Modal Strain Energy Research Articles

Vibration and damping of carbon fiber reinforced polymer orthogonal lattice truss sandwich panels manufactured by a new manufacturing process

A new method of fabricating carbon fiber reinforced polymer (CFRP) orthogonal lattice truss sandwich panels is proposed. Inner trusses are inserted into outer trusses. Three structures are prepared using different adhesives: epoxy resin, ethylene–vinyl acetate copolymer (EVA), and nitrile butadiene rubber (NBR). The mode shapes, natural frequencies, and loss factors of the structures are tested and predicted using the finite element modal strain energy method with a solid model and two shell models, respectively. The shell stiffness matrixes are calculated using representative volume element (RVE) method and analytical method. The results show that these three theories can accurately predict the sandwich panels with epoxy or EVA adhesive, while the sandwich panel with rubber layer cannot be accurately predicted. The strain energy composition, shell stiffness matrices, influence of node offset and influence of adhesive layer thicknesses are studied. The EVA adhesive improves the loss factors of the structure within an acceptable reduction of natural frequency.

Multi-type dynamic load identification algorithm in continuous system: A numerical and experimental study based on SSM-Newmark-β

Dynamic load identification based on structural responses is an important problem in the field of engineering and plays an important role in the condition assessment of mechanical structures. Current popular load identification methods such as the state-space method (SSM) and the Green's kernel function method (GKFM) are implemented on discrete systems with outstanding performance, but when dealing with complex continuous systems, there are some limitations such as low efficiency and inaccuracy. In this paper, a continuous system load identification algorithm based on SSM and Newmark-β is proposed for the first time. Using modal coordinate transformation and modal truncation methods, the number of infinite vibration differential equations of a continuous system in physical space are converted to a finite number of vibration differential equations in modal space, where the modal truncation order and the optimal layout of the sensors are combined by modal strain energy. The Newmark-β method in modal space is derived and thus combined with SSM to obtain a load identification model Y=HF called SSM-Newmark-β method, which reduces the size of the transfer matrix H. The solution time of the proposed algorithm is 0.38 s for continuous systems, which is rather shorter than that for discrete systems. Furthermore, the simulations show that it has better accuracy and noise immunity than SSM and GKFM in the identification of sinusoidal load, impact load, and random load. The effect of time step is also discussed which reveals that the larger time step has less effect on the proposed algorithm. An experimental study is carried out on a cantilever beam system. The result verifies that the SSM-Newmark-β algorithm has better accuracy in load identification for the continuous system. This research provides a new sight for the real-time identification of dynamic loads for complex structures.

Free vibration and damping characteristics of carbon-fiber-reinforced sandwich cylindrical shells with 3D reentrant auxetic core

This article investigates the free vibration and damping characteristics of carbon fiber-reinforced sandwich cylindrical shells with 3D reentrant auxetic cores (3D RSCSs). Finite element analysis based on the modal strain energy method is utilized for simulated predictions, while a theoretical model based on the Rayleigh-Ritz method and third-order shear deformation theory (TOSDT) is used for theoretical predictions. Through a combination of hot press molding and interlocking assembly, all-composite 3D RSCSs specimens are manufactured. The modal characteristics of 3D RSCSs are obtained by hammer excitation modal tests. The prediction for modal properties shows good agreement with the experimental tests. Furthermore, the influences of fiber ply angles and geometric parameters on the natural frequency and damping loss factor are thoroughly investigated, which could be helpful to guide vibration analysis of lightweight metamaterials cylindrical shells with negative Poisson’s ratio and promote its engineering application in vibration reduction.

An efficient model for predicting complex delamination front of elastic coupling laminates

This work proposes a simple and efficient model to predict the variable crack front with any shape. The model contains a propagation criterion which defines the local growth direction of the delamination crack front by the vector perpendicular to the connection line of two adjacent mesh points. The angle between this vector and the pre-crack direction is calculated by the coordinates of two delamination front points. Crack front can be obtained by the local direction changes of the historical crack front. This model avoids the computing time caused by a high-fidelity finite element model. Its applicability is verified for composite laminates without coupling and with different couplings. The predicted crack front shows good agreements with the numerical results obtained by a high-fidelity FE model with refined mesh. Factors controlling the crack front shape are further discussed by analyzing strain energy release rate and mode mixture distribution at the crack front.

