Modal Strain Energy Research Articles

Analysis and optimization of the dynamic response characteristics of aircraft cargo rack

In order to effectively achieve the optimization design of the aircraft cargo rack, based on finite element modal simulation, the structure was redesigned and analyzed using two schemes of surrogate model size optimization and topology optimization, ensuring the strength requirements while improving the natural frequency and reducing the weight. According to the modal shape of vibration, additional bridge structures were added at the weak points to improve the dynamic stiffness of the structure. According to the optimization design requirements, the response surface function was constructed, and the particle swarm optimization algorithm was applied in the size optimization and surrogate model solution. A multi-objective optimization model was established for flexibility and low-order natural frequencies, and topology optimization was carried out in HyperWorks. The structural dynamic modification of the topology optimization model was performed using the modal strain energy analysis method. The research results show that both optimization methods can achieve good lightweight design. The static performance of the optimized structure is stable, and the overall modal frequency is improved.

A novel damage index for crack identification of a drilling riser during deployment based on the modal vibration energy flow

Early detection of structural damage especially small cracks in marine deepwater drilling risers is of paramount importance. Small cracks are always hard to detect because of weak vibration signals if using traditional damage indices, such as natural frequencies and mode shapes including modal displacements, cross-section slopes, and curvatures. Especially when the deepwater riser is during deployment, the variable suspension riser length and strong sea environment noise make the small crack identification more difficult. To address this problem, this study formulates a new concept of damage detection by integrating the vibration energy flow theory into the vibration-based damage detection (VDD) technique. A novel damage-sensitive feature (DSF) named modal vibration energy flow (MVEF) is established for detecting and locating the small cracks in deepwater drilling risers. The capability of the approach is verified by using the same riser model and the numerical results in the literature. The sensitivities versus crack positions and depths, variable suspension riser length, and sea noise are studied in detail. Results show that the proposed index MVEF is more sensitive than the classic traditional DSFs, i.e., modal slope, modal strain (or curvature), and modal strain energy. In total, the MVEF approach can accurately identify the small cracks and is robust against noise interference, suitable for detecting and locating small cracks in the deepwater drilling riser during deployment.

Damping optimization of a fully viscoelastic structure with enforced mass reduction

Current damping methods employed in industry, such as Constrained Layer Damping (CLD), all require the introduction of additional mass and a secondary material to the structure. In transportation industries, this weight addition is often correlated with an increase in operational costs. Additionally, in applications with large temperature changes, such as in space, the secondary material introduces an additional source of stress during thermal expansion and contraction. This work presents a methodology to significantly improve the damping performance of a fully viscoelastic, single material structure while also enforcing a mass reduction. The work expands upon the modal strain energy (MSE) method to calculate the damping performance of a fully viscoelastic structure and develops a novel weighting scheme to make the optimization more robust. The methodology is then implemented on a technology demonstration thermoplastic lunar rover. This implementation demonstrates the ability to optimize a fully viscoelastic structure to significantly improve the damping performance while also achieving a large decrease in mass. The implementation also demonstrates the robustness of the weighting scheme as it allows the natural frequencies to shift between iterations. The skin thickness of the rover’s base panel was optimized. After optimization, the base panel of the rover achieved a 20% damping improvement for Mode 1 with a 9% mass reduction. The skin thickness of the full rover was optimized and achieved a 15% damping improvement for Mode 2 with an 11% mass reduction.

Vibration based dual-criteria damage detection method using deep neural networks in highway bridges with steel girders

This article introduces a new method for assessing the damage in steel girders of highway bridges using deep neural networks. The method uses modified forms of modal strain energy damage index and modal flexibility damage index to train the neural network and prevent unsafe decisions. The neural network is trained using damage indexes achieved from numerical simulations of the bridge with different damage scenarios. Three types of neural networks, including convolutional neural network (CNN), Long short-term memory (LSTM) neural network, and conventional artificial neural network (ANN) are compared to achieve the best performance. The proposed method overcomes previous detection problems such as false-positive indications, limited damage locations, and scenarios, and insufficient accuracy in cases with multiple damage scenarios. The results show that the proposed method and CNN can accurately identify unspecified damage locations and severity in multi-span highway bridges. The new training method of the CNN deep neural network systems overcomes some shortcomings in ANN, such as being time-consuming, having a low convergence rate, and experiencing data overfitting. Additionally, the CNN training scheme can limit the need for massive amounts of input data and increase the speed and accuracy of network training, especially in multiple damage scenarios.

