Effective Modal Mass Research Articles

Study on Vibration and Failure of Transverse Flow Turbine Based on Fluid–Structure Interaction

During the operation of a turbine, the water level drop can cause vibration and damage to the flow components, severely threatening its stability and reliability. Investigating the impact of operational parameters on the internal flow field and flow structures of tidal turbines under low flow conditions is crucial for peak shaving and deployment of tidal power stations. This paper takes a 24[Formula: see text]MW turbine as the research object, using numerical calculations to analyze the effects of tailwater height on the flow characteristics and structural properties of the unit under low flow conditions. It studies the hydraulic impact on the flow component walls under different operating parameters and verifies the reliability of numerical calculations through vibration and stress tests. The results show that the increase in tailwater level affects the turbine’s flow characteristics, forming large-scale, high-intensity vortices in the internal flow field and causing pressure pulsations near the wall surface. Modal analysis reveals that under different tailwater heights, the maximum modal effective mass exists along the axis of the impeller, with modal frequencies higher than the main frequencies of pressure pulsations. The impeller region corresponds to the turbine chamber wall bearing significant stress, which induces strain. The magnitude of stress and the degree of strain are positively correlated with the tailwater height. The research findings provide guidance for tailwater regulation and stable operation of tidal power stations.

Optimization of column-in-column system based on non-conventional TMD concept

Previous studies showed that the non-conventional tuned mass damper (TMD) with large mass ratio outperforms the traditional one in respect to the structural vibration control efficiency and robustness. The authors recently proposed a novel control system based on the non-conventional TMD concept, namely the column-in-column (CIC) system, which was composed of a primary column, a secondary column and a series of interconnected springs/dashpots. In this novel system, the secondary column connected to the primary one with springs/dashpots could act as a large TMD to attenuate adverse vibration of the primary structure, and its control effectiveness was preliminarily verified through numerical investigations. However, the control robustness was found not sufficient based on the existing optimal formulae in the literature for CIC optimization. This paper presents a new design method for optimizing the CIC system for better harnessing its control effectiveness and robustness in reducing structural response. The CIC system consists of two columns with distributed mass and uniform flexural rigidity, connected by springs along the column height. The effective modal mass and modal stiffness of a specific vibration mode of the system can be straightforwardly calculated by using the Euler-Bernoulli beam theory. Considering the fundamental vibration mode of the system as the target response mode for vibration control, the multiple degree-of-freedom (DOF) CIC is simplified into a two DOF with three springs (2DOF3S) structural model, the design parameters, i.e., the optimal tuning frequency ratio and damping ratio of this system are derived to minimize the displacement response of the primary structure. To demonstrate the proposed design method, the effectiveness and robustness of the CIC system in controlling seismic induced structural vibrations are assessed in both the frequency and time domains. Results show that the derived optimum formulae are applicable for optimizing the TMD system with consideration of the distributed mass and deformation of the mass damper, i.e., a column in this study. The optimized CIC system has good control robustness even if the CIC is mistuned with its design parameters deviate from the optimal values by ±50 %. The conventional TMD system with lumped mass as the mass damper is a special case of the proposed CIC system. The optimized CIC system has favorable control efficiency in mitigating the seismic responses of structures with reduction ratios averagely varying within the range of 15 % ∼ 55 % with a probability of 92.67 %. It is concluded that the proposed method is reliable and can be used for the optimum design and control of the CIC system.

The contribution of higher order modes in the dynamic response of slender vertical structures with application to wind turbine towers

Understanding the contribution of the vibration modes to the response of a tower-like structure subjected to base excitations is crucial for a safe and optimized design. The modal contributions to the structural response are generally assessed through modal participation factors and effective masses; however, relatively recent studies pointed out the variability of the modal contributions depending on the response effect (e.g., top displacement, base shear force, base bending moment). The formulation proposed here derives the shear force and the bending moment at the base of a tower-like structure by combining the influence function technique with the quasi-static equivalent forces technique. The resulting formulation of the tower response relies on the concept of modal contribution factors, which provides a straightforward indication of the modal contributions associated with a given response effect. The proposed methodology is applied to the case of wind turbine towers erected on temporary foundations at the port quayside without rotor nacelle assembly to assess the forces on the foundations due to the seismic loading on the towers. This technique may be of great relevance for assessing the tower integrity during installation and for the design of the temporary foundations at the quayside of harbors in seismic area, also considering the quick expansion of the offshore wind energy in countries prone to earthquakes.

