Modal Analysis Procedure Research Articles

Extended consecutive modal pushover procedure for estimating seismic responses of one-way asymmetric plan tall buildings considering soil-structure interaction

Performance based design becomes an effective method for estimating seismic demands of buildings. In asymmetric plan tall building the effects of higher modes and torsion are crucial. The consecutive modal pushover (CMP) procedure is one of the procedures that consider these effects. Also in previous studies the influence of soil-structure interaction (SSI) in pushover analysis is ignored. In this paper the CMP procedure is modified for one-way asymmetric plan mid and high-rise buildings considering SSI. The extended CMP (ECMP) procedure is proposed in order to overcome some limitations of the CMP procedure. In this regard, 10, 15 and 20 story buildings with asymmetric plan are studied considering SSI assuming three different soil conditions. Using nonlinear response history analysis under a set of bidirectional ground motion; the exact responses of these buildings are calculated. Then the ECMP procedure is evaluated by comparing the results of this procedure with nonlinear time history results as an exact solution as well as the modal pushover analysis procedure and FEMA 356 load patterns. The results demonstrate the accuracy of the ECMP procedure.

Structural damage evolution assessment using the regularised time step integration method

This paper presents an approach to identify both the location and severity evolution of damage in engineering structures directly from measured dynamic response data. A relationship between the change in structural parameters such as stiffness caused by structural damage development and the measured dynamic response data such as accelerations is proposed, on the basis of the governing equations of motion for the original and damaged structural systems. Structural damage parameters associated with time are properly chosen to reflect both the location and severity development over time of damage in a structure. Basic equations are provided to solve the chosen time-dependent damage parameters, which are constructed by using the Newmark time step integration method without requiring a modal analysis procedure. The Tikhonov regularisation method incorporating the L-curve criterion for determining the regularisation parameter is then employed to reduce the influence of measurement errors in dynamic response data and then to produce stable solutions for structural damage parameters. Results for two numerical examples with various simulated damage scenarios show that the proposed method can accurately identify the locations of structural damage and correctly assess the evolution of damage severity from information on vibration measurements with uncertainties.

Mechanical properties of nanocomposite laminated structure and its sensibility to modal analysis procedure

In this work, tensile and shear modulus, as well as Poisson's ratio of a woven orthotropic nanocomposite plate were determined from vibration data. Plates used in the experiment were 16 layers S2-glass/epoxy composite manufactured by vacuum assisted wet layup. The nanocomposite plate was obtained by adding 0%, 1%, 2%, 5% and 10% nanoclays in weight to the epoxy matrix. A Finite Element model of the composite plate combined with a gradient method was applied to obtain an approximate numerical solution to experimental data in order to estimate the mechanical properties. Two different modal procedures were employed: the Laser Anemometry and Hammer test. A modal analysis was made in both cases to determine structural mode shape and associated frequencies, modal and mechanical properties for different nanoclay composite plates, as well as assessing its sensitivity to Modal Analysis.

An improved multidimensional MPA procedure for bidirectional earthquake excitations.

Presently, the modal pushover analysis procedure is extended to multidimensional analysis of structures subjected to multidimensional earthquake excitations. an improved multidimensional modal pushover analysis (IMMPA) method is presented in the paper in order to estimate the response demands of structures subjected to bidirectional earthquake excitations, in which the unidirectional earthquake excitation applied on equivalent SDOF system is replaced by the direct superposition of two components earthquake excitations, and independent analysis in each direction is not required and the application of simplified superposition formulas is avoided. The strength reduction factor spectra based on superposition of earthquake excitations are discussed and compared with the traditional strength reduction factor spectra. The step-by-step procedure is proposed to estimate seismic demands of structures. Two examples are implemented to verify the accuracy of the method, and the results of the examples show that (1) the IMMPA method can be used to estimate the responses of structure subjected to bidirectional earthquake excitations. (2) Along with increase of peak of earthquake acceleration, structural response deviation estimated with the IMMPA method may also increase. (3) Along with increase of the number of total floors of structures, structural response deviation estimated with the IMMPA method may also increase.

