Theory Of Structural Dynamics Research Articles

Linear 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.

Vibration control of beams with active constrained layer damping

An analytical methodology is presented to study the active vibration control of beamstreated with active constrained layer damping (ACLD). This analytical method is based onthe conventional theory of structural dynamics. The process of deriving equations is preciseand easy to understand. Hamilton’s principle with the Rayleigh–Ritz method is usedto derive the equation of motion of the beam/ACLD system. By applying anappropriate external control voltage to activate the piezoelectric constraining layer,a negative velocity feedback control strategy is employed to obtain the activedamping and effective vibration control. From the numerical results it is seenthat the damping performances of the beam can be significantly improved bythe ACLD treatment. With the increase of the control gain, the active dampingcharacteristics are also increased. By equally dividing one ACLD patch into two andproperly distributing them on the beam, one can obtain better active vibrationcontrol results than for the beam with one ACLD patch. The analytical methodpresented in this paper can be effectively extended to other kinds of structures.

Theoretical Concept to Understand Plan and Design Smooth Blasting Pattern

Considering different mechanical cutting tools for excavation of rock, drilling and blasting is said to be inexpensive and at the same time most acceptable and compatible to any geo-excavation condition. Depending upon strength properties of in-situ rock mass, characteristics of joint pattern and required quality of blasting, control blasting techniques viz., pre-split and smooth blasting are commonly implemented to achieve an undamaged periphery rock-wall. To minimize magnitude of damage or overbreak, the paper emphasized that in-situ stresses and re-distribution of stresses during the process of excavation should be considered prior to selection of explosive parameters and implementation of any suitable blast pattern. Rock structure being not massive in nature, the paper firstly explains the influence of discontinuities and design parameters on smooth-wall blasting. Considering the empirical equations for estimation of stress wave’s magnitude and its attenuation characteristics through transmitting medium, the paper has put forward a mathematical model for smooth blasting pattern. The model firstly illustrates that rock burden for each hole should be sub-divided into thin micro strips/slabs to understand the characteristics of wave transmission through the medium and lastly with the help of beam theory of structural dynamics have put forward a mathematical model to analyze and design an effective smooth blasting pattern to achieve an undamaged periphery rock-wall.

Reduced-Order Active Control for Structural System with Nonlinear Uncertainty Based on Genetic Algorithm

This paper presents a new active control strategy based on linear matrix inequality (LMI) and genetic algorithm (GA) for the structural systems with nonlinear uncertainties and exogenous disturbances. Based on structural dynamics theory, the nonlinear uncertain structure system state-space model is established. Then, based on all-order H∞ control and GA, the controller of minimum order is obtained by searching the object function globally. The concerning genetic algorithm adopts float coding, stochastic tournament, elitist model, linear crossover and uniform mutation. Finally, a three-degree-of-freedom building model subjected to EI Centro earthquake is considered using this method and the simulation results show that the provided controller has almost the same control effect as all-order H∞ controller.

Dynamics of Structures—Theory and Applications to Earthquake Engineering, Third Edition