A reconstruction method for structural stress distribution of wind turbine tower using optimised mathematical model

Wind turbine towers experience complex dynamic loads during actual operation, and these loads are difficult to accurately predict in advance, which may lead to inaccurate structural strength assessment during the structural design phase, thereby posing safety risks to the wind turbine tower. Therefore, a reconstruction method for structural stress distribution of wind turbine tower was developed based on modal expansion and linear superposition theory to estimate the full-field stress distribution of a tower, which can be used for online monitoring of structural strength. The dynamic stress distribution of the tower is assumed to be the superposition of several structural modal stress distributions, in the reconstruction method for structural stress distribution developed in this study. The modes with the greatest contribution to the wind turbine structural response were selected based on the modal effective mass, and used for the base functions of an initial mathematical model for the reconstruction of structural stress distribution of the tower, in which many candidate strain gauge locations and directions were considered. Then, the initial mathematical model was expressed as a linear system of equations. Two numerical examples were used to verify the accuracy and stability of the initial mathematical model for the reconstruction of structural stress distribution of the tower, and the reconstruction results indicate that the initial mathematical model combined with the Moore–Penrose inverse algorithm can provide stable and accurate reconstruction results. However, the initial mathematical model uses too many sensors, which is not conducive to engineering applications. Therefore, D-optimal and C-optimal design methods were used to reduce the dimensions of the initial mathematical model, optimise the system of equations, and determine the location, direction and number of strain gauges. Finally, the numerical examples of stress distribution reconstruction show that dimensionality reduction of the mathematical model leads to higher accuracy, in which the C-optimal design algorithm providing a more robust reconstruction outcome.

Definition and calculation method of modal effective mass of asymmetric fluid-structure interaction system for seismic analysis

In this paper, modal effective mass for asymmetric fluid-structure interaction system is defined and equations for its calculation is derived. To establish consistency, modal effective mass in symmetric structure only system is briefly reviewed, followed by a definition of the modal effective mass in asymmetric system. The equations for calculating modal effective mass in asymmetric system are derived by utilizing the properties of left and right eigenvectors. To simplify the equations, the assumption is made that the mass matrix is only affected by the fluid. The simplified equation is then compared to the equation already used in ANSYS. Finally, the validity of the modal effective mass definition and derivation in this paper is demonstrated through a simple example.

Identifying elastic wave polarization and bandgaps in periodic solid media

We present a new computational method to accurately identify the elastic wave propagation modes and polarizations in periodic solid structures and metamaterials. The method uses the eigenvectors associated with each propagating wave solution to calculate the contribution of each translational and rotational component of the total mass-in-motion. We use this information to identify the dominant wave propagation mode by defining a relative effective modal mass vector. Then, we associate each wave solution with its correct polarization by defining a polarization factor that quantifies the relative orientation between the wave propagation and lattice motion directions and provides a positive numerical value between 0 (pure S-wave) and 1 (pure P-wave). Further, we suggest a graphical representational scheme for easier visualization of the wave polarization within traditional dispersion plots. To validate the method, we compare our predictions against previously published results for various elastodynamic problems. Finally, we use the proposed method to analyze the effect of various lattice and structural parameter perturbations on the elastic wave propagation and polarized bandgap behavior of a square planar beam lattice. Our analysis reveals the emergence of previously unobserved dynamic characteristics, including various polarized bandgaps, fluid-like behavior, and ultralow-frequency SH- and SV-bandgaps that extend to 0 Hz. Our proposed method provides an alternative computational approach to the typically employed visual mode inspection technique and provides a robust method for analyzing the elastic wave response of periodic solid media.

