms of the parameter functions for various nonlinear structures. Numerical case studies using both a Duffing oscillator and a combined viscous and coulomb damped oscillator are presented. Also, experimental data from a highly nonlinear aircraft landing gear strut are used to evaluate different model forms. The results from these studies show the potential for future applications of nonlinear time‐series models.     

Dimensional Analysis of Bilinear Oscillators under Pulse-Type Excitations

In this paper the response of a bilinear oscillator subjected to pulse-type motions is revisited with dimensional analysis. Using Buckingham’s Π theorem the number of variables in the response analysis is reduced from six (6) to four (4). When the response is presented in terms of dimensionless Π terms remarkable order emerges. It is shown that for a given value of dimensionless strength and dimensionless yield displacement, the response (relative dimensionless displacements and dimensionless base shears) is self-similar regardless of the intensity and duration of the pulse excitation. These self-similar solutions scale better with the peak pulse acceleration rather than with the peak pulse velocity, indicating that peak pulse acceleration is a superior intensity measure of the induced shaking. Most importantly, the paper demonstrates that for relatively small values of strength (larger values of ductility) the value of the normalized yield displacement is immaterial in the response, a finding that shows that the response of the bilinear single-degree-of-freedom oscillator exhibits a complete similarity (similarity of the first kind) in the normalized yield displacement. This finding implies that under a strong earthquake an isolated bridge will exhibit the same maximum displacement regardless if it is supported on lead-rubber bearings or friction pendulum bearings that exhibit the same strength and offer the same isolation period.     

链带铸型机运动特征测试与分析

构建了铸型机运动特征测试系统,在现场测试的基础上分析了铸型机链带系统爬行与工况的关系,及爬行发生时的时域、频域特征。通过两主动链轮的时域、频域分析,探讨了铸锭打印及链轮多边形效应对主动链轮速度稳定性的影响,并对两主动链轮的运动相位差、轴承磨损、不对中特征与铸型爬行的关联性进行了分析。     

倒频谱分析在高速线材精轧传动箱故障诊断中的应用

倒频谱分析是故障诊断的一种有效手段,常用于从复杂的信号中提取周期信号.简要介绍了倒频谱的分析原理及特点,通过对现场工况的分析,运用时域、频域分析方法对高线精轧传动箱轴承故障进行诊断,并采用倒频谱方法从复杂谱线中提取出周期信号,对轴承故障做出判断,分析诊断结果与实际结果一致,验证倒频谱分析可提高轴承故障的准确性.     

Two-Dimensional Nonlinear Analysis of Long Cables

A simple finite-difference iterative model is presented here for the nonlinear analysis of a long inclined cable due to its self-weight and other concentrated loads in between. The input requires the end coordinates, area of cross section, modulus of elasticity, and initial tension of the cable. If the ends of the cable are subjected to displacements, the tension in the cable varies nonlinearly and the new deformed shape is computed using an iterative procedure. Unlike finite-element methods, initial cable geometry is not required here, and the method automatically computes the initial geometry even with concentrated loads.     

Slope Stability Analysis with Nonlinear Failure Criterion

A linear failure criterion is widely used in slope stability analyses. However, the strength envelope of almost all geomaterials has the nature of nonlinearity. This paper computes rigorous upper bounds on slope stability factors under the condition of plane strain with a nonlinear yield criterion by employing the upper bound theorem of plasticity. A stability factor (or a limit load) computed using a linear Mohr-Coulomb (MC) failure criterion which circumscribes the actual nonlinear failure criterion is an upper bound value of the actual stability factor (or limit load). In this paper, an improved method using a “generalized tangential” technique to approximate a nonlinear failure criterion is proposed to estimate the stability factor of a slope on the basis of the upper bound theorem of plasticity. Using the “generalized tangential” technique, the curve of the nonlinear failure criterion is simplified as a set of straight lines according to the linear MC failure criterion. The straight line is tangential to the curve of the nonlinear failure criterion. The set of straight lines of the linear MC failure criterion is employed to formulate the slope stability problem as a classical optimization problem. The objective function formulated in this way is minimized with respect to the location of sliding body center and the location of tangency point. Two typical slope stability problems (a homogeneous soil slope with two slope angles and a vertical cut slope with a tension crack) are analyzed using the proposed method. For the soil slope with two slope angles, the computed results are compared with published solutions by others. The comparison shows that the proposed method gives reasonable and consistent values of the stability factor of the slope. For the vertical cut slope with a tension crack, a statically admissible stress field is constructed for the slope. The stress field does not violate the nonlinear failure criterion. Lower bound solutions are obtained by satisfying stress equilibrium conditions. The upper bound solutions obtained from the proposed method are equal to the lower bound solutions for the vertical cut slope. The agreement further supports the validation of the proposed approach. The influences of the strength parameters in the nonlinear criterion on the stability of slopes are also studied and discussed in this paper.     

