Modal Mass Research Articles

A Comparative Study On The Seismic Performance Of Multi-storey Buildings With Different Structural Systems

The increasing need of shelter in urban cities due to overpopulated spaces and land inadequacy has forced people to limit their needs and spaces. High-rise buildings are the best solution for providing people space for living and to work on, as the buildings are getting higher and slender, they are exposed to different loading condition, which leads the building to experience higher lateral deformations. With the help of different structural systems, the lateral stiffness of the buildings can be improved, there are many structural systems introduced for the high-rise structures which can provide the buildings adequate strength and stability against lateral loading. This paper examines behaviour of Special Moment Resisting Frame System with shear wall, Outrigger Core Belt Truss Structural System and Braced Frame System on a 30 storey building under worst seismic conditions in India i.e. Zone V. To understand effectiveness of the structural systems subjected to lateral loads, three different structural system are modelled using 3D finite element software ETABS 2018, all the models are subjected to the same loading conditions with same geometrical dimension and typical storey height. Comparison is examined on the basis of different parameters like Modal Mass Participation, Base shear, storey shear, Time period, Lateral displacement, storey drift, storey stiffness, and performance points. It was observed by the dynamic analysis method i.e., response spectrum analysis, and non-liner static analysis, the parameters which were compared between three structural system observed that building with outrigger core belt truss system performs better than Special Moment Resisting Frame + Shear Wall and Braced Frame Structural System.

Predictions for the perturbed root mean square displacement of a vibrating structure using modal parameters

A harmonically vibrating structure is considered for this study and divided into segments. The objective of the proposed research is to use knowledge from the nominal structure to make predictions as to how the root mean squared (RMS) displacement of the structure will change when either the mass or stiffness of a segment is scaled. Typically, to calculate the value for the modified RMS displacement, a linear solve is required to determine the new displacement vector. Additionally, the Neumann series may be used. However, this approach requires computations of matrix-vector products, which may become expensive for larger Degrees of Freedom (DOF) systems. Here, a method is proposed to predict the RMS displacement for the modified system from scalar values of the nominal system. Since only scalar values from the nominal system are required, predictions for the perturbed system can be made cheaply. The proposed method is based on the modal displacement equation and the assumption that the system is forced near a natural frequency. This assumption is used in Rayleigh’s quotient to approximate the new natural frequency as a function of the approximated modal stiffness and mass. The limitations and accuracy will be explored. [Work supported by ONR Grant N00014-19-1-2100.]

Periods and Mode Shapes for Uniform Shear Wall Buildings: Importance of Selecting the Appropriate Dynamic Behavior

The distribution of seismic loading to each storey of a building depends on a number of factors, mainly on the periods, mode shapes and modal participation. The estimation of these dynamic characteristics is essential in analyzing the seismic response of multi-storey buildings. Based on a rigorous dynamic analytical model of the building, this research provides a novel database of vibration modes of multi-storey buildings with reinforced concrete (RC) shear walls. The Stodola–Vianello iterative method was used to determine these. The first modes of vibration, cumulating a modal mass participation ratio (MMPR) greater than 90%, are summarized and presented in a table form. The results are equally valid for uniform buildings with masonry infill walls. The research has highlighted that the eigenvectors are independent of the values of the mass and the mechanical characteristics of the structure (the modulus of elasticity, the moment of inertia and height) but also on the variation of these characteristics over the height of the building. Consequently, for shear wall buildings with identical storeys, the eigenvectors, the MMPRs and the modal participation factors are accurately determined for this type of structure. The significance of the research consists of providing a table that engineers and researchers can easily use to determine the dynamic characteristics of the building, thus avoiding repetition of the calculations relating to this type of buildings. The study has also highlighted the importance of selecting the appropriate dynamic behavior of the structure for seismic design.