A VAM-based equivalent model for random vibration of composite sandwich plate with arrowhead-on cores

The composite sandwich plate with an arrowhead-on core (arrowhead-on CSP) is a new type of composite structure that has the advantages of a low weight, high specific strength, high specific stiffness, and negative Poisson’s ratio. In this study, the equivalent plate properties were obtained using the variational asymptotic method (VAM) to asymptotically analyze the energy functional stored in the unit cell. On this basis, a two-dimensional virtual equivalent model was constructed for random vibration analysis using the pseudo excitation method. To verify the accuracy and effectiveness of the equivalent model, the dynamic behaviors (free and random vibrations) of arrowhead-on CSPs under different conditions were analyzed. The power spectral density (PSD), the root mean square (RMS) values of the lateral displacement, velocity, and acceleration responses under a base acceleration excitation, and the modal effective mass fraction under vibrations were also investigated. Finally, the effects of the layup configuration of the composite facesheets and the geometric parameters of the arrowhead-on core on the dynamic characteristics of the equivalent plate were studied. The study revealed that the equivalent model was very efficient and accurate in free and random vibration analysis, which provided a reference for the dynamic characteristic optimization of arrowhead-on CSPs.

Shake table tests on a reinforced concrete waffle‐flat plate structure with new hybrid energy dissipation devices

AbstractThis paper presents a new hybrid energy dissipation device and investigates experimentally its capability to improve the seismic response of an inherently very flexible structural system: a reinforced concrete waffle‐flat plate structure. The new device combines in parallel within a single device a low‐cost viscoelastic (VE) component and a metallic yielding (MY) component. The device has a gap that prevents deformations on the MY component in the range of displacements caused by wind or low intensity earthquakes, to avoid high‐cycle fatigue damage. The MY component is expected to activate under the design or the maximum credible earthquake, providing the main structure with lateral stiffness, and a reliable and large source of energy dissipation capacity. Six new hybrid energy dissipation devices (energy dissipation system) were installed in a scaled two‐story portion of a prototype RC waffle‐flat plate structure (main structure) designed only for gravity loads, without considering special ductility detailing or capacity design rules for the columns. The VE component of the hybrid energy dissipation devices reduced the translational periods with largest effective modal mass along the horizontal directions X and Y to 60%, and increased the fraction of damping to about 12%. The main structure with the energy dissipation system was subjected to bidirectional shake table tests that represented frequent, design and maximum credible earthquakes. In the tests, the main structure remained basically undamaged under the frequent and the design earthquakes, whereas it suffered minor (reparable) damage under the maximum credible earthquake. The MY component remained undeformed under low intensity earthquakes.

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.

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.

A Compensation Method for Active Phased Array Antennas: Using a strain-electromagnetic coupling model

Physical deformation due to service loads seriously degrades the electromagnetic performance of active phased array antennas. However, traditional displacement-based compensation methods are moderately difficult to use because displacement measurements generally require stable references, which are hard to realize for antennas in service. For deformed antennas, strain information is directly related to their displacement, and strain sensors can overcome carrier platform constraints to measure real-time strain without affecting the antenna radiation-field distribution. We thus present a compensation method based on strain information for in-service antennas. First, the minimum number of strain sensors is determined as the main modal-order-based modal effective mass fraction. According to the modal method and analysis of spatial phase-distribution errors related to strain, a coupled strain-electromagnetic model is established to evaluate antenna performance from the measured strain. The corresponding excitation phase from the measured strain is adjusted to compensate antenna performance. Finally, the method is experimentally validated using an X-band active phased array antenna under the influence of typical deformation conditions for both boresight and scanned beams. The results demonstrate that the presented method can effectively compensate for the performance of service antennas directly from the measured strain information.

Dynamic research of dome structures

In this paper the dynamic responses of discrete single-layer domes are discussed. As objects of the study, computational models of domes have been analysed. These models differ in the type of their boundary conditions, the grid configuration, and in the height of the spheres. The analysis was conducted in two stages: a modal and a spectral analysis. In the modal analysis, a coefficient of the effective modal mass and the type of natural forms of vibration have been observed. Comparison has been made between CQC and SRSS being two different methods for combining modal contributions, as well as between two other methods of combining modal responses in the direction of seismic effects, namely: SRSS method and the “Rule of 30%”. The purpose of the study is to work out the dynamic response of the discrete single-layer spherical domes.

Plate-type acoustic metamaterials with strip masses.