Damage detection of wooden beams based on the modal strain energy change and evidence theory

A damage detection and localization method for wooden beams was proposed based on the modal strain energy (MSE) change and evidence fusion. The fused damage indicator was deduced using the first three mode shapes of the wooden beams before and after damage. The finite element modal analysis of the free-supported undamaged and damaged wooden beams with different damage severities at one or two locations was performed. The first three mode shapes were extracted from the corresponding modal analysis, with which the damage indicator based on the MSE change and the fused damage indicator of each damage case were computed. The simulation results show that the fused damage indicator accurately detected and located the damage with different severities at one or two locations. Finally, the modal test was completed using the same damage cases as the finite element simulation. The frequency functions of the whole beam were first obtained, with which the first three experimental mode shapes were then acquired, and the damage indicator based on the MSE change and the fused indicator were further computed. The test results verified the validity and reliability of the proposed damage indicator.

Modal identification of structures with a dynamic behaviour characterised by global and local modes at close frequencies

Identification of modal parameters of a space frame structure is a complex assignment due to a large number of degrees of freedom, close natural frequencies, and different vibrating mechanisms. Research has been carried out on the modal identification of rather simple truss structures. So far, less attention has been given to complex three-dimensional truss structures. This work develops a vibration-based methodology for determining modal information of three-dimensional space truss structures. The method uses a relatively complex space truss structure for its verification. Numerical modelling of the system gives modal information about the expected vibration behaviour. The identification process involves closely spaced modes that are characterised by local and global vibration mechanisms. To distinguish between local and global vibrations of the system, modal strain energies are used as an indicator. The experimental validation, which incorporated a modal analysis employing the stochastic subspace identification method, has confirmed that considering relatively high model orders is required to identify specific mode shapes. Especially in the case of the determination of local deformation modes of space truss members, higher model orders have to be taken into account than in the modal identification of most other types of structures.

Effect of CNTs on Dynamic Performance of Carbon Fiber Composite Boring Bar

In this paper, through the secondary development of the finite element software ABAQUS, we try to add different contents of CNT to the CFRP composite boring bar, and establish the finite element models with different CNT contents. Firstly, on the basis of the classical laminated plate theory, combined with the composite damping loss factor model and finite element analysis method, an improved numerical model of CFRP hollow shaft damping based on inverse deviatoric transformation is adopted. Secondly, the Lanczos method was used for modal analysis, and the natural frequencies, vibration modes, stress and strain components under different fiber orientation angles (0°, 30°, 45°, 60°, 90°) and different CNT content structure constraint modes were extracted. Combined with the finite element method, the damping numerical model based on modal strain energy is established, and the damping loss factor calculation program based on strain energy is compiled by using the powerful calculation ability of MATLAB. The extracted strain component data are brought into the compiled damping loss factor calculation program, and the damping loss factors under different modes can be calculated.

Role of Dynamic Response in Inclined Transverse Crack Inspection for 3D-Printed Polymeric Beam with Metal Stiffener.

This paper aims to quantify the relationship between the dynamic response of 3D-printed polymeric beams with metal stiffeners and the severity of inclined transverse cracks under mechanical loading. Very few studies in the literature have focused on defects starting from bolt holes in light-weighted panels and considered the defect's orientation in an analysis. The research outcomes can be applied to vibration-based structure health monitoring (SHM). In this study, an acrylonitrile butadiene styrene (ABS) beam was manufactured through material extrusion and bolted to an aluminium 2014-T615 stiffener as the specimen. It simulated a typical aircraft stiffened panel geometry. The specimen had seeded and propagated inclined transverse cracks of different depths (1/1.4 mm) and orientations (0°/30°/45°). Then, their dynamic response was investigated numerically and experimentally. The fundamental frequencies were measured with an experimental modal analysis. The numerical simulation provided the modal strain energy damage index (MSE-DI) to quantify and localise the defects. Experimental results showed that the 45° cracked specimen presented the lowest fundamental frequency with a decreased magnitude drop rate during crack propagation. However, the 0° cracked specimen generated a more significant frequency drop rate with an increased crack depth ratio. On the other hand, several peaks were presented at various locations where no defect was present in the MSE-DI plots. This suggests that the MSE-DI approach for assessing damage is unsuitable for detecting cracks beneath stiffening elements due to the restriction of the unique mode shape at the crack's location.