Effect of Directional Added Mass on Highway Bridge Response during Flood Events

This article presents a new analysis to determine the variation in modal dynamic characteristics of bridge superstructures caused by hydrodynamic added mass (HAM) during progressive flooding. The natural frequency variations were numerically and experimentally extracted in various artificial flood stages that included dry conditions, semi-wet conditions, and fully wet conditions. Three-dimensional finite element modeling of both subscale and full-scale models were simulated through a coupled acoustic structural technique using Abaqus®. Experiments were performed exclusively on a subscale model at a flume laboratory to confirm the numerical simulations. Finally, an approach to quantify the directional HAM in the dominant axes of vibration was pursued using the concept of effective modal mass. It is shown that specific vibrating modes with the largest effective mass are strongly affected during artificial flood events and are identified as the dominant modes. Numerical simulation shows that large directional HAM is introduced on those dominant modes during flood events. For the full-scale representative bridge, the magnitude of the HAM along the first structural mode was estimated to be over 5.8 times the bridge’s structural modal effective mass. It is suggested that directional HAM should be included during the design of bridges over streamways that are prone to flooding in order to potentially be appended to the AASHTO code.

Deformation Performance Analysis of a Truss Structure Based on the Deformation Decomposition Method

Trusses are among the basic components of large-span bridges and large-space structures. A method is proposed to conduct a comprehensive deformation analysis of a truss in terms of the basic rigid body displacements and the tension and compression deformation based on complete mathematical orthogonality and mechanical equilibrium. The correctness of the proposed method is verified by comparison with a traditional strain analysis. Furthermore, a relative deformation decomposition of the mode shape is proposed to analyse in detail its relative displacement and deformation. The correctness and superiority of the proposed method are verified by comparison with the modal mass participation coefficient method and the animation from observation method. Additionally, the relative deformation decomposition of a plane truss structure is realized under any load conditions based on the superposition of mode shapes. The quantitative analysis of the basic deformation performance of a plane truss structure can also be conducted by countable mode shapes, which do not involve load conditions. Finally, the number of mode shapes that must be considered differs when using the maximum displacement and the tension and compression deformation analysis indicators.

Shifted Resonance of Railway Bridges Under Trains Passing by Each Other

Dynamic vehicle–bridge interaction (VBI) plays a crucial role in the train-induced vibrations of a railway bridge for its coupling effects may reduce the bridge response and down-shift the resonant speed. The commonly used nominal theoretical resonant speed ([Formula: see text] of a typical railway bridge, however, is only related to the bridge frequency ([Formula: see text] and car length ([Formula: see text], but it neglects the VBI effects of the moving trains. Such a shifted resonance phenomenon would become significant for a bridge under two trains passing by each other. This study develops a method using an equivalent modal mass to be added onto the bridge to account for the frequency shift due to the presence of multiple train cars for estimation of the shifted resonant speed. The numerical study demonstrates that the proposed method can predict the shifted resonant speed and explain the shifted-resonance phenomenon of railway bridges under train passages.

Effect of Dynamic Vibration Absorber on Seismic Response of Piping Systems

The purpose of this study is to clarify the seismic response reduction effect of the piping system by a dynamic vibration absorber. The piping system with a dynamic vibration absorber was modeled into a two-degree-of-freedom system composed of a simple modal mass and a dynamic vibration absorber. Using this model, the floor response spectrum for the observed seismic waves was calculated. By comparing the changes in the two floor response spectra of the piping system with the dynamic vibration absorber and the piping system without the dynamic vibration absorber, the response reduction effect of the dynamic vibration absorber and the magnitude of the added damping ratio were discussed. When a dynamic vibration absorber was installed, the peak height of the floor response spectrum of the piping system decreased, and the effect was useful for the piping system with a smaller damping ratio. Dynamic vibration absorbers are suggested to be an effective method for reducing the seismic response of small-bore piping systems with a small damping ratio.

A comparative study on seismic analysis of regular and plan irregular buildings resting on different soils

As the occurrence of earthquakes is increasing day by day, understanding and predicting the structural behavior of buildings in seismic-prone regions is a challenging task, particularly when the buildings are plan irregular. The present research work focuses on analyzing a plan irregular building located in Seismic zone-V and for three different types of soil conditions considered according to Indian Standard (IS 1893 (Part 1): 2016). The analysis has been carried out using the Response Spectrum method in ETABS (Extended Three dimensional Analysis of building Systems) software. Steel fibers, high-strength steel and high-performance concrete are used for the earthquake-resistant design of buildings. The results obtained from the numerical analysis of the irregular buildings are compared with that of a plan regular building for hard, medium and soft soils. The various dynamic response parameters like story displacement, story drift, story shear, story stiffness, fundamental time period and modal mass participation ratio are obtained from the numerical analysis and a comparative study is carried out.