Two-stage structural damage detection using modal strain energy and natural frequencies: Numerical and experimental study

Two-stage structural damage detection using modal strain energy and natural frequencies: Numerical and experimental study

Structural damage identification based on dual sensitivity analysis from optimal sensor placement

Structural damage identification (SDI) methods using incomplete modal information can avoid the extension for unmeasured degrees of freedom, but the absence of essential damage information often leads to the failure of SDI. To address this problem, a novel SDI method based on dual sensitivity analysis and optimal sensors placement technique is proposed in this study. Firstly, in the optimal sensor placement technique, an improved eigenvector sensitivity method combined with weighted modal kinetic energy is proposed, which enables the acquisition of eigenvector information related to damage sensitivity, and incorporates it into the modal strain energy sensitivity matrix to obtain the dual sensitivity analysis matrix. Then, the sparsity of structural damage is considered, and the L1 sparse regularization is selected and introduced into the dual sensitivity analysis damage equation for better SDI results. Finally, to assess the effectiveness of the proposed method, a series of numerical simulations and experimental verifications were carried out under different structural damage scenarios. The results indicate that the proposed method can efficiently localize and quantify the structural damage with minimal modal information in one single step.

Application of Modal Strain Energy Analysis to Localize an Added Mass on an Aluminium Plate.

The modal strain energy method is a vibration-based damage detection method that allows the use of passive measurements. The method is based on the measurement and analysis of the modal response of the structure under investigation. The aim of this work is to investigate the application of this method to detect and localise a local change in a structure using acoustic measurements in a fluid around the structure. Firstly, the modal strain energy is presented. The technique is based on the analysis of the modal shapes of undamaged and damaged samples obtained by operational modal analysis. The application of modal strain energy to off-contact acoustic measurements is then discussed. The method is used to detect and locate a local change (an additional mass) in an aluminium plate subjected to a mechanical force. The study begins with numerical simulation using finite element models, followed by experiments on the aluminium plate.

Multiscale simulation and experimental studies on modal damping of ultra‐thick CFRP laminates

AbstractThe vibration characterization of ultra‐thick laminates widely used in aerospace and marine industries was different from that of thin laminates. However, modal testing and simulation methods were generally limited to relatively thin laminates. To explore the vibration behavior of ultra‐thick laminates, a novel multiscale simulation technology based on the representative volume modal strain energy (RVMSE) method is presented for predicting modal damping in this paper. The adaptive Greedy‐Based Generation (GBG) algorithm is used to create a 3D random distribution of fibers for composites. Modal shape information of the structure is obtained according to the Lanczos algorithm, which is used as an input parameter for the microscopic model. This is followed by homogenization based on the volumetric analysis performed on representative volume elements (RVEs) to determine the strain energy in six directions. The calculation of modal damping is performed by using the modal strain energy (MSE) method and the damping properties of the six directions. The fast rate of convergence and high accuracy of the method are demonstrated through different examples. The vibration response predictions produced by novel RVMSE methodology are shown to closely match experimental measurements, providing scope to expand the application of this approach to more complex, ultra‐thick laminate components.Highlights The RVMSE method uses a higher level of homogenization to overcome the limitations of the traditional MSE method for calculating the damping of ultra‐thick CFRP laminates. The modal parameter error is controlled to less than 10%, and the experimental results fill the gap of the damping data of ultra‐thick CFRP structure. The proposed RVMSE model improves the accuracy of dynamic response prediction for ultra‐thick laminates.

Modal characteristics analysis and vibration control of long-span cable-stayed-suspension hybrid bridge based on strain energy method

The research on the modal characteristic analysis of long-span bridges is crucial for vibration analysis and control, yet literature regarding the modal characteristics of long-span bridges remains limited. This study thus aims to introduce a strain energy-based damping model to estimate the modal damping of long-span cable-supported bridges. Two different systems of cable-supported bridges are analyzed, and the strain energy proportions and modal damping ratios of various substructures for each mode are calculated. Based on the analysis of modal strain energy results, a strategy to control the vibration of long-span bridges is proposed and validated using the finite element methods. The results indicate that the main girder exhibits the highest strain energy proportion in low-order lateral bending modes, while it is the main cable in low-order vertical bending modes. Different substructures in higher-order modes contribute to the strain energy in varying proportions. For a specific mode, increasing the material damping of the substructure with the highest strain energy proportion effectively suppresses the vibration amplitude of the main girder in that mode. Additionally, installing V-shaped damping cables to control the vibration of substructures with higher strain energy proportions effectively suppresses the vibration of the main girder.