Discussion of paper: “Estimating optimum parameters of tuned mass dampers using harmony search” [Eng. Struct. 33 (9) (2011) 2716–2723

In the aforementioned paper, optimum design of tuned mass dampers (TMD) installed on multiple degree of freedom (MDOF) structures under seismic excitations is proposed. Equations of motion for structures with and without TMD were solved by the modal analysis procedure. Results of numerical studies in this discussion show that using modal method for solving the differential equations governing the motion of controlled structures by TMD dampers usually is not corrected because such systems essentially have not classical damping.

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

SUMMARYAn envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.

Survivability of integrated PVDF film sensors to accelerated ageing conditions in aeronautical/aerospace structures

This work validates the use of integrated polyvinylidene fluoride (PVDF) film sensors for dynamic testing, even after being subjected to UV-thermo-hygro-mechanical accelerated ageing conditions. The verification of PVDF sensors’ survivability in these environmental conditions, typically confronted by civil and military aircraft, is the main concern of the study. The evaluation of survivability is made by a comparison of dynamic testing results provided by the PVDF patch sensors subjected to an accelerated ageing protocol, and those provided by neutral non-aged sensors (accelerometers). The available measurements are the time-domain response signals issued from a modal analysis procedure, and the corresponding frequency response functions (FRF). These are in turn used to identify the constitutive properties of the samples by extraction of the modal parameters, in particular the natural frequencies. The composite specimens in this study undergo different accelerated ageing processes. After several weeks of experimentation, the samples exhibit a loss of stiffness, represented by a decrease in the elastic moduli down to 10%. Despite the ageing, the integrated PVDF sensors, subjected to the same ageing conditions, are still capable of providing reliable data to carry out a close followup of these changes. This survivability is a determinant asset in order to use integrated PVDF sensors to perform structural health monitoring (SHM) in the future of full-scale composite aeronautical structures.

Tuning of centrifugal pendulum vibration absorbers for translational and rotational vibration reduction

This note provides an analytical proof of the optimal tuning of centrifugal pendulum vibration absorbers (CPVAs) to reduce in-plane translational and rotational vibration for a rotor with N cyclically symmetric substructures attached to it. The reaction forces that the substructures (helicopter or wind turbine blades, for example) exert on the rotor are first analyzed. The linearized equations of motion for the vibration are then solved by a gyroscopic system modal analysis procedure. The solutions show that the rotor translational vibrations are reduced when one group of CPVAs is tuned to order N−1 and another group is tuned to order N+1. Derivation of this result is not available in the literature. The current derivation also yields the better known result that tuning CPVAs to order N reduces rotational rotor vibration.

Modal analysis of hydraulic pipelines

The laminar flow of a weakly compressible Newtonian fluid in a pipeline is treated by modal methods, aiming at a theoretical basis for the experimental modal analysis of hydraulic pipelines. For two points located at arbitrary positions along a pipeline, the frequency response function between flow rate excitation and pressure response is calculated in closed form, expanded into a modal series including transcendental modal transfer functions, and approximated by finite sums of rational fraction expressions. The preferred modal approximation is recognized as mobility function of a structurally damped mechanical multi-degrees-of-freedom system. Experimental modal analysis procedures for structurally and viscously damped mechanical systems are adapted for hydraulic pipelines and pipeline systems.

Theoretical Basis of Modal Analysis

There is given the theoretical background of the modal analysis in this paper. In the first part modal analysis, its theoretical and experimental procedure of vibration analysis is defined. In document one degree of freedom system and its behavior, equations and next modification as system of free vibration, harmonic excitation, structural damping is defined. Also, there is defined important property of the modal model - orthogonal property. In the next step is discussed multi degrees of freedom system, its properties, damping and solution.

