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Mode Shapes (mode + shape)
Selected AbstractsColumn restraint in post-tensioned self-centering moment framesEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 7 2010Chung-Che Chou Abstract Gaps between beam-to-column interfaces in a post-tensioned (PT) self-centering frame with more than one column are constrained by columns, which causes beam compression force different from the applied PT force. This study proposes an analytical method for evaluating column bending stiffness and beam compression force by modeling column deformation according to gap-openings at all stories. The predicted compression forces in the beams are validated by a cyclic analysis of a three-story PT frame and by cyclic tests of a full-scale, two-bay by first-story PT frame, which represents a substructure of the three-story PT frame. The proposed method shows that compared with the strand tensile force, the beam compression force is increased at the 1st story but is decreased at the 2nd and 3rd stories due to column deformation compatibility. The PT frame tests show that the proposed method reasonably predicts beam compression force and strand force and that the beam compression force is 2 and 60% larger than the strand force with respect to a minor restraint and a pin-supported boundary condition, respectively, at the tops of the columns. Therefore, the earlier method using a pin-supported boundary condition at upper story columns represents an upper bound of the effect and is shown to be overly conservative for cases where a structure responds primarily in its first mode. The proposed method allows for more accurate prediction of the column restraint effects for structures that respond in a pre-determined mode shape which is more typical of low and mid-rise structures. Copyright © 2009 John Wiley & Sons, Ltd. [source] ASOM applied to column stabilityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2008A. Ranjbaran Abstract A new method for computation of buckling load and mode shape of a non-uniform column is proposed. Based on the principles of calculus of variations the stability analysis of the column is defined as an optimization problem. Different known techniques of optimization are candidates for solution process. Through analysis of typical columns and comparison of the results with those of other methods, the basic theory and implementation of the presented method is verified. Copyright © 2007 John Wiley & Sons, Ltd. [source] Damage Identification of a Composite Beam Using Finite Element Model UpdatingCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2008B. Moaveni As a payload project attached to a quasi-static test of a full-scale composite beam, a high-quality set of low-amplitude vibration response data was acquired from the beam at various damage levels. The Eigensystem Realization Algorithm was applied to identify the modal parameters (natural frequencies, damping ratios, displacement and macro-strain mode shapes) of the composite beam based on its impulse responses recorded in its undamaged and various damaged states using accelerometers and long-gage fiber Bragg grating strain sensors. These identified modal parameters are then used to identify the damage in the beam through a finite element model updating procedure. The identified damage is consistent with the observed damage in the composite beam. [source] Parameter identification of torsionally coupled shear buildings from earthquake response recordsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 11 2008Ganesh Hegde Abstract This paper presents an efficient procedure to determine the natural frequencies, modal damping ratios and mode shapes for torsionally coupled shear buildings using earthquake response records. It is shown that the responses recorded at the top and first floor levels are sufficient to identify the dominant modal properties of a multistoried torsionally coupled shear building with uniform mass and constant eccentricity even when the input excitation is not known. The procedure applies eigenrealization algorithm to generate the state-space model of the structure using the cross-correlations among the measured responses. The dynamic characteristics of the structure are determined from the state-space realization matrices. Since the mode shapes are obtained only at the instrumented floor (top and first floors) levels, a new mode shape interpolation technique has been proposed to estimate the mode shape coefficients at the remaining floor levels. The application of the procedure has been demonstrated through a numerical experiment on an eight-storied torsionally coupled shear building subjected to earthquake base excitation. The results show that the proposed parameter identification technique is capable of identifying dominant modal parameters and responses even with significant noise contamination of the response records. Copyright © 2008 John Wiley & Sons, Ltd. [source] Algorithms for time synchronization of wireless structural monitoring sensorsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 6 2005Ying Lei Abstract Dense networks of wireless structural health monitoring systems can effectively remove the disadvantages