Response Of Complex Structures Research Articles

Spatial statistics of diffuse elastodynamic modes

Spatial statistics of the modes in an elastic body plays a useful role in predicting certain average elastodynamic responses of complex structures, such as transmitted power or nonlinear spectral energy redistribution. For single wave-speed fields, extensive evidence exists that high-frequency modes in the interior of a generic ray-chaotic body resemble a superposition of plane waves with random amplitudes and phases. This implies centered Gaussian statistics for the field amplitude and a specific form for the two-point correlation function. The former can also be linked to the imaginary part of the Green’s function averaged over a frequency band or over a characteristic ensemble of body realizations, which allows extension to the boundaries and inclusion of effects of finite body size. In the present study we analyze and compare theoretical expressions for a number of spatial statistics, such as intensity distribution, wave-type energy equipartition, and two-point correlation function, with numerical results for an ensemble of 2D plane-strain elastic bodies with rough boundaries.

Identification of nonlinear parameters for reduced order models

Constructing nonlinear structural dynamic models is a goal for numerous research and development organizations. Such a predictive capability is required in the development of advanced, high-performance aircraft structures. Specifically, the ability to predict the response of complex structures to engine induced and aero acoustic loading has long been a United States Air Force (USAF) goal. Sonic fatigue has plagued the USAF since the advent and adoption of the turbine engine. While the problem has historically been a maintenance one, predicting the dynamic response is crucial for future aerospace vehicles. Decades have been spent investigating the dynamic response and untimely failure of aircraft structures, yet little work has been accomplished towards developing practical nonlinear prediction methods. Further, the last decade has witnessed an appreciable amount of work in the area of nonlinear parameter identification. This paper outlines a unique and important extension of a recently introduced nonlinear identification method: Nonlinear Identification through Feedback of the Outputs (NIFO). The novel extension allows for a ready means of identifying nonlinear parameters in reduced order space using experimental data. The nonlinear parameters are then used in the assembly of reduced order models, thus providing researchers with a means of conducting predictive studies prior to expensive and questionable experimental efforts. This paper details both an analytical and experimental study conducted on a well-characterized clamped–clamped beam subjected to broadband random loading. Amplitude dependent, constant stiffness parameters were successfully identified for a multiple-degree-of-freedom (MDOF) nonlinear reduced order model. The nonlinear coefficients identified from the analytical scenario compare well with previously published studies of the beam. Nonlinear parameters were also successfully identified from the raw experimental data. Finally, a MDOF nonlinear reduced order model, constructed from experimental data, was used to predict the experimental response of the beam to other loading conditions. Beam response spectra and average displacement values from the prediction model also compare well with the experimental results.

SEA를 이용한 차량 진동 특성 해석

Statistical Energy Analysis(SEA) has been considered as a Possible method for predicting responses of complex structures, especially at higher frequencies. In this paper, an SEA model of a vehicle was built using 138 energy storing subsystems connected together using 1019 Junctions. SEAM software program was used to build and calculate the model. To demonstrate the accuracy of the SEA model, predicted response levels were compared with measured levels. The source Input levels were measured at the engine mounting parts. There is good agreement between the estimated and the experimental results. This paper also identifies some dominant energy flow paths from sources. It is finally presented that the SEA model can optimize the design parameters of vehicles using model parameters and energy flow paths.

Effect of variation of normal force on seismic performance of resilient sliding isolation systems in highway bridges

AbstractIn this study, a series of shaking table tests are carried out on scaled models of two seismically isolated highway bridges to investigate the effect of rocking motion and vertical acceleration on seismic performance of resilient sliding isolators. In addition, performance of RSI is compared with system having solely natural rubber bearings. Test results show that variation of normal force on sliders due to rocking effect and vertical acceleration makes no significant difference in response of RSI systems. In addition, analytical response of prototype isolated bridge and the model used in experiments is obtained analytically by using non‐linear model for isolation systems. It is observed that for seismically isolated bridges, dynamic response of full‐scale complex structures can be predicted with acceptable accuracy by experiments using a simple model of the structure. Copyright © 2005 John Wiley & Sons, Ltd.

Robust component modal synthesis method adapted to the survey of the dynamic behaviour of structures with localised non-linearities

This paper deals with a method to study closely the stationary solution of non-linear dynamic systems at several degrees of freedom (dof) subjected to harmonic excitations with or without parametric modifications. This solution is obtained basically with the utilisation of an iterative algorithm adapted to the first approximation of Newton–Raphson method. This method is based on the exploitation of the eigensolutions of the associated conservative linear system with or without parametric modifications as well as on the characteristics of localised non-linearities and finally on the exploitation of the equivalent linearisation method. With the application of this method at first on linear models initially condensed by modal synthesis, the predictions of non-linear responses can be obtained rapidly. In a second step, this method is adapted to a condensed linear model used in the first optimisation procedure of the non-linear dynamic behaviour. In fact, before the non-linear analysis, the appropriate choice of the basis of reduction, that is referred to as “robust” obtained from the initial linear system is necessary. This robust basis will be used as condensation basis of the modified model local per zone or global by substructure leads to a prediction of vibratory responses of complex structures greatly modified and affected by localised non-linearities.At the end of this article, two examples are given to illustrate the efficiency and the performances of the proposed method.