Seismic analysis of irregular buildings with Re-Entrant corners and Autoclaved Aerated concrete blocks

In the modern era, the lack of availability of building space in locations of prime importance in high-tier cities has led architects to plan buildings that are asymmetrical in shape. This pushes the building during ground motion due to earthquake to its peak performance, but these irregularities bring different challenges for a structural engineer who must design the building in such a way that it can resist these lateral forces and perform appropriately in these critical situations without putting the life of the structure or its occupants in danger.In this study a building having an irregular plan (L-shape) is being considered with a re-entrant corner, a total of 31 models are taken into consideration for this study such as 15 types (five frames having varying heights with brick infills, five frames having varying heights with brick infills & shear wall at the core, & five frames having varying heights with brick infills & shear walls inside the plan.) same 15 types are considered again by replacing brick infills with AAC blocks to observe the reduction in the seismic weight of the building & one regular RC frame to serve as a control.Linear static Dynamic analysis is carried out for this study such as Response Spectrum Analysis for seismic zone IV as per IS 1893-(Part 1): 2016 & soil type II, to study the behavior of the building by observing various important parameters such as base shear, time period, Storey drift, maximum displacement, Storey response plots, modal mass participation ratio & sway of the building. All these buildings are modelled & analyzed using CSI ETABS 2019.

Evaluation of critical connections in an irregular precast building

This study aims at analyzing and designing the precast columns and beams in an irregular precast building. This building is designed as a moment-resisting framed structure with infill walls for Seismic and Wind loading using the Finite element software ETABS. Based on the structural analysis results one critical interior beam-column connection and one critical exterior beam-column connection are identified and an emulative connection is proposed. The element sizes and the reinforcement detailing of these critical columns and beams are presented. An emulative column-beam junction detail is proposed to achieve a moment-resisting action. This connection is simple and similar to a cast-in-place connection and doesn’t require sophisticated methods of connection such as prestressing, welding etc. The structural response of the building in terms of story displacement, story shear, story stiffness, story drift, time period and modal mass participation are also discussed. The use of advanced materials like micro concrete, engineered cementitious composites, Ultra high-performance concrete, and high strength steel rebar for in-situ concreting in the beam-column junction has advantages like reduced congestion, and reduction in cracking of concrete under severe seismic loading conditions.

Physical modelling techniques for the dynamical characterization and sound synthesis of historical bells

Capable of maintaining characteristics practically intact over the centuries, bells are musical instruments able to provide important and unique data for the study of musicology and archaeology essential to understand past manufacturing and tuning techniques. In this research we present a multidisciplinary approach based on both direct and reverse engineering processes for the dynamical characterization and sound synthesis of historical bells which proven particularly useful to extract and preserve important information for Cultural Heritage. It allows the assessment of the bell’s 3D morphology, sound properties and casting and tuning techniques over time. The accuracy and usefulness of the developed techniques are illustrated for three historical bells, including the oldest recognized bell in Portugal, dated 1287, and two eighteenth century bells from the Mafra National Palace carillons (Portugal). The proposed approach combines non-invasive up-to-date imaging technology with modelling and computational techniques from vibration analysis, and can be summarized in the following steps: (1) For the diagnosis of existing bells, a precise assessment of the bell geometry is achieved through 3D scanning technologies, used for the field measurement and reconstruction of a 3D geometry model of each bell; (2) To access the modal properties of the bells, for any given (at the design stage) or measured geometry, a finite element model is built to compute the significant frequencies of the bell partials, and the corresponding modal masses and modeshapes. In the case of existing bells, comparison of the computed modes with those obtained from vibrational data, through experimental modal identification, enables the validation (or otherwise correction) of the finite element model; (3) Using the computed or experimentally identified modes, time-domain dynamical responses can be synthesized for any conceivable bell, providing realistic sounds for any given clapper and impact location. Although this study primarily aimed to better understand the morphology and sounds of historical bells to inform their conservation/preservation, this technique can be also applied to modern instruments, either existing or at design stages. To a larger extent, it presents strong potential for applications in the bell industry, namely for restoration and re-tuning, as well as in virtual museology.

