Response Of Complex Structures Research Articles

Random Vibration Model in Linear and Non Linear Structure, Application in Engineering Structure


 
 
 Response of linear or complex nonlinear structures takes form in a characteristic functions and in the deterministic or stochastic external loads. Non linear model with non linear structure stiffness is a type of Duffing equation. Stochastic external loads system is referred to a random signal white noise with a constant power spectral density (So), while non linear system identification of deterministic system's is based on time history, phase plane and Poincare map. Methods of Galerkin and Runge-Kutta are used to solve the partial non linear governing diferential equations. Mean value , Standard deviation and Probability Density Function (PDF) is stated as statistical responses due to stochastic response of random variables. The analysis of random vibration in the solution of non linear stochastic differential equation is solved 
 
 

The effect of elastic point contact: theory and experiment

It has recently been pointed out that nearfield deformation in the neighborhood of an elastic point contact can have significant phenomenological effects, producing shifts of resonance frequencies and serving as a source of loss. In order to take these effects into account, it is necessary to employ three dimensional elasticity theory, precluding the use of lower dimensional dynamic models, for example, plate elements in a finite element analysis (FEA) computation. This is a very significant limitation because the frequency response of many large complex structures can only be predicted using such models. We propose here a theoretical modeling approach that resolves this problem and enables the use of lower dimensional models in the analysis of such systems. We have found the predictions of the model to be in good agreement with experimental measurements in the cases we have examined so far, translational and cantilever resonators. Research funded by the Office of Naval Research.

Structural Identification and Monitoring based on Uncertain/Limited Information

The goal of the present study is to propose a structural identification framework able to exploit both vibrational response and operational condition information in extracting structural models, able to represent the systemspecific structural behavior in its complete operational spectrum. In doing so, a scheme need be derived for the extraction of salient features, which are indicative of structural condition. Such a scheme should account for variations attributed to operational effects, such as environmental and operational load variations, and which likely lie within regular structural condition bounds, versus variations which indicate short- or long-term damage effects. The latter may be achieved via coupling of sparse, yet diverse, monitoring information with appropriate stochastic tools, able to infer the underlying dependences between the monitored input and output data. This in turn allows for extraction of quantities, or features, relating to structural condition, which may further be utilized as performance indicators. The computational tool developed herein for realizing such a framework, termed the PCE-ICA scheme, is based on the use of Polynomial Chaos Expansion (PCE) tool, along with an Independent Component Analysis (ICA) algorithm. The benefits of additionally fusing a data-driven system model will further be discussed for the case of complex structural response. The method is assessed via implementation on field data acquired from diverse structural systems, namely a benchmark bridge case study and a wind turbine tower structure, revealing a robust condition assessment tool.

Low-velocity impact response of fiberglass/magnesium FMLs with a new 3D fiberglass fabric

The main objective of the present study is to introduce a new fiber metal laminate (FML), formed by sandwiching a 3D fiberglass fabric in between thin sheets of magnesium alloy. In particular, the low-velocity impact (LVI) response and failure modes of this new FML composite are investigated experimentally and computationally. In addition, to gain a more comprehensive understanding of the response of the FML, its performance is compared against those of conventional FMLs, made with various layers of biaxial woven fabrics in place of the 3D fabric. The failure modes of the specimens are characterized based on the quantitative measurements of shape, type, and extent of damage on the FMLs’ constituents. The impact characteristics of all panels are further examined by characterizing and comparing their energy absorption capacity, residual deformation and maximum deformation due to LVI. The characteristics of the new 3D glass fabric are specifically discussed, and its positive attributes and limitations, in comparison to woven fabrics, are highlighted. The results would reveal that FML made by the 3D fabric exhibits outstanding impact absorption capacity; however, their impact energy resistance is lower than FMLs formed by woven fabrics. Moreover, as a major part of this study, a finite element analysis (FEA) framework is constructed, using the commercial finite element code ABAQUS, in order to simulate the response of such complex structures. Good agreement between the experimental and computational results demonstrate that the simulation framework can be further used to optimize the configuration of FMLs for different loading situations.

Geometrically nonlinear dynamic analysis of thin shells by a four-node quadrilateral element with in-plane rotational degree of freedom

A simple and effective finite element incremental formulation based on the updated lagrangian corotational description for geometrically nonlinear dynamic analysis of shell structure is presented in this work. The flat shell element used is the classical four-node quadrilateral DKQ shell finite element, combined with the improvements of the in-plane behaviour by incorporation of the drilling rotation degree of freedom. The main goal is to have a good flat shell element of quadrilateral geometry, leading to reliable solutions in linear and geometrically nonlinear dynamic analysis. The Newmark’s direct time integration method is adopted to integrate the equations of motion, while the Newton–Raphson method is used for iterating within each time step increment until equilibrium is achieved. The results obtained through a series of selected examples demonstrate the effectiveness of the used shell finite element to predict the nonlinear dynamic response of complex structures, and the robustness of this nonlinea...