Numerical Analysis for the Nonlinear Free Vibration of Shallow Shells

A variational approach for the nonlinear free vibration of shallow shells having a quadrilateral boundary is presented in this paper. Natural coordinates ξ and η are used to map the prescribed geometry in the x–y plane. Displacement fields corresponding to u, v, w, β1, and β2 are expressed in terms of the product of two algebraic functions, the form of which is so chosen that the displacement boundary condition can be imposed by manipulating the coefficients. In arriving at the stiffness matrix, no simplification is applied to the nonlinear strains and the variation of the complete energy equation is considered. For the plate problems numerical results are obtained and compared with approximate analytical results by other researchers. Numerical results for the shallow shells are also presented and their characteristics are found to be significantly different from the results for the plates.     

Nonlinear Models for Predicting Hoisting Times of Tower Cranes

Accuracy in estimating activity duration is one of the key prerequisites for successful construction planning. Efficient material transportation plays an important role in reducing costs and time. Time measurement and work-study techniques can provide good estimation of activity duration, but forming the databank for various conditions is expensive. The use of empirical models has been developed as an alternative to overcome the deficiency while maintaining a reasonable accuracy. In this research traditional linear regression models and nonlinear neural network models have been developed for predicting hoisting times of a tower crane. It is found that nonlinear neural network models can achieve higher accuracy. However, planners may find that the regression models, which describe the relationship between the variables in more simplistic terms, could allow them to shorten the hoisting times by manipulating the input variables. The results and the merits of the models are discussed.     

Nonlinear Finite-Element Analysis Software Architecture Using Object Composition

Object composition offers significant advantages over class inheritance to develop a flexible software architecture for finite-element analysis. Using this approach, separate classes encapsulate fundamental finite-element algorithms and interoperate to form and solve the governing nonlinear equations. Communication between objects in the analysis composition is established using software design patterns. Root-finding algorithms, time integration methods, constraint handlers, linear equation solvers, and degree of freedom numberers are implemented as interchangeable components using the Strategy pattern. The Bridge and Factory Method patterns allow objects of the finite-element model to vary independently from objects that implement the numerical solution procedures. The Adapter and Iterator patterns permit equations to be assembled entirely through abstract interfaces that do not expose either the storage of objects in the analysis model or the computational details of the time integration method. Sequence diagrams document the interoperability of the analysis classes for solving nonlinear finite-element equations, demonstrating that object composition with design patterns provides a general approach to developing and refactoring nonlinear finite-element software.     

Computer-Aided Model Generation for Nonlinear Structural Analysis Using a Structural Component Model Database

This paper presents an approach for efficiently building analytical models for nonlinear analysis. The objective has been achieved by establishing structural component model database by collecting various structural component models addressing various structural details. A common data structure and a relational database schema for storing structural component models were proposed in this study. The proposed structural component model database can serve as a decision supporting system for building nonlinear analytical models manually. In addition, the modeling information stored in this database can be presented in XML document format to be parsed and manipulated by computer system for generating nonlinear analytical model in file automatically. A school building database is used as a case study to show the feasibility of automatic modeling for nonlinear analysis using the proposed structural component database. A semiautomatic model generation system was developed to provide an efficient modeling process, which is in the manner of form filling and option selecting on web-based user interfaces, so that the model builder can focus on making engineering decisions. The modeling details are handled automatically by the proposed system based on user selection and setting.     