Modified consecutive modal pushover procedure for seismic investigation of one-way asymmetric-plan tall buildings

The effects of higher modes and torsion have a significant impact on the seismic responses of asymmetric-plan tall buildings. A consecutive modal pushover (CMP) procedure is one of the pushover methods that have been developed to consider these effects. The aim of this paper is to modify the (CMP) analysis procedure to estimate the seismic demands of one-way asymmetric-plan tall buildings with dual systems. An analysis of 10-, 15- and 20-story asymmetric-plan buildings is carried out, and the results from the modified consecutive modal pushover (MCMP) procedure are compared with those obtained from the modal pushover analysis (MPA) procedure and the nonlinear time history analysis (NLTHA). The MCMP estimates of the seismic demands of one-way asymmetric-plan buildings demonstrate a reasonable accuracy, compared to the results obtained from the NLTHA. Furthermore, the accuracy of the MCMP procedure in the prediction of plastic hinge rotations is better than the MPA procedure. The new pushover procedure is also more accurate than the FEMA load distribution and the MPA procedure.

The use of strain sensors in an experimental modal analysis of small and light structures with free–free boundary conditions

Small and light structures have distinctive features, which cause difficulties in the measurement of their modal parameters. The major issues are the mass, which is added to the measured structure by sensors, and the very high resonant frequencies. Those difficulties occur with a measurement of the excitation force. An innovative procedure for the experimental modal analysis of small and light structures was developed in this study. This procedure involves a measurement of the excitation force, which was performed by a piezo strain gauge that enables an analysis of the aforementioned structures with free–free support. The main advantage of this sensor in comparison with other devices used for force measurements is that it adds a very small mass to the measured structure (≈0.4 g) but at the same time enables an accurate measurement of the modal parameters in a wide frequency range (up to 20 kHz). This makes it suitable for a measurement of the frequency-response functions of light structures that have high resonant frequencies. Consequently, an experimental modal analysis can be performed. The presented approach was experimentally tested on a sample with small dimensions and mass. The results of the experiment (modal parameters) were compared with the results of the numerical model. The good agreement between the results indicates that this procedure can be used on other similar structures.

The cause of unproportionately large higher mode contributions in the inelastic seismic responses of high‐rise core‐wall buildings

SUMMARYIn the conventional seismic design of high‐rise reinforced concrete core‐wall buildings, the design demands such as design shear and bending moment in the core wall are typically determined by the response spectrum analysis procedure, and a plastic hinge is allowed to form at the wall base to limit the seismic demands. In this study, it is demonstrated by using a 40‐story core‐wall building that this conventional approach could lead to an unsafe design where the true demands—the maximum inelastic seismic demands induced by the maximum considered earthquake—could be several times greater than the design demands and be unproportionately dominated by higher vibration modes. To identify the cause of this problem, the true demands are decomposed into individual modal contributions by using the uncoupled modal response history analysis procedure. The results show that the true demands contributed by the first mode are reasonably close to the first‐mode design demands, while those contributed by other higher modes are much higher than the corresponding modal design demands. The flexural yielding in the plastic hinge at the wall base can effectively suppress the seismic demands of the first mode. For other higher modes, however, a similar yielding mechanism is either not fully mobilized or not mobilized at all, resulting in unexpectedly large contributions from higher modes. This finding suggests several possible approaches to improve the seismic design and to suppress the seismic demands of high‐rise core‐wall buildings. Copyright © 2012 John Wiley & Sons, Ltd.