On the dynamic behavior interpretation of sandwich beams with axially graded face sheets and magnetorheological core using modal strain energy approach

On the dynamic behavior interpretation of sandwich beams with axially graded face sheets and magnetorheological core using modal strain energy approach

Modal strain energy based enhanced approaches for damage detection and severity estimation

Structural health monitoring (SHM) has been utilized to assess structural deficiency for preventing the invisible failure turning into collapses. Damage localization and severity assessment based on vibration-based characteristics have received considerable attention in civil and engineering fields during recent decades. This study presents a modal strain energy (MSE) based damage detection of a beam-like system. Particularly, based on the performances of existing MSE based damage indices (DIs), a robust and fast technique, called averaging scheme is developed. Observing from the two original DIs that one of them leads to underestimations while overestimations are witnessed using the other one when estimating damage severity, the average of their severity estimations absolutely is supposed to result in better anticipations. Furthermore, another MSE-based updating procedure that was also established based on the original method to reach more accurate predictions is also improved in this study. However, the updating technique considers only the fundamental mode while higher modes are ignored. It is assumed that damage can be caused by higher modes and therefore accounting for more modes possibly lead to better failure identification. Hence, in this study, a numerical investigation is carried out to examine the feasibility of the averaging scheme’s deployment on a cantilever beam. The contribution of higher modes to the performance of the proposed technique as well as the updating procedure is also evaluated. The numerical validation shows that the proposed averaging scheme is outstanding since it results in damage identification results comparable to that of the updating procedure but more promptly. Furthermore, compared to using only the fundamental mode, the cumulative contribution of higher modes, particularly, the lowest four modes, tremendously leads to more accurate damage identification, especially under noisy conditions.

Free Vibration Characteristics of CFRP Laminate with One-Dimensional Periodic Structures.

This paper proposes an approach of stacking prepreg periodically for carbon fiber-reinforced polymer composites (CFRP) laminate. This paper will discuss the natural frequency, modal damping, and vibration characteristics of CFRP laminate with one-dimensional periodic structures. The damping ratio of CFRP laminate is calculated using the semi-analytical method which combines modal strain energy with the finite element method. The finite element method is used to calculate the natural frequency and bending stiffness which are verified with experiments. The numerical results of the damping ratio, natural frequency, and bending stiffness are in good agreement with the experiment results. Finally, the bending vibration characteristics of CFRP laminate with one-dimensional periodic structures and traditional CFRP laminate are investigated with experiments. The finding confirmed that the CFRP laminate with one-dimensional periodic structures exists band gaps. This study provides theoretical support for the promotion and application of CFRP laminate in the field of vibration and noise.

Nonlinear vibration characteristics of composite pyramidal truss sandwich cylindrical shell panels with amplitude dependence

Recently studies on the bending, compression, buckling, and other static issues of composite pyramidal truss sandwich cylindrical shell (CPTSCS) panels have been reported. However, rare literature has explored the nonlinear vibration characteristics of the CPTSCS panels. In this paper, their amplitude-dependent vibration properties are studied both experimentally and theoretically. First, a fabrication flowchart is proposed to obtain such panel specimens, and a pulse excitation method via a hammer and sweeping frequency and fixed excitation techniques provided by a base vibration shaker are employed to measure the nonlinear variation of vibration parameters. As a result, the amplitude-dependent vibration phenomenon is confirmed to exist in both the pyramidal truss core and composite skins. After the nonlinear assumptions of Young's moduli, shear moduli, and loss factors of the pyramidal truss core and composite skins are defined based on Jones-Nelson nonlinear material theory, complex modulus method, Gibson equivalent principle, etc., a novel theoretical model is developed to predict the nonlinear natural frequencies, damping ratios, and resonant responses under different base excitation energies, in which the first order shear deformation theory, Rayleigh Ritz variation method, modal strain energy approach, and modal superposition technique are adopted to solve key vibration parameters. The pre-defined amplitude-dependent fitting coefficients that are vital to the completeness of the current model are further identified using the measured frequency and damping data. Also, detailed tests are done to make sure that both the proposed model and the predictions are correct. Finally, the effects of critical geometric and material parameters of the CPTSCS panels on the amplitude-dependent vibration characteristics are evaluated based on the calculated dynamic results, with some practical suggestions being refined for improving the vibration suppression capability of such advanced composite structures.