주파수응답함수를 이용한 감쇠가 있는 유한요소모형의 개선

The finite element analysis is frequently used to prediet dynamic responses of complex structures. Since the predicted responses often differ from experimentally measured ones, updating of the finite element models is performed to make the finite element results agree with the measured ones. Among several model updating methods, one is to use FRF(frequency response funetion) data without a modal analysis. This paper investigates characteristics of the model updating method in order to improve the method. The investigation is focused on hOw to obtain FRfs for unmeasured rotational displacements and how to consider damping. For the investigation simulated data and experimental data for a cantilever beam are used.

Unit-cell finite element analysis of the response of complex structures to flow excitation

Analytic estimation of the vibration response of rib-reinforced structures excited by turbulent boundary layer (TBL) wall pressure fluctuations is a subject of ongoing interest for numerous applications in airborne and underwater acoustics. Previous investigators have developed a variety of closed form and approximate analytic methods for estimating the response of structures of interest. Fluid-loading and rib-reinforcement effects make problems involving the response of sea-going vessels particularly challenging. Recent advances in finite element based methods and the enhanced capabilities of modern computer hardware now permit the application of the FEA method to such flow-induced vibration problems. This paper describes the application of the unit-cell capability in BBN’s SARA-2D finite element code to evaluate the response of fluid-loaded, rib-reinforced cylinders to TBL excitation. An overview of the unit-cell modeling method is presented, and example results are provided to illustrate the effects of variations in rib and shell dimensions.

Modelling delaminations in postbuckling stiffened composite shear panels

A method has been developed to predict the effect of delaminations in a postbuckling stiffened structure manufactured from laminated composite materials. The emphasis of the technique, driven by aircraft certification requirements, was towards establishing whether delamination growth would initiate under given loading conditions. A geometric nonlinear finite element analysis was used to calculate the strain energy release rate around the circumference of a circular delamination using the virtual crack closure technique. In order to deal with the complex structural response in a computationally efficient manner, the structure was modelled using plate elements with two layers of plate elements used in the delaminated region. The effect of delamination size on the strength of postbuckling panels was shown to be a complex phenomenon in which trends were difficult to predict. Large delaminations could significantly affect the global and sub-laminate buckling modes and therefore be less critical than smaller delaminations. It was concluded that the method could accurately predict the load and location at which delamination growth would initiate, given suitable critical strain energy release rate data.

Damage indices and damage measures

This article reviews the ground motion parameters than can be assumed as structural and non-structural damage measures. Measures of seismic damage potential based on ground motion records are first described, followed by a discussion of the damage measures relating to simple (linear) and more complex (non-linear) structural responses. The second section reviews the measures of damage phenomena which govern structural degradation and/or collapse, including experimental results and analytical models. The relationship between earthquake characteristics and type and level of damage on the seismic response of structures is examined, and data from different well-known destructive earthquakes are given.

The dynamic response of complex structures using hybrid methods

Within many complex structures, there are regions which easily lend themselves to closed-form analytic solutions. A hybrid analytic-numeric formulation for the time harmonic structural vibration response of such structures is presented. The seamless inclusion of analytic solutions into the Galerkin finite element method is accomplished by using transition elements which couple the tractions between analytic and numeric solution regions. The main advantage of this formulation is to increase the overall efficiency of a model by eliminating regions of the structure from the computational domain. In this way, the total number of degrees-of-freedom will be reduced, which in turn reduces memory requirements and computational time. This allows for the analysis of higher frequency or more complex problems. One application is the study of systems comprised of structural members which are coupled at nonidealized joints. Using a discretization of the equations of elasticity for a joint, its response may be represented to a desired level of accuracy. This elasticity model is coupled to the reduced beam or shell theory producing an efficient model of the complete structure. The effect of the joint and the level of modeling detail for prediction of the time harmonic response are studied.

Modal effective parameters in structural dynamics

Modal superposition techniques are generally used to analyse low frequency dynamic responses of complex structures. Within this context, modal effective parameters allow us to characterize in a com...

Frequency Response Smoothing and Structural Path Analysis: Application to Beam Trusses

A new approach has been recently developed for estimating the mean frequency responses of complex structures subjected to broadband mechanical excitation. The formulation is based on frequency response smoothing by geometric mean values, in conjunction with a solution in terms of structural path analysis (SPA). In this short paper, this approach is applied to a relatively complex test case involving a two-dimensional beam truss, confirming the SPA capabilities for dynamic analysis up to high frequencies.

Frequency response smoothing, matrix assembly and structural paths: A new approach for structural dynamics up to high frequencies

Frequency response smoothing by geometric mean values, in conjunction with a solution written in terms of structural paths, provides a new approach for estimating the mean frequency responses of complex structures subjected to mechanical excitation from low to high frequencies. A theoretical formulation is derived for continuous structures with discrete connections between components. This formulation is based on the assembly of the smoothed dynamic stiffnesses of each component in a classical way, followed by a manipulation in terms of structural paths to provide the smoothed frequency responses of the whole structure. The results can be easily interpreted due to the physical meaning of the structural paths. This approach is applied to trusses for illustration; however, it can be extended to any structure provided that the formulation of each component is established, as in a finite element approach. Computer time efficiency for large structures will depend on the selection of the “shortest” paths (similar to modal truncation for modal superposition approach). Finally, the application to dynamic substructuring with component dynamic stiffnesses or flexibilities is presented, showing promising capabilities for analysis and testing of complex structures up to high frequencies.