associated with current wire-based sparse sensing systems. However, recorded data sets may have relative time-delays due to interference in radio transmission or inherent internal sensor clock errors. For structural system identification and damage detection purposes, sensor data require that they are time synchronized. The need for time synchronization of sensor data is illustrated through a series of tests on asynchronous data sets. Results from the identification of structural modal parameters show that frequencies and damping ratios are not influenced by the asynchronous data; however, the error in identifying structural mode shapes can be significant. The results from these tests are summarized in Appendix A. The objective of this paper is to present algorithms for measurement data synchronization. Two algorithms are proposed for this purpose. The first algorithm is applicable when the input signal to a structure can be measured. The time-delay between an output measurement and the input is identified based on an ARX (auto-regressive model with exogenous input) model for the input,output pair recordings. The second algorithm can be used for a structure subject to ambient excitation, where the excitation cannot be measured. An ARMAV (auto-regressive moving average vector) model is constructed from two output signals and the time-delay between them is evaluated. The proposed algorithms are verified with simulation data and recorded seismic response data from multi-story buildings. The influence of noise on the time-delay estimates is also assessed. Copyright © 2004 John Wiley & Sons, Ltd. [source] Experimental study of the semi-active control of building structures using the shaking tableEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 15 2003Qing Sun Abstract A magnetorheological (MR) damper has been manufactured and tested and a non-linear model is discussed. The parameters for the model are identified from an identification set of experimental data; these parameters are then used to reconstruct the force vs. displacement and the force vs. velocity hysteresis cycles of the MR damper for the hysteretic model. Then experiments are conducted on a three-storey frame model using impact excitation, which identifies dynamic parameters of the model equipped with and without the MR damper. Natural frequencies, damping ratios and mode shapes, as well as structural properties, such as the mass, stiffness and damping matrices, are obtained. A semi-active control method such as a variable structure controller is studied. Based on the ,reaching law' method, a feedback controller is presented. In order to evaluate the efficiency of the control system and the effect of earthquake ground motions, both numerical analysis and shaking table tests of the model, with and without the MR damper, have been carried out under three different ground motions: El Centro 1940, Taft 1952, and Ninghe 1976 (Tangshan Earthquake in Chinese). It is found from both the numerical analysis and the shaking table tests that the maximum accelerations and relative displacements for all floors are significantly reduced with the MR damper. A reasonable agreement between the results obtained from the numerical analysis and those from the shaking table tests is also observed. On the other hand, tests conducted at different earthquake excitations and various excitation levels demonstrate the ability of the MR damper to surpass the performance of a comparable passive system in a variety of situations. Copyright © 2003 John Wiley & Sons, Ltd. [source] System identification of linear structures based on Hilbert,Huang spectral analysis.EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 10 2003Part 2: Complex modes Abstract A method, based on the Hilbert,Huang spectral analysis, has been proposed by the authors to identify linear structures in which normal modes exist (i.e., real eigenvalues and eigenvectors). Frequently, all the eigenvalues and eigenvectors of linear structures are complex. In this paper, the method is extended further to identify general linear structures with complex modes using the free vibration response data polluted by noise. Measured response signals are first decomposed into modal responses using the method of Empirical Mode Decomposition with intermittency criteria. Each modal response contains the contribution of a complex conjugate pair of modes with a unique frequency and a damping ratio. Then, each modal response is decomposed in the frequency,time domain to yield instantaneous phase angle and amplitude using the Hilbert transform. Based on a single measurement of the impulse response time history at one appropriate location, the complex eigenvalues of the linear structure can be identified using a simple analysis procedure. When the response time histories are measured at all locations, the proposed methodology is capable of identifying the complex mode shapes as well as the mass, damping and stiffness matrices of the structure. The effectiveness and accuracy of the method presented are illustrated through numerical simulations. It is demonstrated that dynamic characteristics of linear structures with complex modes can be identified effectively using the proposed