Combining iterative modal strain energy method with BEM-SEA to predict structural noise from railway composite bridge damped with CLD

ABSTRACT This paper presents a combined method to predict structural noise from railway composite bridge damped with constrained layer damping (CLD), in which the frequency-dependent properties of the viscoelastic material are accurately considered through the iterative modal strain energy (IMSE) method. To efficiently determine the forces transmitted to bridge, a simplified vehicle-track coupling model is proposed. Taking 200 Hz as the boundary frequency, the IMSE-boundary element method (BEM) and the IMSE-statistical energy analysis (SEA) are used in the frequency range of 20 ~ 200 Hz and 200 ~ 2000 Hz to realize the full-band noise prediction. Then, the on-site noise tests of a three-span railway composite bridge are carried out to verify the proposed method. Finally, the influences of the key design parameters of CLD on noise reduction are discussed, so as to provide reference for the research and application of CLD in railway bridge engineering.

Modeling of flexible bevel gear rotor systems: Modal and dynamic characterization

Bevel gears, a crucial part of aircraft transmission systems, are more susceptible to wheel body vibration issues as lightweight requirements rise. In the past, the gear wheel body was often considered rigid while assessing the dynamic properties of gear systems. Constructing a bevel gear model with a thin-walled structure might not be appropriate for this modeling technique; this research suggests a dynamic model that considers the flexibility of bevel gears. The web and teeth structure of the gear are preserved by realistic modeling using three-dimensional hexahedral components. The component mode synthesis (CMS) approach reduces the model order for increased computational efficiency. To confirm the accuracy of the modeling method, the modal frequencies and vibration shapes of the proposed model single-gear shaft are compared with results from experiments and ABAQUS. By contrasting ABAQUS system-level meshing modal frequencies and vibration shapes, the accuracy of the system model assembly is further confirmed. The model examines the impact of bevel gear flexibility on the modal frequencies, modal vibration shapes, and system dynamic properties. The mode shape diagram at dangerous modal frequencies found using the modal strain energy technique and the vibration displacement cloud maps at resonance speeds computed using the Newmark-β method are mutually verified, and this demonstrates that lightweight bevel gears are more susceptible to excitation due to nodal diameter type vibrations. Proposed and traditional models anticipate substantially different resonance speeds since the traditional model assumes that the gear, being a rigid disk, can only excite the shaft's bending mode of vibration. The proposed model provides a more comprehensive description of the dynamic characteristics of bevel gear systems, providing a theoretical basis and optimization tool for the high-performance design, vibration reduction, and noise control of high-speed lightweight gear transmission systems.

Quantum‐Based Combinatorial Optimization for Optimal Sensor Placement in Civil Structures

Over the last decade, concepts such as industry 4.0 and the Internet of Things (IoT) have contributed to the increase in the availability and affordability of sensing technology. In this context, structural health monitoring (SHM) arises as an especially interesting field to integrate and develop these new sensing capabilities, given the criticality of structural application for human life and the elevated costs of manual monitoring. Due to the scale of structural systems, one of the main challenges when designing a modern monitoring system is the optimal sensor placement (OSP) problem. The OSP problem is combinatorial in nature, making its exact solution infeasible in most practical cases, usually requiring the use of metaheuristic optimization techniques. While approaches such as genetic algorithms (GAs) have been able to produce significant results in many practical case studies, their ability to scale up to more complex structures is still an area of open research. This study proposes a novel quantum‐based combinatorial optimization approach to solve the OSP problem approximately, within the context of SHM. For this purpose, a quadratic unconstrained binary optimization (QUBO) model formulation is developed, taking as a starting point of the modal strain energy (MSE) of the structure. The framework is tested using numerical simulations of Warren truss bridges of varying scales. The results obtained using the proposed framework are compared against exhaustive search approaches to verify their performance. More importantly, a detailed discussion of the current limitations of the technology and the future paths of research in the area is presented to the reader.