Simulation of soil–foundation–structure interaction of Hualien large-scale seismic test using dynamic centrifuge test

Understanding the soil–structure interaction (SSI) mechanism is crucial in the seismic design of nuclear power plant (NPP) containment systems. Although the numerical analysis method is generally used in seismic design, there is a need for experimental verification for the reliable estimation of SSI behavior. In this study a dynamic centrifuge test was performed to simulate the SSI behavior of a Hualien large-scale seismic test (LSST) during the Chi-Chi earthquake. To simulate the soil profile and dynamic soil properties of the Hualien site, a series of resonant column (RC) tests was performed to determine the model soil preparation conditions, such as the compaction density and the ratio of soil–gravel contents. The variations in the shear wave velocity (VS) profiles of the sand, gravel, and backfill layers in the model were estimated using the RC test results. During the centrifuge test, the VS profiles of the model were evaluated using in-flight bender element tests and compared with the in-situ VS profile at Hualien. The containment building model was modeled using aluminum and the proper scaling laws. A series of dynamic centrifuge tests was performed with a 1/50 scale model using the base motion recorded during the Chi-Chi-earthquake. In the soil layer and foundation level, the centrifuge test results were similar to the LSST data in both the time and frequency domains, but there were differences in the structure owing to the complex structural response as well as the material damping difference between the concrete in the prototype and aluminum in the model. In addition, as the input base motion amplitude was increased to a maximum value of 0.4g (prototype scale), the responses of the soil and containment model were measured. This study shows the potential of utilizing dynamic centrifuge tests as an experimental modeling tool for site specific SSI analyses of soil–foundation–NPP containment system.

Nonintrusive Structural Dynamic Reduced Order Modeling for Large Deformations: Enhancements for Complex Structures

This paper focuses on the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting “large” deformations, i.e., a geometrically nonlinear behavior, which are nonintrusive, i.e., the structure is originally modeled within a commercial finite element code. The present investigation builds on a general methodology successfully validated in recent years on simpler beam and plate structures by: (i) developing a novel identification strategy of the reduced order model parameters that enables the consideration of the large number of modes (>50 say) that would be needed for complex structures, and (ii) extending a step-by-step strategy for the selection of the basis functions used to represent accurately the displacement field. The above novel developments are successfully validated on the nonlinear static response of a nine-bay panel structure modeled with 96,000 degrees of freedom within Nastran.

Parametric time‐domain identification of multiple‐input systems using decoupled output signals

SUMMARYCivil engineering structures are often subjected to multidirectional actions such as earthquake ground motion, which lead to complex structural responses. The contributions from the latter multidirectional actions to the response are highly coupled, leading to a MIMO system identification problem. Compared with single‐input, multiple‐output (SIMO) system identification, MIMO problems are more computationally complex and error prone. In this paper, a new system identification strategy is proposed for civil engineering structures with multiple inputs that induce strong coupling in the response. The proposed solution comprises converting the MIMO problem into separate SIMO problems, decoupling the outputs by extracting the contribution from the respective input signals to the outputs. To this end, a QR factorization‐based decoupling method is employed, and its performance is examined. Three factors, which affect the accuracy of the decoupling result, including memory length, input correlation, and system damping, are investigated. Additionally, a system identification method that combines the autoregressive model with exogenous input (ARX) and the Eigensystem Realization Algorithm (ERA) is proposed. The associated extended modal amplitude coherence and modal phase collinearity are used to delineate the structural and noise modes in the fitted ARX model. The efficacy of the ARX‐ERA method is then demonstrated through identification of the modal properties of a highway overcrossing bridge. Copyright © 2013 John Wiley & Sons, Ltd.

Retrieval of relevant parameters of natural multilayer systems by means of bio-inspired optimization strategies

Natural photonic structures exhibit remarkable color effects such as metallic appearance and iridescence. A rigorous study of the electromagnetic response of such complex structures requires to accurately determine some of their relevant optical parameters, such as the refractive indices of the materials involved. In this paper, we apply different heuristic optimization strategies to retrieve the real and imaginary parts of the refractive index of the materials comprising natural multilayer systems. Through some examples, we compare the performances of the inversion methods proposed and show that these kinds of algorithms have a great potential as a tool to investigate natural photonic structures.