method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Approximate analysis methods for asymmetric plan base-isolated buildingsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 1 2002Keri L. Ryan Abstract An approximate method for linear analysis of asymmetric-plan, multistorey buildings is specialized for a single-storey, base-isolated structure. To find the mode shapes of the torsionally coupled system, the Rayleigh,Ritz procedure is applied using the torsionally uncoupled modes as Ritz vectors. This approach reduces to analysis of two single-storey systems, each with vibration properties and eccentricities (labelled ,effective eccentricities') similar to corresponding properties of the isolation system or the fixed-base structure. With certain assumptions, the vibration properties of the coupled system can be expressed explicitly in terms of these single-storey system properties. Three different methods are developed: the first is a direct application of the Rayleigh,Ritz procedure; the second and third use simplifications for the effective eccentricities, assuming a relatively stiff superstructure. The accuracy of these proposed methods and the rigid structure method in determining responses are assessed for a range of system parameters including eccentricity and structure flexibility. For a subset of systems with equal isolation and structural eccentricities, two of the methods are exact and the third is sufficiently accurate; all three are preferred to the rigid structure method. For systems with zero isolation eccentricity, however, all approximate methods considered are inconsistent and should be applied with caution, only to systems with small structural eccentricities or stiff structures. Copyright © 2001 John Wiley & Sons, Ltd. [source] Efficient modal analysis of systems with local stiffness uncertaintiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6-7 2009S. F. Wojtkiewicz Abstract The characterization of the uncertainty in modal quantities of an uncertain linear structural system is essential to the rapid determination of its response to arbitrary loadings. Although the size of many computational structural models used is extremely large, i.e. thousands of equations, the uncertainty to be analyzed is oftentimes localized to very small regions of the model. This paper addresses the development of an efficient, computational methodology for the modal analysis of linear structural systems with local stiffness uncertainties. The newly developed methodology utilizes an enriched basis that consists of the sub-spectrum of a nominal structural system augmented with additional basis vectors generated from a knowledge of the structure of the stiffness uncertainty. In addition, methods for determining bounds on the approximate modal frequencies and mode shapes are discussed. Numerical results demonstrate that the algorithm produces highly accurate results with greatly reduced computational effort. Copyright © 2009 John Wiley & Sons, Ltd. [source] Use of equivalent mass method for free vibration analyses of a beam carrying multiple two-dof spring,mass systems with inertia effect of the helical springs consideredINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Jia-Jang Wu Abstract This paper investigates the free vibration characteristics of a beam carrying multiple two-degree-of-freedom (two-dof) spring,mass systems (i.e. the loaded beam). Unlike the existing literature to neglect the inertia effect of the helical springs of each spring,mass system, this paper takes the last inertia effect into consideration. To this end, a technique to replace each two-dof spring,mass system by a set of rigidly attached equivalent masses is presented, so that the free vibration characteristics of a loaded beam can be predicted from those of the same beam carrying multiple rigidly attached equivalent masses. In which, the equation of motion of the loaded beam is derived analytically by means of the expansion theorem (or the mode superposition method) incorporated with the natural frequencies and the mode shapes of the bare beam (i.e. the beam carrying nothing). In addition, the mass and stiffness matrices including the inertia effect of the helical springs of a two-dof spring,mass system, required by the conventional finite element method (FEM), are also derived. All the numerical results obtained from the presented equivalent mass method (EMM) are compared with those obtained from FEM and satisfactory agreement is achieved. Because the equivalent masses of each two-dof spring,mass system are dependent on the magnitudes of its lumped mass, spring constant and spring mass, the presented EMM provides an effective technique for evaluating the overall inertia effect of the two-dof spring,mass systems attached to the beam. Furthermore, if the total number of two-dof spring,mass systems attached to the beam is large, then the order of the overall property matrices for the equation of motion of the loaded beam in EMM is much less than that in FEM and the computer storage memory required by the former is also much less than that required by the latter. Copyright © 2005 John Wiley & Sons, Ltd. [source] Free vibration analysis of arches using curved beam elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003Jong-Shyong Wu Abstract The natural frequencies and mode shapes for the radial (in-plane) bending vibrations of the uniform circular arches were investigated by means of the finite arch (curved beam) elements. Instead of the complicated explicit shape functions of the arch element given by the existing literature, the simple implicit shape functions associated with the tangential, radial (or normal) and rotational displacements of the arch element were derived and presented in matrix form. Based on the relationship between the nodal forces and the nodal displacements of a two-node six-degree-of-freedom arch element, the elemental stiffness matrix was derived, and based on the equation of kinetic energy and the implicit shape functions of an arch element the elemental consistent mass matrix with rotary inertia effect considered was obtained. Assembly of the foregoing elemental property matrices yields the overall stiffness and mass matrices of the complete curved beam. The standard techniques were used to determine the natural frequencies and mode shapes for the curved beam with various boundary conditions and subtended angles. In addition to the typical circular arches with constant curvatures, a hybrid beam constructed by using an arch segment connected with a straight beam segment at each of its two ends was also studied. For simplicity, a lumped mass model for the arch element was also presented. All numerical results were compared with the existing literature or those obtained from the finite element method based on the conventional straight beam element and good agreements were achieved. Copyright © 2003 John Wiley & Sons, Ltd. [source] Flapwise bending vibration of rotating platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2002H. H. Yoo Abstract Linear equations of motion for the flapwise bending vibration analysis of rotating plates are derived in the present work. The equations of motion are transformed into dimensionless forms in which three dimensionless parameters are identified. The effects of the dimensionless parameters on the characteristics of the flapwise bending vibration of rotating plates are investigated. The accuracy of the present modelling method is verified through comparing its numerical results to those obtained by an existing method in the related literature. Eigenvalue loci crossing and eigenvalue loci veering phenomena are observed and discussed. The variations of mode shapes associated with the phenomena are also exhibited. Copyright © 2002 John Wiley & Sons, Ltd. [source] Asymptotic and spectral properties of operator-valued functions generated by aircraft wing modelMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2004A. V. Balakrishnan Abstract The present paper is devoted to the asymptotic and spectral analysis of an aircraft wing model in a subsonic air flow. The model is governed by a system of two coupled integro-differential equations and a two parameter family of boundary conditions modelling the action of the self-straining actuators. The differential parts of the above equations form a coupled linear hyperbolic system; the integral parts are of the convolution type. The system of equations of motion is equivalent to a single operator evolution,convolution equation in the energy space. The Laplace transform of the solution of this equation can be represented in terms of the so-called generalized resolvent operator, which is an operator-valued function of the spectral parameter. More precisely, the generalized resolvent is a finite-meromorphic function on the complex plane having a branch-cut along the negative real semi-axis. Its poles are precisely the aeroelastic modes and the residues at these poles are the projectors on the generalized eigenspaces. The dynamics generator of the differential part of the system has been systematically studied in a series of works by the second author. This generator is a non-selfadjoint operator in the energy space with a purely discrete spectrum. In the aforementioned series of papers, it has been shown that the set of aeroelastic modes is asymptotically close to the spectrum of the dynamics generator, that this spectrum consists of two branches, and a precise spectral asymptotics with respect to the eigenvalue number has been derived. The asymptotical approximations for the mode shapes have also been obtained. It has also been proven that the set of the generalized eigenvectors of the dynamics generator forms a Riesz basis in the energy space. In the present paper, we consider the entire integro-differential system which governs the model. Namely, we investigate the properties of the integral convolution-type part of the original system. We show, in particular, that the set of poles of the adjoint generalized resolvent is asymptotically close to the discrete spectrum of the operator that is adjoint to the dynamics generator corresponding to the differential part. The results of this paper will be important for the reconstruction of the solution of the original initial boundary-value problem from its Laplace transform and for the analysis of the flutter phenomenon in the forthcoming work. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||