Methodology to design a vibration absorption footplate for motorcycle application: From phenomena investigation to prototype performance evaluation

The aim of this research is to reduce driver vibration exposure by acting on the modal response of key contact structures.The footplate is one of the components with which the driver comes into contact while riding. For this reason, footplate geometry and structural properties were investigated with a view to re-designing this component in order to reduce driver exposure.Due to the massive chassis area on which the footplate is constrained, vibrations induced by engine unbalances easily propagate in quasi-steady conditions on all surrounding components, inducing a width frequency band of load excitation. Even though the footplate geometry allows for fairly high natural frequencies, these could occur in the excitation range. Therefore, the first step of the methodology proposed entails the use of a numerical and experimental (modal analysis) procedure to identify the local vibration modes of the original components to detect if/when/how the resonances of the above mentioned components are excited.Due to an awareness of the weakness of the original solution, structural modifications, using numerical models, were studied. The footplate geometry was modified to minimize nodal displacement of the footrest beam binding. All structural modifications were designed, developed and installed on the vehicle.Finally, in order to predict modification efficiency, both the new footplate and the original one were experimentally compared. The comparison was made by means of modal investigations and by positioning the reference vehicle on a suitable roller test bench in order to simulate real working conditions.

Assessment of FEMA356 nonlinear static procedure and modal pushover analysis for seismic evaluation of buildings

Nonlinear static analysis as an essential part of performance based design is now widely used especially at design offices because of its simplicity and ability to predict seismic demands on inelastic response of buildings. Since the accuracy of nonlinear static procedures (NSP) to predict seismic demands of buildings affects directly on the entire performance based design procedure, therefore lots of research has been performed on the area of evaluation of these procedures. In this paper, one of the popular NSP, FEMA356, is evaluated and compared with modal pushover analysis. The ability of these procedures to simulate seismic demands in a set of reinforced concrete (RC) buildings is explored with two level of base acceleration through a comparison with benchmark results determined from a set of nonlinear time history analyses. According to the results of this study, the modal pushover analysis procedure estimates seismic demands of buildings like inter story drifts and hinges plastic rotations more accurate than FEMA356 procedure.

Modified-modal-pushover-based seismic optimum design for steel structures considering life-cycle cost

A modified-modal-pushover-based optimization technique is presented to design steel moment resisting frame buildings for minimizing the life-cycle cost based on the framework of performance based earthquake engineering. Modified modal pushover analysis (MMPA) procedure capturing the higher mode effect well is utilized to analyze the inelastic seismic demands of the structures subjected to the considered design earthquakes in terms of the Chinese seismic code for buildings, especially for the medium- to high-rise buildings. Furthermore, the life-cycle cost is formulated as the summation of the initial material cost and the future expected damage loss, which can be stated as a function of seismic performance levels and their corresponding failure probability by means of a statistical model. Meanwhile, the damage loss is explicitly and continuously expressed by the defined interstory drift index using the fuzzy-decision theory. Moreover, the powerful adaptive simulated annealing algorithm is applied to solve the discrete optimization problem due to the discreteness of standard steel sections. Finally, a 9-story planar steel frame is provided to illustrate the effectiveness of the proposed optimization design technique, which achieves not only more cost-effective design but greatly improves the robustness of the optimum design as well.

Étiologie de 51 clinodactylies de la phalange distale après arthrodèse métatarso-phalangienne de l’hallux à propos d’une série continue de 180 cas (étude prospective et prévention)

Operational modal analysis procedures are efficient techniques to identify modal properties of structures excited through unknown random noise produced during operation. In many practical cases, harmonic excitations are often present in addition to the white-noise and, if the harmonic frequency is close to structural frequencies, standard identification techniques fail. Here, a method is presented to take into account the harmonic excitations while doing modal parameter identification for operational modal analysis (OMA). The proposed technique is based on the Ibrahim Time Domain method and explicitly includes the harmonic frequencies known a priori. Therefore, the modified technique allows proper identification of eigenfrequencies and modal damping even when harmonic excitation frequencies are close to the natural frequencies of the structures. Experimental results are shown in the presence of multi-harmonic loads for a steel plate to validate the method.