Next-generation parametric reduced-order models

Novel parametric reduced-order models are proposed for fast reanalysis to predict the dynamic response of complex structures, which suffered thickness variations caused by design changes or damage in one or more substructures. Parametric reduced-order models developed previously have two important challenges to overcome to improve accuracy and performance: (a) the transformation matrix is not mathematically stable and (b) the Taylor series parameterization techniques do not capture thickness variations of the structure modeled with solid-type elements due to the highly nonlinear dependence on thickness changes. Thus, herein, a new transformation matrix and novel parameterization techniques are proposed. Usual reduced-order models have an additional challenge, namely the difficulty in reducing the interface degrees of freedom. Thus a way of reducing the interface degrees of freedom is also proposed. The predicted vibration responses of complex structures are shown to agree very well with results obtained using a much more computationally expensive commercial tool.

Radiation efficiency, impedance, and the acoustics of rattle

Rattle issues consistently rank as one of the top consumer complaints in initial quality surveys for many new products. Predicting the acoustics of rattle is complicated by the need to model the vibro-acoustic response of large complex structures across a broad frequency range. The complexity of the analysis can be reduced by making use of standard methods derived almost 50 years ago. In particular, this paper discusses a computationally efficient method for assessing the propensity for rattle in large complex structures. A finite element model is used to predict the probability that impacts will occur when a product is exposed to a particular low frequency random vibro-acoustic environment. The expected contact forces arising from each impact are then estimated by making use of expressions involving the drive point impedances of infinite structures. Finally, the vibration and acoustic radiation associated with the various impacts are predicted and ranked using a SEA model. A number of examples are presented including one which makes use of a radiation efficiency formula due to G. Maidanik. The results are in very good agreement with analytical reference results.

Simulation of stochastic wind field for large complex structures based on modified Fourier spectrum

Simulation for stochastic wind field is very important in analyzing dynamic responses of large complex structures due to strong wind. The typical simulation method is the spectrum representation method (SRM), but the SRM has drawbacks of inferior precision in lower frequency and slow calculating speed. In view of this, the modified Fourier spectrum method (MFSM) is introduced into the simulation of stochastic wind field in this paper. In this method, phase information of wind velocity time history is determined by cross power spectral density (CPSD) between adjacent points, and the wind velocity time history with time and space correlation is generated by iterative modification for CPSD considering auto power spectral density (APSD). Simulation of the wind field for a long-span bridge is undertaken to verify the effectiveness of the MFSM. Simulation results of the SRM and the MFSM are compared. It can be concluded that the MFSM is more accurate and has higher calculation speed than the SRM.

Dynamic Response of Complex Structure in Half Space

The problems of SH-wave scattering caused by a subsurface circular lining structure and a beeline crack with arbitrary length at an arbitrary position were studied by using the methods of Green's function, complex variables and multi-polar coordinates. A adaptive Green's function, an essential solution to the displacement field for the elastic space possessing circular lining structure while bearing out-plane harmonic lining loads at an arbitrary point, was constructed firstly, and then a crack was created using “crack-division”. Thus the expressions of displacement and stress were established while the crack and the inclusion both existed. Finally, we give some numerical examples to discuss the variety of the horizontal surface displacement in the case of different parameters.

A Least Square Support Vector Machine Approach Based on Uniform Design Method for Structural Reliability Analysis

Since the performance functions of large complex structures can not be expressed explicitly in the process of reliability analysis, support vector machines (SVM) with good ability of generalization are used as the response surface function based on the small training samples. The uniform design method was adopted in selecting the training data. The least support vector machines (LS-SVM) were used to find the support vectors. The limit state function was expressed by the LS-SVM regression. Reliability analysis was then performed by the usual reliability method (e.g., the first-order reliability method, the second-order reliability method or Monte Carlo) on the response surface. The results of calculations of numerical examples and a typical cable-stayed bridge show that LS-SVM using the uniform design method can well approximate the real response of complex structures which has a good efficiency and accuracy and can be applied in complex structures.

Parametric reduced-order models for predicting the vibration response of complex structures with component damage and uncertainties

Modeling and fast reanalysis techniques are proposed for predicting the dynamic response of complex structures with uncertainty represented by parameter variability (in geometric and material properties) at component-level. The novel models allow for accurate reanalyses and are useful in many applications where the model of the pristine structure may not capture the changes in the system-level response due to component-level parameter variations. Herein, such models are obtained by using a novel approach based on a modified concept of component mode synthesis. The novel models, referred to as parametric reduced-order models, are developed for the general case of multiple substructures with parameter variabilities. Three types of parameteric variabilities are considered: (a) geometric (thickness) variability, (b) structural deformations (dents), and (c) cracks. For the first case, a novel parametrization of component-level mass and stiffness matrices is employed to predict the system-level response. For the second case, a novel approximate method based on static mode compensation is implemented. For the third case (cracks), a generalized formulation for the bi-linear frequency approximation is used. The predicted vibration responses of complex structures are shown to agree very well with results obtained using a much more computationally expensive commercial tool.