Previous editions of Anil Chopra’s Dynamics of Structures set the standard as textbook of choice for teaching structural dynamics with an eye to earthquake engineering. This third edition has come out nearly eleven years after the first hit the bookshelves, and what a fruitful decade this has been for earthquake engineering (see review of the second edition in Earthquake Spectra 17, 549). Performance-based earthquake engineering, which was in its infancy when the first edition of this book was published, is now entering its second generation. Application of nonlinear dynamics, which was limited to small academic circles and graduate studies, is now center stage for evaluation and design of major structures. Today, hardly any serious evaluation or retrofit of a substantial building is complete without at least considering either static or dynamic nonlinear analyses. The revisions included in the third edition of Dynamics of Structures reflect the changing characteristics of structural dynamics as applied in practice; as such, this book can be useful in teaching future engineers what they need to know to hit the ground running when they graduate. As previous editions did, the book can also serve as a comprehensive reference on the subject for practicing engineers who need to understand old as well as cutting-edge topics of structural dynamics. The major revisions to the book are reflected in Part III, the section that covers earthquake response and design of multistory buildings. In particular, Chapter 19, which deals with earthquake analysis and response of inelastic buildings, has been completely rewritten. In the second edition, this chapter contained only 23 pages; in this edition it has been expanded to 60 pages. Furthermore, the chapter has been divided into two separate parts. The first part covers what has been traditionally referred to as nonlinear time-history analysis, which is recently and more accurately referred to as nonlinear response-history analysis. The second part deals with approximate methods of nonlinear analysis consisting of various pushover analysis techniques, including modal pushover analysis, for which the author has been one of the leading pioneers. Based on structural dynamics theory, the modal pushover analysis procedure is developed and its accuracy evaluated. Chapter 21, which deals with various building code interpretations of structural dynamics principles, has also been significantly revised and enhanced, and now includes explanation and discussion of the relevant provisions of the 2006 International Building Code, 2005 National Building Code of Canada, 2004 Mexico Federal District Code, and 2004 Eurocode 8. New in the third edition, Chapter 22 discusses methods for estimating seismic demands promulgated in performance-based guidelines for evaluat-

Towards a disequilibrium theory of structural dynamics: Goodwin's contribution

In this paper, we reconstruct the complex itinerary towards the solution of a conceptual and mathematical problem, how to obtain growth and fluctuations in a framework where structural change is an endogenous, though intermittent, phenomenon and irregularity a natural dynamic property. This has been Goodwin's life-long research program, driven by the effort of marrying Poincaré's qualitative approach to dynamical systems with the earliest (and some of the later) attempts to formalise economic structure as a set of interacting economic units, i.e. the cells of the modern cellular dynamics. This eventually led him to computational dynamics. Our interpretation integrates the more conventional one that emphasises conceptual connections with the thoughts of Marx, Schumpeter and Keynes. Focussing upon modelling issues of an apparently pure technical nature permits a comparison of Goodwin's evolving views with those that have emerged more recently in dynamics, e.g. in the real business cycle and endogenous theories of growth. In a brief assessment towards the end of the paper, it is argued that while there is still much to be done along the path he chose, Goodwin left enough indications for us to know in which direction to go.

Modeling Of Higher-mode Effects Using AnOptimal Multi-modal Pushover Analysis

An accurate optimal pushover analysis is developed to predict the higher-mode influence in multi degree of freedom (DOF) buildings. Performance levels are determined and seismic demands are calculated using two different ground acceleration records. The methodology is based on elastic structural dynamics theory and retains the simplicity of standard pushover procedures that rigorous time history analyses do not provide. A variant inertial load pattern is determined by updating the building’s vibration properties at each stage of yielding. Each load pattern is derived using one mode shape at every yielding stage thereby capturing the higher-mode effects (HME). Using the energy under the building’s capacity curve then enables a single optimal mode shape to be determined; this defines a representative single-DOF system (R-SDOF). Towards this end, an optimization algorithm is written to minimize the target displacement error between the pushover and nonlinear time-history analyses of a few buildings for a certain ground record. Optimal capacity and demand parameters are then determined and used to combine the individual mode shapes from each stage of yielding into the single optimal mode shape. This approach enables HME and phenomena such as HME and P-∆ effects to be captured through the optimal parameter identification. These same parameters are then applied in a pushover analysis of other buildings. The results are shown to compare favorably to a separate nonlinear time-history analysis.

Response To: B. Maison's Discussion of “Evaluation of Modal and FEMA Pushover Analyses: SAC Buildings”