In-Plane Nonlinear Buckling Analysis of Deep Circular Arches Incorporating Transverse Stresses

Large discrepancies exist among current classical theories for the in-plane buckling of arches that are subjected to a constant-directed radial load uniformly distributed around the arch axis. Discrepancies also exist between the classical solutions and nonlinear finite-element results. A new theory is developed in this paper for the nonlinear analysis of circular arches in which the nonlinear strain-displacement relationship is based on finite displacement theory. In the resulting variational equilibrium equation, the energy terms due to both nonlinear shear and transverse stresses are included. This paper also derives a set of linearized equations for the elastic in-plane buckling of arches, and presents a detailed analysis of the buckling of deep circular arches under constant-directed uniform radial loading including the effects of shear and transverse stresses, and of the prebuckling deformations. The solutions of the new theory agree very well with nonlinear finite-element results. Various assumptions often used by other researchers, in particular the assumption of inextensibility of the arch axis, are examined. The discrepancies among the current theories are clarified in the paper.     

Nonlinear Analysis of Torsionally Loaded Piles in a Two-Layer Soil Profile

This paper presents a method for predicting the nonlinear response of torsionally loaded piles in a two-layer soil profile, such as a clay or sand layer underlain by rock. The shear modulus of the upper soil is assumed to vary linearly with depth and the shear modulus of the lower soil is assumed to vary linearly with depth and then stay constant below the pile tip. The method uses the variational principle to derive the governing differential equations of a pile in a two-layer continuum and the elastic response of the pile is then determined by solving the derived differential equations. To consider the effect of soil yielding on the behavior of piles, the soil is assumed to behave linearly elastically at small strain levels and yield when the shear stress on the pile-soil interface exceeds the corresponding maximum shear resistance. To determine the maximum pile-soil interface shear resistance, methods that are available in the literature can be used. The proposed method is verified by comparing its results with existing elastic solutions and published small-scale model pile test results. Finally, the proposed method is used to analyze two full-scale field test piles and the predictions are in reasonable agreement with the measurements.     

Dynamic Analysis of Nonlinear Frames by Prandtl Neural Networks

A new type of activation function, based on the use of the Prandtl–Ishlinskii operator, has been developed and used in the feed forward neural networks in order to improve their capabilities in learning to identify and analyze nonlinear structures subject to dynamic loading. The genetic algorithm has been used in its training. The neural network, which is referred to as the Prandtl neural network here, has been trained and used in the analysis of two shear frames, a single degree of freedom (SDOF) and a 3DOF, both subjected to earthquake excitations. To assess the capabilities of the Prandtl neural network under ideal situations, the data on the response of the frames have been obtained through the integration of their governing nonlinear equations of motion. The training has been based on the white noise while the strong earthquakes of 200% El Centro in 1940 and Gilroy have been used for testing. Results have shown the high precision of the Prandtl neural network in solving highly hysteretic problems. The issue is important for two main applications in structural dynamics and control: (1) analysis of highly nonlinear structures where it is desired to train a neural network to directly learn the behavior of a structure from experimental data; and (2) intelligent active control of structures where neural network emulators are designed to provide as precise predictions about the future response of the structures as possible, in order to be used in the determination of the required control forces.     

Large Membrane Roof Analysis: Nonlinear Modeling of Structures, Connectors, and Experimental Evidences

This work discusses the numerical and physical models developed for the design of a membrane roof for the Baptist Church of Fortaleza as well as the fabrication and construction of the actual membrane, comparing results of the models with those of the real structure. The roof area amounts to about 2,900?m2, a national record for flexible border membranes and, to the writers’ knowledge, the first case of a fully computer-assisted design process within Brazil. The paper initially outlines procedures to form finding, stress analysis, and patterning, and then focuses on the physical models developed to validate them. Finally, construction of the actual membrane is described, and comparison is made with the previous numerical and physical models. Determination of the mechanical properties of the fabrics used to construct the membrane is also briefly discussed. Additionally, analyses of the geometric configuration and definition of the structural response of typical connectors of such a tension structure, collecting and distributing stresses coming from sails and anchoring cables and elements acting to transfer loads to the foundations, are developed. Unilateral contact is considered to develop among the aforementioned connector and the cable/rings welded to the slabs and the redance, imposing localized directional variations to the cable; furthermore, geometric (large strains) and material nonlinearities are accounted for.     