Plate-type acoustic metamaterials (PAM) consist of a thin plate with periodically added masses. Similar to membrane-type acoustic metamaterials, PAM exhibit anti-resonances at low frequencies at which the transmission loss can be much higher than the mass-law without requiring a pretension. Most PAM designs previously investigated in literature require the addition of up to thousands of masses per square meter. This makes manufacturing of such PAM prohibitively expensive for most applications. In this contribution, a much simpler PAM design with strip masses is investigated. An analytical model is derived which can be used to estimate the modal properties, effective mass, and oblique incidence sound transmission loss of PAM with strip masses. For high strip masses (compared to the baseplate), this analytical model can be simplified to yield explicit expressions to directly calculate the resonance and anti-resonance frequencies of such PAM. The analytical model is verified using numerical simulations and laboratory measurement results are presented to demonstrate the performance of PAM with strip masses under diffuse field excitation and finite sample size conditions.

The effects of period and nonlinearity on energy demands of MDOF and E-SDOF systems under pulse-type near-fault earthquake records

The use of the concept of earthquake input energy under far-filed earthquakes and types of internal energy in structures has recently been mentioned to develop the performance-based design method. However, the extension of these studies to near-fault pulse-like earthquakes has been less considered. This paper calculates the applied ratios of energy types in the E-SDOF and MDOF systems and identifies the relationship between them. For this purpose, five steel frames (4, 10, 15, 20, and 30 story steel MRFs with 3-span) were designed, and obtained the E-SDOF structure equivalent to the first mode, using modal pushover analysis (MPA) method. All models were analyzed under 10 near-fault pulse-like earthquake records using nonlinear time history analysis. The results show that the total dissipated energy of the structure (TDE) depends on its nonlinear degree and period. The TDE of the MDOF and E-SDOF systems is equal for long periods, and its size is independent of the design resistance (R) and the degree of nonlinearity. However, in short periods, this ratio is close to the effective modal mass coefficient corresponding to the first mode. The story normalized hysteretic energy ratio is also a function of the height, nonlinear degree and period of the structure.

Numerical and Experimental Analysis of Torsional Vibration and Acoustic Noise of PMSM Coupled With DC Generator

The magnetic field inside a machine is responsible for the mechanical excitation of the stator structure, generating vibrations and thus, audible noise. In this article, the Permanent Magnet Synchronous Motor (PMSM) is driven by using sinusoidal pulsewidth modulation technique and then an investigation (cause and effect) of Acoustic Noise and Vibration (ANV) is presented. An equivalent lumped parametric modeling of end-to-end coaxially coupled shafts between PMSM and DC generator along with effective modal mass and modal participation factor accuracy enhancement technique is presented to predict the torsional vibration. The modal analysis approach is used to analyze the torsional vibration response, which is used to estimate the source of acoustic noise, and a mathematical approach is presented at the end to calculate ANV of electric drives. Theoretical and experimental investigations are carried out on a 1.07- kW, 4-poles, 36-slots, 3-phase PMSM drive. Analytical and numerical results are validated by experimental studies.

Optimal Three-Dimensional Sensor Placement for Cable-Stayed Bridge Based on Dynamic Adjustment of Attenuation Factor Gravitational Search Algorithm

Structural health monitoring (SHM) is essential when detecting damage in large and complex structures in order to provide a comprehensive assessment of the structural health state. Optimal sensor placement (OSP) is critical in the structural health monitoring system, which aims to use a limited number of sensors to obtain high-quality structural health diagnosis data. However, the current research mainly focuses on OSP for structures, without considering the values contributed by different modes to the bridge structure. In this article, an optimal sensor placement method based on initial sensor layout, using the dynamic adjustment of attenuation factor gravitational search algorithm (DGSA), is proposed. The effective modal mass participation ratio is introduced to ensure the validity of the initial data of optimal sensor placement. In view of the insufficient developmental ability of the gravitational search algorithm, the attenuation factor α adjusted dynamically aids the global search in the early iteration and the local fine search in the late iteration. The double coding method is used to apply the DGSA algorithm to OSP; taking cable-stayed bridges as an example, the feasibility of the algorithm is verified. The results show that the improved algorithm has a good optimization ability and can accurately and efficiently determine the optimal placement of sensors.