Shake‐table simulation study of small scale layered models

PurposeThe purpose of this paper is to investigate the correlation between the dynamic behavior of a full‐scale steel prototype and a small‐scale plastic model fabricated using fused deposition modeling (FDM).Design/methodology/approachBased on the use of a known input excitation, the small‐scale model is tested on a shake‐table. Experimental results are compared with results of a full prototype study and with computational models in an effort to assess the feasibility of testing small‐scale FDM models.FindingsTime History Records present strong correlation with prototype data and are reproducible using computational methods. Matching the first natural frequency of the studied structure proved to be a large part of achieving the desired response.Research limitations/implicationsIncluding the direct measurement of floor displacements will potentially highlight different aspects of model behavior not observed by recording accelerations only. Further investigation into the damping properties of acrylonitrile butadiene styrene plastic is recommended towards further understanding the model response.Practical implicationsAlthough this paper is based on a simple structure, the benefits of layered manufacturing (LM) methods include speed and ease of generating geometrically complex solids. The implications of the success of this pilot study include the ease in which the dynamic response of complex structures can be assessed using small‐scale LM models.Originality/valueThis project obtained baseline information on the dynamic behavior of FDM plastic parts. It provides assessment of the value of using small‐scale LM models to accurately predict the dynamic response of structures subjected to earthquake excitation.

Prediction condensed models adapted to the nonlinear structures in time domain

This paper deals with a method to study closely the stationary solution of nonlinear dynamic systems in time domain. This method is based on the exploitation of Karhunen–Loève decomposition with or without parametric modifications as well as on the characteristics of localized nonlinearities. With the application of this method at first on linear models initially condensed by Karhunen–Loève, the predictions of nonlinear responses can be obtained rapidly. This method is adapted to a condensed linear model used in the first optimization procedure of the nonlinear dynamic behaviour. This robust basis will be used as condensation basis of the modified model local per zone, which leads to a prediction of vibratory responses of complex structures modified and affected by localized nonlinearities.

System identification-guided basis selection for reduced-order nonlinear response analysis

Reduced-order nonlinear simulation is often times the only computationally efficient means of calculating the extended time response of large and complex structures under severe dynamic loading. This is because the structure may respond in a geometrically nonlinear manner, making the computational expense of direct numerical integration in physical degrees of freedom prohibitive. As for any type of modal reduction scheme, the quality of the reduced-order solution is dictated by the modal basis selection. The techniques for modal basis selection currently employed for nonlinear simulation are ad hoc and are strongly influenced by the analyst's subjective judgment. This work develops a reliable and rigorous procedure through which an efficient modal basis can be chosen. The method employs proper orthogonal decomposition to identify nonlinear system dynamics, and the modal assurance criterion to relate proper orthogonal modes to the normal modes that are eventually used as the basis functions. The method is successfully applied to the analysis of a planar beam and a shallow arch over a wide range of nonlinear dynamic response regimes. The error associated with the reduced-order simulation is quantified and related to the computational cost.

Structural reliability analysis using Monte Carlo simulation and neural networks

This paper examines a methodology for computing the probability of structural failure by combining neural networks (NN) and Monte Carlo simulation (MCS). MCS is a powerful tool, simple to implement and capable of solving a broad range of reliability problems. However, its use for evaluation of very low probabilities of failure implies a great number of structural analyses, which can become excessively time consuming. The proposed methodology makes use of the capability of a NN to approximate a function for reproducing structural behavior, allowing the computation of performance measures at a much lower cost. This approach seems very attractive, and its main challenge lies in the ability of a NN to approximate accurately complex structural response. In order to assess the validity of this methodology, a test function and two structural examples are presented and discussed. The second example is also used to show how this methodology can be used to perform reliability-based structural optimization.

Orthonormal Vector Fitting: A Robust Macromodeling Tool for Rational Approximation of Frequency Domain Responses

Vector Fitting is widely accepted as a robust macromodeling tool for approximating frequency domain responses of complex physical structures. In this paper, the Orthonormal Vector Fitting technique is presented, which uses orthonormal rational functions to improve the numerical stability of the method. This reduces the numerical sensitivity of the system equations to the choice of starting poles significantly and limits the overall macromodeling time