A consecutive modal pushover procedure for nonlinear static analysis of one-way unsymmetric-plan tall building structures

Seismic responses of unsymmetric-plan tall buildings are substantially influenced by the effects of higher modes and torsion. Considering these effects, in this article, the consecutive modal pushover (CMP) procedure is extended to estimate the seismic demands of one-way unsymmetric-plan tall buildings. The procedure uses multi-stage and classical single-stage pushover analyses and benefits from the elastic modal properties of the structure. Both lateral forces and torsional moments obtained from modal analysis are used in the multi-stage pushover analysis. The seismic demands are obtained by enveloping the peak inelastic responses resulting from the multi-stage and single-stage pushover analyses. To verify and appraise the procedure, it is applied to the 10, 15, and 20-storey one-way unsymmetric-plan buildings including systems with different degrees of coupling between the lateral displacements and torsional rotations, i.e. torsionally-stiff (TS), torsionally-similarly-stiff (TSS) and torsionally-flexible (TF) systems. The modal pushover analysis (MPA) procedure is implemented for the purpose of comparison as well. The results from the approximate pushover procedures are compared with the results obtained by the nonlinear response history analysis (NL-RHA). It is demonstrated that the CMP procedure is able to take into account the higher mode influences as well as amplification or de-amplification of seismic displacements at the flexible and stiff edges of unsymmetric-plan tall buildings. The extended procedure can predict to a reasonable accuracy the peak inelastic responses, such as displacements and storey drifts. The CMP procedure represents an important improvement in estimating the plastic rotations of hinges at both flexible and stiff sides of unsymmetric-plan tall buildings in comparison with the MPA procedure.

Identification of Discontinuities in Resin Layer of Grouted Rock Bolts

The rock bolt support system is one of the major elements of safe maintenance of roof sections in coal mines almost all over the world. Leading coal producers such as the USA, South Africa, and Australia use the rock bolt system as practically the only one in roadways, room, and pillar sections. It has also been increasingly popular in other coal-producing countries including Poland. The function of the rock bolt support system is to anchor and reinforce the rock zone in the near field of an underground opening to deeper rock strata. In contrast to the conventional steel framework, the crucial part of the rock bolt support system is concealed from the observer. The developed method uses modal analysis procedures and is based on impact excitation. It consists of two main phases: experimental, which entails the measurement of modal characteristics of an investigated object; and theoretical involving reference to the Finite Element (FE) model databases. The main assumption of the method is that boundary conditions have to be such that the in situ bolt behaves like a cantilever. Since an installed rock bolt acts as an oscillator, different lengths of grouting discontinuity form different boundary conditions and change its modal parameters.

Numerical studies on the application of tuned liquid dampers with screens to control seismic response of structures

AbstractTuned liquid damper (TLD) systems are nowadays increasingly being used as one of the economical and effective passive vibration absorbers. A TLD system consists of a water tank having the fundamental sloshing fluid frequency tuned to the frequency near to the natural frequency of structure. This research focuses on modelling tall buildings equipped with TLDs having inside screens subjected to strong ground motions. Strong excitation can cause wave‐breaking phenomenon and makes turbulent in shallow rectangular tanks which could also contribute to the additional damping due to TLDs. On the other hand, wire screens placed inside a liquid tank can play an important role in reducing the structural response due to increasing the inherent damping of the structure. Based on equalizing dissipated energies, a TLD equipped with internal screens can be modelled by equivalent amplitude‐dependent tuned mass damper (TMD). In this study, adopting this simple method, equations of motion for shear‐type buildings equipped with nonlinear amplitude‐dependent TMDs were developed. A complex modal analysis procedure was used to solve the governing equations. Coupling of TMD properties and structural response was solved with iteration on structural response and updating TMD properties. Performing a set of parametric studies on three proposed tall structures equipped with TLD subjected to different ground excitations showed that if the TLD is tuned to a frequency close to the natural frequency of the structure considering hardening behaviour of TLD, it could significantly reduce the seismic response (displacements and base shears) of the structures. Copyright © 2009 John Wiley & Sons, Ltd.