Numerical computation of damped vibration and sound radiation for structures having a porous layer sandwiched by double walls with an acoustic black hole

Vibration and noise reduction are important technology to realize comfort products with safe structures. In this paper, we carry out numerical simulation of damped vibration and sound radiation for structures having a porous material sandwiched by double walls. The double walls are consisted of a steel base plate and a steel cover plate. The cover plate in double walls has a Krylov type acoustic black hole. Damping material is on the surface of the black hole. One point in the base plate is excited by white noise. Numerical analysis is performed to clarify changes of vibration transmission from the base plate to the cover plate due to the acoustic black hole using FEM and MSKE method(Modal Strain and Kinetic Energy method) proposed by Yamaguchi et al. Sound radiation from the cover plate is also investigated. The vibration transmission were reduced for the model having acoustic black hole in the cover plate. Vibration energy flows into the black hole in the cover plate. This causes that vibration acceleration of the cover plate is damped effectively. Sound radiation from the cover plate also decreased. This is because high damping and shorter wave length of vibration in the acoustic black hole.

The strain energy in loosening the clamped end of a beam (part I)

Using analytical equations, the paper aims to solve the dynamic behaviour of beams where a clamped end of the beam does not respect the ideal boundary conditions by introducing a weakening coefficient. In the paper, the characteristic equation for determining the eigenvalues and the relationship of the modal function and strain energy are derived. The results show the first six vibration modes for different values of the weakening coefficient which is considered in the clamped end and the evolution of the strain energy.

Structural damage detection based on modal strain energy assurance criterion using adaptive region shrinkage assisted IGOA

The efficiency in high-dimension optimization, premature convergence and noise robustness are common challenges that restrict the application of swarm-based algorithms in structural damage detection (SDD). In order to overcome these limitations, an improved grasshopper optimization algorithm (IGOA) based SDD approach assisted with adaptive region shrinkage strategies is proposed using modal strain energy assurance criterion. Firstly, the effectiveness of GOA in handling SDD is investigated, and an improved version is subsequently introduced with two adaptive region shrinkage strategies: adaptive Lévy flight mechanism and elite opposition-based learning, aiming to achieve more accurate and stable SDD results. Additionally, a novel objective function is defined, combining the frequency change ratio (FCR) and modal strain energy assurance criterion (MSEAC). To assess the performance of the proposed algorithm, a comparative analysis is conducted with four other selected swarm intelligent algorithms and GOAs with individual modification using four CEC benchmark functions. The results demonstrate that the proposed algorithm achieves improved convergence rate and accuracy. Furthermore, the effectiveness and efficiency of the proposed algorithm in SDD are validated through two numerical simulations and an experimental test. The SDD results obtained from both numerical simulations and experimental tests confirm the accuracy and robustness of the proposed method.

A Review on Vibration-Based Damage Detection Methods for Civil Structures

Vibration-based damage detection is a range of methods that utilizes the dynamic response of a structure to evaluate its condition and detect damage. It is an important approach for structural health monitoring and has drawn much attention from researchers. While multiple reviews have been published focusing on different aspects of this field, there has not been a study specifically examining the recent development across the range of methods, including natural frequency, mode shape, modal curvature, modal strain energy, and modal flexibility-based damage detection methods. This paper aims to fill this gap by reviewing the recent application of these methods in civil structures, including beams, plates, trusses, frames, and composite structural members. The merits and limitations of each method are discussed, and research opportunities are presented. This broader review also provides an opportunity for critical comparison across this range of methods. While predominantly reviewing experiment-based studies, this review also considers some numerical studies that may motivate further research.

Damping performance and its influencing factors of wind turbine towers with constrained layer damping treatment

Constrained layer damping (CLD) is proposed as an energy dissipation measure for vibration control of offshore monopile wind turbine towers (OMWTT). The damping performance and influencing factors of OMWTT with CLD treatment are studied in this paper. First, a theory for calculating the first-order modal loss factor provided by CLD for composite structures is derived using the modal strain energy (MSE) method; second, the error of the theoretical formulation is analyzed using the finite element method; and finally, the influence of each parameter of the CLD on the first-order modal loss factor is discussed. The modal loss factor’s temperature dependence is described with the theory’s aid. The modal damping calculation theory proposed in this paper can rapidly determine the optimal design of CLD, considering the influence of multiple parameters and a complex environment, which could be helpful in the efficient vibration reduction of OMWTT.