The authors agree with the discusser that even improved pushover analysis procedures can be inaccurate for buildings deforming far into the inelastic range—in the region of negative post-yield stiffness with significant degradation of lateral capacity. However, estimates of seismic demands obtained by MPA were much better than from FEMA force distribution over a wide range of responses—from essentially elastic response of Boston buildings to strongly inelastic response of Los Angeles buildings. For a wide range of buildings and ground motions, MPA estimates of seismic demands were accurate enough relative to the results of nonlinear RHA to be useful in the seismic evaluation of buildings. The potential and limitations of every approximate analysis procedure, including the NSP used in current practice and MPA, should be documented so that the procedure is not used outside its range of applicability. This was one of the objectives of our paper. Because MPA is based on structural dynamics theory, it offers three theoretical advantages. First, when applied to elastic systems it is equivalent to standard response spectrum analysis (RSA) (Chopra and Goel 2002, 2004) available in commercial software used by the profession. Second, although modal pushover analysis theory is strictly not valid for inelastic systems, the fact that elastic modes are coupled only weakly in the response of inelastic systems to modal inertia forces (Chopra and Goel 2002, 2004) permitted development of MPA, an approximate procedure. Third, the theory and concepts underlying MPA are extendable to unsymmetric-plan buildings (Chopra and Goel 2004). Contrary to the discusser’s interpretation of MPA as ‘‘an intricate ten-step procedure,’’ MPA retains the conceptual simplicity of current NSP with invariant force distribution, now common in structural engineering practice. Because higher-mode pushover analyses are similar to the first-mode analysis, MPA is conceptually no more difficult than procedures now standard in structural engineering practice. Because pushover analyses for the first two or three modal force distributions are typically sufficient in MPA, it requires computational effort that is comparable to the FEMA-356 procedure,

A modal pushover analysis procedure to estimate seismic demands for unsymmetric‐plan buildings

Abstract An Erratum has been published for this article in Earthquake Engng. Struct. Dyn. 2004; 33:1429. Based on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric‐plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by non‐linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each floor level. These ‘modal’ demands due to the first few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems. When applied to elastic systems, the MPA procedure is equivalent to standard response spectrum analysis (RSA). The MPA estimates of seismic demand for torsionally‐stiff and torsionally‐flexible unsymmetric systems are shown to be similarly accurate as they are for the symmetric building; however, the results deteriorate for a torsionally‐similarly‐stiff unsymmetric‐plan system and the ground motion considered because (a) elastic modes are strongly coupled, and (b) roof displacement is underestimated by the CQC modal combination rule (which would also limit accuracy of RSA for linearly elastic systems). Copyright © 2004 John Wiley & Sons, Ltd.

Investment–productivity dynamics and distribution dynamics in a multisector economy: some theory and an application to Italian regions

In this paper, we study the investment–productivity dynamics in the Framework Space, presented by Böhm and Punzo [Cycles, Growth and Structural Change, Routledge, London (2001) 47], as the distribution dynamics of the production sectors of an economy. We apply such theoretical framework to data from Italian regions to identify differences in sectoral behaviors both within and across regions. Our main findings are: sectors within a region generally follow different regime dynamics; Southern Italian regions are generally characterized by higher degrees of heterogeneity in sectoral growth behaviors and of regime instability. Also, we find support to the hypothesis of a positive relation between this type of instability and unemployment, as argued by the Neo-Austrian theory of structural dynamics.

W-1-1-4 INTRODUCTION OF DAMPING MATRIX INTO ABSOLUTE NODAL COORDINATE FORMULATION

Accurate seismic analysis of large deformable moving structures is still unsolved problems in the field of earthquake engineering. In order to analyze the problems, the dynamics of flexible beam undergoing large deformation has been studied by the authors. Generally this type problem is tackled by the finite element method. There are three basic finite element formulations which are used in the dynamics of flexible beams. There are the floating frame of reference approach [1,2,3], the finite segment method [4,5], and the large rotation vector approach [6] Recently, the absolute nodal coordinata (ANC) formulation for beam elements was proposed by A. A. Shabana [7,8]. In this procedure, there is no need to transform the element matrices into the global ones because the equations of motion are already defined in terms of the absolute nodal coordinates defined in the global reference frame. Consequently, the mass matrix becomes constant with time, whereas the stiffness matrix becomes nonlinear function of time, even in case of linear elastic deformation. One possible method to avoid such cumbersome of the absolute nodal coordinate formulation in calculating elastic forces is to assume the infinitesimal deformation theory for beams undergoing large rotation. A new time independent formulation for bending motion in calculating elastic forces of the beam, and consequently the constant stiffness matrix were derived by the authors [9]. In this formulation, the elastic force for axial deformation is still time dependent. When we calculate the dynamic problems of a flexible moving structure such as a crane during earthquakes, application of large deformation theory for the structures composing of the beam elements is unavoidable to obtain accurate results. Respose calculation, in this case, requires the damping property as well as mass and stiffness properties of the structures. This paper firstly summarizes the former researches done by the authors and then considers the introduction of damping property into the flexible system described by the absolute nodal coodinates. In the practical linear theory of structural dynamics, Rayleigh damping is often used to describe the system damping because of its simplicity and practicality. It may be attractive in the response calculation if we introduce Rayleigh type damping into nonlinear equations of motion described by ANC formulation. We have tried to develop a procedure of introduction of Rayleigh type and other type damping matrices into ANC formulation. Reasonable assumptions lead to practical damping matrices for calculating structual seismic responses. Our former formulation for ANC plays an important role for our present study.