Geometrically nonlinear flutter analysis with corotational shell finite element analysis and unsteady vortex-lattice method

In this paper, an aeroelastic framework developed in the previous works has been extended for a geometrically nonlinear aeroelastic stability analysis. In the aeroelastic stability analysis, modal mass and stiffness matrices are constructed using shell finite elements with the corotational approach, which can take into account the geometric stiffening under large deformations. A generalized aerodynamic force matrix is derived by accommodating the unsteady vortex-lattice method based on a modal approach. The derived modal aeroelastic equations are solved using the p-k method. Individual modules to calculate generalized structural matrices with the corotational approach and aerodynamic forces based on the unsteady vortex-lattice method are verified. The present geometrically nonlinear aeroelastic framework for aeroelastic stability analysis is also validated in a comparison with an experimental result in the flutter wind tunnel test showing a reasonable accuracy for a prediction of flutter speed, while there still is room for further improvement in the estimation of flutter frequency. In addition, the present method allows studying the flutter characteristics of flexible wings with different incident angles, which cannot be evaluated by traditional linear flutter simulations. Finally, effects of geometric nonlinearity and large deformation on flutter characteristics of flexible and high-aspect-ratio wings were explored by using the present method. The present method can help to understand aeroelastic stability characteristics for such high-aspect-ratio wings.

Analytical approach for vertical floor acceleration of regular RC frames under earthquake excitation

Vertical floor acceleration (VFA) analysis arises as an important issue for seismic design of floor-attached nonstructural components (e.g., ceilings). However, to date, estimating the VFA is hardly accessible in the literature. In this paper, an analytical method is proposed for the VFA of regular RC frames. Here “regular” means the frame has uniform spans along each principal direction, so the structure can be represented by a single-span analogy. Firstly, the fundamental frequency, modal mass, and modal participation factor of a clamped floor slab are analyzed based on the classic thin-plate theory. Then, the dynamic properties of the clamped floor slab are adjusted to account for the effect of the flexible beam restraints (non-clamped). According to the adjusted dynamic parameters, the beam-restrained slab is substituted by a single-degree-of-freedom system, and is assembled with the column-beam system to form the global dynamic model for the structure. Based on the assembled model, the analytical process for the VFA is presented. The feasibility of the model is validated using the finite element modelling (FEM) method. The vertical dynamic properties and the peak VFA of a single-, 3-, 6-, and 9-story frame are computed using the FEM and the proposed analytical approach. Results show that the VFA obtained from the analytical approach is close to the FEM outcomes. Furthermore, important features of VFA are revealed by the computation. It is shown that the VFA could be 10 times as large as the peak vertical ground acceleration. A larger VFA appears at the higher stories, yet the relationship between the VFA and the height is nonlinear because of the effects of the higher-order modes.

Comparative Study of Seismic Acceleration Amplification Models for RC Frame Structures

As the current aspect, the nonstructural components (NSCs) linked with the structures are more affected during the seismic motion. It causes not only loss of the economy but also affected life. The various codal provision has been available for minimizing the damages of primary components, but for NSCs, a minimal requirement is functional. So that more investigation is required for understating the behavior of NSCs during the seismic motion. The research aims to understand the behavior of acceleration demand on NSCs in a building. Structures subjected to inertia forces due to earthquakes experience damage of nonstructural components (NSC). The inertia force acting the NSCs are related to acceleration amplification factor. For obtaining the peak horizontal floor acceleration with respect to tectonic ground motion, these factors are used. In this paper, mathematical models of the acceleration amplification factor defined as the peak floor acceleration with respect to peak ground acceleration, given by previous researchers, has been compared. For this 2,4,6,8 and 10 storey moment-resisting frame models considering 29 ground motion data ranging between 0.1g to 0.2g, is analyzed using linear time history method. The supports of the models are considered fixed. The ETABS software is used for the analysis of the models. To analyses the models, the modal mass participation ratio plays a significant role. ASCE 7-05 defines that the structure should be investigated and designed when the model mass participation ratio is equal to or more than 90 per cent. Based on the results, a comparison of the reported models is made. There is a strong need for further research to refine the models for the realistic prediction of acceleration amplification factor.