Nonlinear analysis of prestressed concrete box girder bridges under flexure

One-seventh scale direct models of single-cell and two-cell prestressed concrete box girder bridges, tested to destruction at McGill University, are analyzed by the nonlinear finite element technique. The nonlinear program NONLACS, utilized in the analysis, is described in detail together with the material models employed. The objective of the current study is to demonstrate the capabilities of the finite element program NONLACS in predicting the ultimate strength and complete response of prestressed concrete box girder bridges at all stages of loading up to the ultimate load. The load–deflection curves, concrete and steel stresses, and deflected shapes of the bridges at different load levels are compared with the corresponding experimental data. The results verify the applicability of the nonlinear finite element method as an economical and expedient alternative, in some cases, to expensive experimental work aimed at the investigation of the complete response of complex structures to applied loads. Key words: box girder bridges, concrete, concrete and steel strains, experimental data, finite element, load–deflection characteristics, nonlinear analysis, prestressing.

Predicting the transient EM response of complex structures using the compact finite-element method

The compact finite-element model (CFEM) method has been used to model the transient EM (TEM) response of an earth model consisting of a heterogeneous prism in a two-layered, conducting halfspace. The prism can be deformed to simulate any angle of dip and plunge without the effect of 'staircasing'. The present implementation of CFEM (program Samaya) allows for a horizontal-loop transmitter with arbitrarily oriented magnetic dipole receivers which may be on the surface or downhole. Samaya can be run on workstations or on augmented IBM PC-AT's (or clones).The use of Samaya should allow the TEM method to be used to solve a greater range of structural and target identification problems than is possible with existing interpretation aids. Having the ability to predict the TEM response of an expected geology means that surveys can be designed to yield optimum information. The program can also be used to validate hypothesized structural models against field data.The paper concludes with a discussion of the computed downhole TEM response of a dipping target.

Numerical evaluation of the sound power radiated from baffled, rectangular panels

Established methods of evaluating the sound power radiated from baffled, rectangular panels are either unsuitable for use on plates with complex boundary conditions, or prone to errors associated with discrete Fourier transforms. An alternative method described herein avoids Fourier transforms. It evaluates radiated sound power from the predetermined real or complex structural response of the plate, to an accuracy depending on the number of grid points used in a Simpson's rule integration. The method provides an efficient and accurate means of calculating radiated sound power, and is particularly suited to applications in which ease of technique implementation, and ease of error estimation, are of paramount importance.

Direct integration operators and their stability for random response of multi-degree-of-freedom systems

The stochastic central difference and stochastic Houbolt methods are introduced in this paper for the computation of the response of complex structures of nonstationary random excitations. The structures are approximated by the finite element method such that they can be treated as multi-degree-of-freedom systems. These methods can be regarded as equivalents to their deterministic counterparts. They have the potential to deal with highly nonlinear structures and mechanical systems. Stability of algorithms are also reviewed and discussed. It is concluded that within the domain of Newtonian dynamics any attempt to address quantitatively the issue of stability in the nonlinear regime would be futile. Results computed by the stochastic central difference method for two linear multi-degree-of-freedom systems are compared with those obtained by Ito's calculus approach. The implication of the numerical results is discussed.

Response of discretized plates to transversal and in-plane non-stationary random excitations

The investigation reported in this paper constitutes the second phase of an on-going research project that aims at developing techniques for the computation and analysis of response of complex structures excited by non-parametric and parametric non-stationary random disturbances. In this second phase, the technique previously developed by the authors for the analysis of response of a general two-degree-of-freedom system subjected to the aforementioned classes of excitations is extended to handle multi-degree-of-freedom (MDOF) systems. Applications are made for the computation of response of several typical plate structures, approximated by the finite element method so that they can be analyzed as MDOF systems.

The stochastic central difference method in structural dynamics

The stochastic central difference method is introduced for the computation of response of complex structures, discretized by the finite element method, to stationary and nonstationary random excitations. The method can be regarded as the stochastic equivalent of the deterministic central difference scheme employed for the direct integration of the equations of motion of discretized structures in structural dynamics. A systematic procedure for the stability and accuracy analysis of the proposed stochastic central difference method is also presented. Applications and advantages of the latter are made and discussed.

On the application of the mode‐acceleration method to structural engineering problems

AbstractMode‐superposition has been extensively used in computing the dynamic response of complex structures. Two versions of mode‐superposition, namely the mode‐displacement method and the mode‐acceleration method, have been employed. The present paper summarizes the results of a systematic study comparing the accuracy of the mode‐displacement and mode‐acceleration methods when applied to structures with various levels of damping or various excitation frequencies. The paper also discusses several details concerning the implementation of the mode‐acceleration method.