Conflation of modal strain energy, spectral finite element, and machine learning techniques for damage detection in multi-span steel girder bridges with variable sections

A new approach is proposed to detect micro and small damages in multi-span bridges constructed with variable sections by combining modal strain energy and spectral finite element through the use of machine learning techniques. The traditional finite element methods are inefficient in detecting and estimating structures' micro-damages. Therefore, wave propagation-based methods must be applied. Micro-damages can be modeled through the spectral finite element method, widely adopted in wave propagation simulation. Among the frequency-based methods used in damage identification, the modal strain energy is more sensitive, especially in complicated structures. However, this method is difficult to apply to steel girders with variable sections and different support conditions. By combining the modal strain energy and the spectral finite element and applying the support vector regression method, the location and severity of damage in steel girders could be accurately identified to overcome the difficulties of detection in complicated elements. To improve the ability of the support vector regression method, in the damage severity estimation, it was combined with feature selection. To evaluate the proposed method's ability, first, an element of the beam- type, with the characteristics of a spectral finite element, is defined in the OpenSees software. To assess the accuracy of the defined element in detecting micro-damages, a tested numerical model was adopted to measure the accuracy of the provided element. Next, to detect small damages, the model of the steel girder bridge with the defined element was prepared, and the modal properties of the structure were extracted. Due to the change in cross-section along each girder, the modified modal strain energy-based damage index (β) equation was used in the subject model. By applying the damages of different severities in steel girders in single and multiple damage scenarios, the modified damage index β was calculated. With the damage indexes calculated in the different scenarios and applying the machine learning method, the severity of damage was estimated. The obtained results indicate that this proposed method is accurate and satisfactory for detecting and estimating micro and small damages with high accuracy in bridges with variable section girders.

Crack detection in reinforced concrete beams under various loadings using the modal strain energy method and confusion matrix model

In this study, a damage detection method for reinforced concrete (RC) beams using the modal strain energy (MSE) method combined with a confusion matrix model is proposed. This method is used for identifying the crack zone position and length of RC beams under various loadings. The beam is modelled by ANSYS APDL software. To prove the finite element model’s validity, the static properties of the model are compared with experimental data and theoretical calculation. From the natural frequencies and mode shapes at different load levels, a damage index is calculated using the MSE method. The crack zone is detected by comparing the damage index with a proposed damage threshold. Then, the damage detection method’s accuracy is evaluated by the confusion matrix model. Finally, the results from this study show that the proposed method can detect the position and length of the crack zone in the RC beam under various loadings with high accuracy.

Modelling of thin constrained layer damping treatment applied to composite floor beams

The Vibration Serviceability Limit State (VSLS) due to human dynamic loading is increasingly becoming the sizing criterion for long-span composite floors. To meet this requirement, structural designers usually tend to increase the stiffness or the mass of the floor. This paper studies a damping technology applicable to these floors since the design stage for improving their dynamic behaviour by increasing their damping capacity and avoiding thus over-sizing the floor structure to meet the VSLS. The studied technology is based on a Constrained Layer Damping (CLD) treatment made of a thin viscoelastic (VE) layer integrated between the concrete slab and the steel profile of the floor, along a percentage of the beam length near the supports. Thus, this paper proposes a simplified Finite Element (FE) approach to model this treatment based on using simple SPRING elements for the VE layer and a corrected version of the modal strain energy method for damping estimation, avoiding thus the use of complex modal analysis. The proposed approach is used to assess the additional damping ratio provided by the CLD treatment. The accuracy of this approach has been validated by comparing it with detailed FE models and widely accepted analytical formulations considering different percentages of the beams’ length treated with CLD. Finally, an application example has been performed with CLD-treated and untreated single-spanning composite floors, showing: i) CLD-treated floors have a better dynamic performance, and ii) CLD technology enables reducing the amount of steel needed to design lightweight floors especially sensitive to vibration.