A modal pushover analysis procedure for estimating seismic demands for buildings

AbstractDeveloped herein is an improved pushover analysis procedure based on structural dynamics theory, which retains the conceptual simplicity and computational attractiveness of current procedures with invariant force distribution. In this modal pushover analysis (MPA), the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by a pushover analysis using the inertia force distribution for each mode. Combining these ‘modal’ demands due to the first two or three terms of the expansion provides an estimate of the total seismic demand on inelastic systems. When applied to elastic systems, the MPA procedure is shown to be equivalent to standard response spectrum analysis (RSA). When the peak inelastic response of a 9‐storey steel building determined by the approximate MPA procedure is compared with rigorous non‐linear response history analysis, it is demonstrated that MPA estimates the response of buildings responding well into the inelastic range to a similar degree of accuracy as RSA in estimating peak response of elastic systems. Thus, the MPA procedure is accurate enough for practical application in building evaluation and design. Copyright © 2001 John Wiley & Sons, Ltd.

Correlation and propagation in time

Developments, through some 35 years, in the theory of electronic structure and reaction dynamics are reviewed from the perspective available to a close collaborator to Yngve Ohrn. © 1994 John Wiley & Sons, Inc.

Structural Dynamics—Theory and Computations (2nd Ed.)

Part I: structures modelled as a single degree-of-freedom system undamped single degree-of-freedom system damped single degree-of-freedom system response of one-degree-of-freedom system to haarmonic loading response to general dynamic loading Fourier analysis and response in the frequency domain generalized co-ordinates and Rayleigh's method nonlinear structural response response spectra. Part II: structures modelled as shear buildings the multistory shear building free vibration of a shear building forced motion of shear buildings damped motion of shear buildings reduction of dynamic matrices. Part III: framed structures modeled as discrete multidegree-of-freedom systems dynamic analysis of beams dynamic analysis of plane frames dynamic anaylsis of grids three-dimensional frames dynamic analysis of trusses time history response of multidegree-of-freedom systems. Part IV: structures modelled with distributed properties dynamic analysis of systems with distributed properties discretization of continuous systems. Part V: introduction to finite element method dynamic analysis of plates dynamic analysis of shells dynamic analysis of three-dimensional solid structures. Part VI: random vibration. Part VII: earthquake engineering equivolent staic lateral force method - uniform Building Code 1994 dynamic method - uniform Building Code - 1994.

Structural Dynamics

While much of the linear theory of structural dynamics has been codified in numerous computer software, important problems remain such as inverse methods (modal synthesis or system identification) and optimization problems. Nonlinear problems, however, are a fertile ground for new research, especially those involving large deformations (e.g., crash simulation) and material nonlinearities. Structure interaction problems will continue to be a fruitful area of research including fluid-structure dynamics and interaction with acoustic noise, thermal fields, soils, and electromagnetic forces. For example, new knowledge about unsteady flows around bluff bodies is needed to make significant progress with dynamic interaction problems with bridge and building structures in unsteady winds. A new field which shows great promise for application is the theory of feedback control of flexible structures. Advances in this area could pay off in near-space engineering and robotics. The training of new researchers with backgrounds in both structural dynamics and control theory and experience is a high priority for the control-structure field, however.