A numerical insight into stress mode shapes of rectangular thin-plate structures

Thin-plate structures are widely exploited in many areas due to their excellent structural properties. This study numerically investigates the mechanics characteristics of the stress mode shapes (SMSs) in thin plates. First, theoretical basis of the SMSs is concisely illustrated for thin-plate structures. Then, finite element models are constructed in numerical simulations. The SMSs of the flat plate are compared with the conventional displacement mode shapes (DMSs). The modal participation factors (MPFs) are used to extract the predominant SMSs. The SMSs in x-, y-, xy- directions and von Mises stress are evaluated in detail. Based on results of the flat plate, local thickness and elastic modulus modifications are performed to examine the changes in SMSs. Modal assurance criterion (MAC) is utilized to evaluate the modal data. The information of SMSs from the modified plates indicates the powerful capability for detecting the local variations of structural properties. Lastly, modal order determination via modal effective mass is numerically verified for accurate dynamic stress calculation.

Earthquake resistance analysis of structural systems of multi-storey civil buildings

Relevance. Increasing the density of urban population requires the use of optimal structural systems of multi-storey civil buildings, however, despite a large number of studies on the rationality of their application, the question of choosing an assessment of seismic resistance of structural systems of multi-storey civil buildings is still open. The aim of the study. This study aims to determine advantages and disadvantages of structural systems of multi-storey buildings in seismic areas. Methods. The results of comparison analysis of five structural systems (columns grid - 6×6 m, storey height - 3 m, number of storeys - 20) are presented in this article. The structural systems are: frame & tube, frame & core, core & walls, framed core & walls, framed core & tube. The calculation were done according to Building Code 14.13330.2018 for an earthquake of 8 points intensity of MSK-64 intensity scale. The SCAD Office software package was used for modeling and analyzing. The sum of the effective modal masses taken in the calculation was at least 90% of the total mass of the system excited in the direction of the seismic action for horizontal impacts and at least 75% - for vertical impacts. Results. The comparison was carried out according to the following criteria: maximum displacements, maximum compressive and tensile stresses, maximum periods of natural oscillations, maximum accelerations.

Influence of the perforation configuration on dynamic behaviors of multilayered beam structure

The novelty of this paper is to investigates the free vibration, frequency response and modal participation factors of the perforated multilayer microbeam structures using finite element analysis with different hole’s geometry, filling ratio and array of hole. The three squared, rectangular, and circular configurations of perforation are considered through analysis. Elasto-dynamic finite element formulation is implemented. The natural frequencies for the three different perforation configurations at different number of holes are investigated. For better understanding of the dynamic behavior of multilayered perforated beam structure, both modal and harmonic responses are presented and discussed. To specify the most suitable vibrational mode for a certain degree of freedom for base excitation, both participation factor and the associated modal effective mass are presented and analyzed. The obtained results show the remarkable effect of perforation configuration and the number of holes throughout the cross-sectional area on the dynamic behavior of multilayered perforated beam structures. Different boundary conditions are considered through analysis. The obtained results are supportive for the design of perforated beam structures in both macro and micro-scales.

Three-Dimensional Numerical Model for Seismic Analysis of Structures

Response Spectrum Analysis (RSA) and modal combination techniques are widely used to estimate the peak response of structures subjected to earthquake vibrations. This paper presents the numerical modeling and seismic analysis of structures. The response spectra based on Eurocode 8 is implemented for a five storey moment-resisting 3D structure to estimate peak response to earthquake-induced vibration. Eigenvector analysis is carried out to determine undamped free vibration mode shapes and frequencies. The lumped mass matrix, stiffness matrix of the full 3D structure is derived and natural periods, modal shapes, modal participation factors, and effective modal mass ratios are calculated. The structural response in different modes is combined to estimate the total dynamic response. The Square Root of Sum of Squares (SRSS), Complete Quadratic Combination (CQC), and Absolute Sum (AbsSum) rules are discussed and compared. The results of the SRSS and CQC rule for the examined building are almost identical as all cross-correlation coefficients are approximately equal to zero, and the responses of the individual modes are completely uncorrelated. CQC rule is appropriate when the natural frequencies are close to each other. AbsSum method shows an upper bound estimate of the total response since it assumes that all modal peaks occur at the same time. The simulation for numerical modeling and response spectrum analysis (RSA) is implemented in MATLAB® software.