用时频分析检测柴油机的爆震

基于分析爆震对柴油机表面振动的影响,给出了用时频分析检测柴油机爆震的方法,代替传统的模式识别方法.实验证明,在时频分布图上可以清楚地分辨所对应的不同的频率响应.     

New Approach for Seismic Nonlinear Analysis of Inelastic Framed Structures

A novel approach for seismic nonlinear analysis of inelastic framed structures is presented in this paper. The nonlinear analysis refers to the evaluation of structural response considering P-delta effect, which is in the form of geometric nonlinearity, and inelastic behavior refers to material nonlinearity. This novel approach uses finite element formulation to derive the elemental stiffness matrices, particularly to derive the geometric stiffness matrix in a general form. At the same time, this approach separates the inelastic displacement from total deflection of the structure by applying two additional constant matrices, namely, the force–recovery matrix and the moment-restoring matrix in the force analogy method. The benefit behind this treatment is explicitly locating and calculating the inelastic response, together with strategically separating the coupling effect between the material nonlinearity and geometric nonlinearity, during the time history analysis. Comparison with the traditional incremental methods shows that the proposed method is very time efficient as well as straightforward. One portal frame and one five-story frame are used as numerical examples to illustrate and verify the robustness of current approach.     

Nonlinear Analysis of Ordinary Bridges Crossing Fault-Rupture Zones

Rooted in structural dynamics theory, three approximate procedures for estimating seismic demands for bridges crossing fault-rupture zones and deforming into their inelastic range are presented: modal pushover analysis (MPA), linear dynamic analysis, and linear static analysis. These procedures estimate the total seismic demand by superposing peak values of quasi-static and dynamic parts. The peak quasi-static demand in all three procedures is computed by nonlinear static analysis of the bridge subjected to peak values of all support displacements applied simultaneously. In the MPA and the linear dynamic analysis procedures, the peak dynamic demand is estimated by nonlinear static (or pushover) analysis and linear static analysis, respectively, for forces corresponding to the most-dominant mode. In the linear static analysis procedure, the peak dynamic demand is estimated by linear static analysis of the bridge due to lateral forces appropriate for bridges crossing fault-rupture zones. The three approximate procedures are shown to provide estimates of seismic demands that are accurate enough to be useful for practical applications. The linear static analysis procedure, which is much simpler than the other two approximate procedures, is recommended for practical analysis of “ordinary” bridges because it eliminates the need for mode shapes and vibration periods of the bridge.     

Analytical Model for Geometric and Material Nonlinear Analysis of Externally Prestressed Beams

The analysis of beams prestressed by external slipping tendons involves various difficulties related to the coupling between the local strain of the tendons and the global deformation of the beam. The structural behavior of the beam–tendon system at collapse is ruled both by the nonlinearity of materials and by geometric nonlinear effects. Recent scientific papers have shown the relevance of the geometric effects in evaluating the failure load of externally prestressed beams by considering the tendon eccentricity variation. The change of eccentricity is however only one of the geometric nonlinear effects. In this work the writers present a complete geometric and mechanical nonlinear analytical model based on the theory of small strains and moderate rotations deduced from the finite deformation theory.     

Nonlinear Analysis of Masonry Arches Strengthened with Composite Materials

The nonlinear behavior of masonry arches strengthened with externally bonded composite materials is investigated. A finite-element (FE) formulation that is specially tailored for the nonlinear analysis of the strengthened arch is developed. The FE formulation takes into account material nonlinearity of the masonry construction and high-order kinematic relations for the layered element. Implementation of the above concept in the FE framework reduces the general problem to a one-dimensional nonlinear formulation in polar coordinates with a closed-form representation of the elemental Jacobian matrix (tangent stiffness). A numerical study that examines the capabilities of the model and highlights various aspects of the nonlinear behavior of the strengthened masonry arch is presented. Emphasis is placed on the unique effects near irregular points and the nonlinear evolution of these effects through the loading process. A comparison with experimental results and a discussion of the correlating aspects and the ones that designate needs of further study are also presented.