A methodology for sensor number and placement optimization for vibration-based damage detection of composite structures under model uncertainty

Structural health monitoring techniques for composite structures are dependent on the data acquired from sensors; thus, optimal sensor network design is important to provide adequate and reliable information. This paper presents a novel framework for optimizing the number of sensors and sensor placement under model uncertainty for vibration-based damage detection in composite structures. The number of target vibration modes to be identified is first determined, based on the sum of modal effective mass fractions, to sufficiently capture dynamic responses. Since any point on the structure can be a candidate sensor position (causing a large design space), a modal kinetic-energy-based index is proposed to narrow the design space. Design objectives simultaneously minimize the number of sensors and the mean and standard deviation values for the root mean square error of off-diagonal terms in the modal assurance criterion matrix. The nondominated sorting genetic algorithm II is adopted to solve this problem. Monte Carlo simulation (MCS) is applied to evaluate the latter two objective functions. To reduce computation costs, real performance evaluations in MCS are replaced with Gaussian process regression models. To validate the optimized sensors, an optimization-based delamination detection process is applied. Case studies are presented to demonstrate the developed optimization framework.

Operational modal analysis application to support structure identification under rotating machinery unbalance

Rotating machines are an essential part of the majority of the power plants. They have to be extremely reliable to avoid power outages, therefore, it is important to predict and monitor their behavior. It is known that these machines are affected by their support structure, thus it is essential to identify its dynamic behavior. The modal analysis is essential in this task being able to identify modal parameters such as natural frequencies, vibrating modes, natural damping, modal stiffness and modal mass. One of the main challenges is to perform this analysis in the rotating machines during their operation. To do this a technique called Operational Modal Analysis (OMA) can be adopted. This technique is performed with the response of the structure subjected to the inherent excitation of the machine operation and is commonly applied to structures and equipment that cannot be turned off due to the high operating costs involved in such process. Contrary to the Experimental Modal Analysis (EMA), where the excitation has to be measured to obtain the frequency response functions (FRFs), in the OMA techniques only outputs are taken into account. OMA usually demand a long time to acquire all the data, which sometimes takes days or weeks. One way to render it faster, it is using the machine start (ramp-up) as an excitation source. Thus, the main objective here is to apply an OMA approach to a rotating system using the ramp-up excitation aiming to extract the modal parameters of the support structure. In order to ensure the validation of the applied OMA methodology, a comparison with a traditional EMA technique is also carried-out. Accelerometers, mounted on the bearings’ housings and on the supporting structure of a test rig, are used to perform the analysis. It is shown that is possible to obtain a good estimative of the modal parameters of the analyzed structure using OMA techniques near the excitation operation range, even when using a reduced set of sensors.

Resonances of railway bridges analysed in frequency domain by the modal-force-excitation, bridge-transfer and axle-sequence spectra

In this article, the passage of different trains over different bridges will be studied for resonant excitation. The intensity of the resonance will be estimated in frequency domain by using three separated spectra. At first, the excitation spectrum of the modal forces is built by the mode shape and the passage time of the train over the bridge. The second spectrum is the frequency response function of the bridge which include the modal frequency, damping and mass. The third part is the spectrum of the axle sequence of the train. The influences of train speed, bridge length, bridge support, track irregularities, and train type on the resonance amplitudes will be analysed for each of these spectra separately for getting a better insight. A variety of axle-sequence spectra and corresponding rules will be presented for different vehicles and trains. As examples, the passage of a slow freight train over a long-span bridge, a normal passenger train over a medium-span bridge, and a high-speed train over a short bridge will be analysed. Corresponding measurements show the amplification, but also the cancellation of the subsequent axle responses. Namely in one of the measurement examples, the first mode of the bridge was amplified and the second mode was cancelled at a low speed of the train and vice versa at a higher speed.

Fuzzy structure theory, statistical energy analysis, and resonant-frequency-distribution of internal mass

The present talk gives a historical perspective on two early and relatively little- known papers having to do with fuzzy structure theory. The first is a letter to the editor by Lyon titled “Statistical energy analysis and structural fuzzy” (JASA 1995). The second paper is a slightly later 1997 Journal of Vibrations and Acoustics (ASME) article titled “Resonant-frequency-distribution of internal mass inferred from mechanical impedance matrices, with application to fuzzy structure theory.” The present paper seeks to clarify and qualify Lyon's statement, “It appears hat the fuzzy structure theory of structural interaction is highly compatible with the SEA framework.” The second paper clarifies the concept of modal mass and gives a proof that, for a lightly damped closed mechanical system, you can express the mechanical displacement fiield as a sum of natural modes. With each natural mode, one can associate a fixed amount of mass. The mass, moreover. is additive and sums to the total mass of the system. The idea goes back to some earlier work (1963) of Cunniff and O'Hara of the U. S. Naval Laboratory. The theory leads to the concept of modal mass per unit natural frequency bandwidth, and leads to a justification for the SEA assumption that interactions are between motions of natural modes with comparable natural frequencies.

Synthesis of a vector-valued intensity measure for improved prediction of seismic demands in Inter-Story-Isolated (ISI) buildings subjected to near fault ground motions

An optimal Intensity Measure (IM) is key to accurate prediction of the Engineering Demand Parameters (EDPs) in structures subjected to seismic excitations. This study synthesizes a structure-specific, vector-valued IM for assessing the EDPs in Inter-Story-Isolated (ISI) buildings under near-fault (pulse and non-pulse type) ground motions. The synthesis is inspired by the comparable modal masses in the fundamental and another higher (generally second) mode in ISI buildings. The synthesis accommodates the dual mode participation by employing the respective pseudo-spectral accelerations Spa and the spectral shape (‘epsilon’ε) parameters in the proposed IM as components. A suite of pulse and non-pulse type motions are employed for the synthesis and subsequently fitting an IM vs. EDP regression model. Thereafter, the “Efficiency” and “Sufficiency” analysis are conducted for validation. The EDPs are obtained by non-linear dynamic analyses on alternative building frames with High Damping Rubber Bearing (HDRB) based ISI systems. A Principal Component Regression (PCR) is employed for accommodating the multi-collinearity in the IM. The choice of the Principal Components (PCs) adopts a leave-one-out cross-validation approach. The proposed IM is shown to offer higher Efficiency and Sufficiency compared with the existing non-structure-specific (Peak Ground Acceleration, Velocity, Displacement, Arias Intensity, Cumulative Absolute Velocity, Characteristic Intensity, Specific Energy Density etc.) and structure-specific (Acceleration/Velocity Spectrum Intensity, Housner Intensity, Pseudo-spectral acceleration at fundamental time period etc.) IMs. Higher Efficiency is also noted under the pulse type motions comparing the non-pulse ones. The IM is more efficient in predicting the Inter-Story Drift Ratios (IDRs), Total Drift Ratios (TDRs) than the Peak Floor Accelerations (PFA) and Bearing Displacements (PBD). The proposed IM is shown to be unbiased and robust.

Modal-Based Ground Motion Selection Method for the Nonlinear Response Time History Analysis of Reinforced Concrete Shear Wall Structures

This paper presents a modification of the modal-based ground motion selection (MGMS) method for improving the reliability of the nonlinear response time history analysis (NLRHA) of reinforced concrete (RC) shear wall structures. The original MGMS procedure quantified the impact of frequency content combinations in the time domain (FCCTD) of input ground motions (IGMs) on the seismic response of building structures using the level of interaction of the first three modes induced by IGMs. However, previous research found that the first two modes have far larger modal mass coefficients than those of higher modes and dominate the vibration of the RC shear wall structures with a symmetric plan. Therefore, the MGMS procedure should be modified by employing the interaction of the first two modes induced by IGMs to properly account for the effect of the FCCTD of IGMs on the seismic response of structures. In the MGMS procedure for RC shear wall structures, seven IGMs that caused the most significant interactions of the first two modes were selected from a suite of twenty seed IGMs, which were chosen with a conventional spectra-matching-based IGMs selection procedure for the NLRHA of the structure. A comprehensive case study involving three RC shear walls with different heights was conducted to investigate the capability of the MGMS in selecting suitable IGMs for the NLRHA of RC shear wall structures. Sets of seed IGMs were selected, adopting conditional mean spectra and design spectra as the target spectra. It was found that the seismic demands computed using MGMS selected IGMs can ensure a more reliable and reasonable computation of seismic demands compared with conventional spectra-matching-based IGMs selection methods.