Damping evaluation of an eight-story steel building with nonlinear oil damper under strong earthquakes

Fluid viscous damper has been applied widely for energy dissipation and shock absorption in dynamic structural systems, specifically the oil damper. Nevertheless, there's an issue of precisely incorporating shaft bearings and pressure sealings for oil dampers, which restricts its wide application in new or existing structures. A type of nonlinear oil damper with viscoelastic polymer packing soft links is posed and investigated to allow for easy production. To explore the effectivity and actual performance of the nonlinear oil dampers, vibration monitoring system has been instrumented both on the dampers and the building since it was built in 2003, which accumulated huge amount of precious data. A Bayesian based order selection of auto-regressive exogenous model is exploited to the recorded earthquake responses to extract dynamic properties of the passively-controlled 8-story steel building. Thus, damping characteristics of the whole structure can be identified and analyzed. Besides, an analytical model for the nonlinear oil damper is investigated and estimated by particle filter improved with Metropolis-Hastings algorithm, which can be incorporated into the whole structure model for model updating, reliability as well as response prediction. Furthermore, the calculation formulas of the additional effective damping ratio provided by oil damper are deduced based on above analysis using modal strain energy, and damping ratio of the main steel frame structure are also estimated. Taking a set of actual ground motion monitoring data as an example, the proposed method is then exploited to estimate the effective damping ratio of oil damper for each floor.

Modal displacement vs Curvature functions as damage identifier for masonry structures

Identification of crack location and severity is a vital step in assessment of deteriorated structures. The current research addresses the sensitivity of using modal displacement, modal curvature, and modal strain energy functions as Damage Indices (D.I.s) for crack detection. Comparison of these indicators at cracked and undamaged conditions was performed. Firstly, Damage Index (D.I.) method was utilized on synthetic data obtained with the aid of finite element modelling on different flexural elements. The technique was again used to identify cracks for physical scaled-down masonry walls. Three clayey bricks walls with different thicknesses and crack configurations were prepared for this purpose. Each wall was tested in its virgin and damaged states. Formal modal analysis was conducted. It was concluded that all the used D.I.s were accepted as damage indicators. It can also be stated that the relative severity between cracks can be obtained. Numerically, D.I. method was found effective in cases of multiple or inclined cracks. Generally, the identification based on curvature functions, were better than displacement functions for the same number of monitoring points and crack severity. Curvature can’t, however, be easily obtained for sophisticated structures with limited data. Moreover, the detection process became easier as the crack dimensions increased.

The bearing capacity parameter analysis and heat energy storage loss test of concrete composite box girder

In order to study the relationship between the bearing capacity of the structure and the damage degree, the author proposed the bearing capacity parameter analysis and the heat storage loss test of the concrete composite box girder. Taking the five-span prestressed concrete composite box girder as an example, different degrees of damage are simulated by reducing the bending stiffness of different parts, and the modal strain energy method and flexibility difference method are used to diagnose the structural damage. The test results show that for the first span, the sum of the structure can meet the corresponding specification requirements under the condi?tion of dense traffic and less than 20% damage. When the damage is greater than 20%, the first span beam cannot meet the driving requirements. Under general traffic conditions, when the damage is less than 30%, the structure can basically meet the driving requirements, and the second and third spans still have a high safety factor. In the case of 30% damage of the first span, although ? it does not meet the requirements, but RF > 0.9. Each monitoring point has good estimation accuracy, and the error between the maximum temperature occurrence time of each monitoring point and the maximum temperature occurrence time of the mon?itoring point is within ? 10 hours . For continuous composite box girder structure, the flexibility difference method is superior to the modal strain energy method.

An Analytical Solution of the Total Strain Energy Release Rate and Mode Partitioning of a Beam Type Delamination Specimen under High Speed Mixed-Mode Loading

In this work an analytical solution for the calculation of the total Stain Energy Release Rate and mode partitioning of beam type delamination specimen, at crack initiation, under high speed, mixed-mode loading is obtained for the first time. The analytical model is based on the dynamic response of a Mixed-Mode End Load Split type specimen subjected to loading with a constant velocity. The Timoshenko beam theory is used to model the specimen's kinematics and the mode partitioning method used is based on the Virtual Crack Closure Technique. To model the bonded region a method based on Lagrangian multipliers is utilized. The specimen is considered as a waveguide and the waves that are allowed to propagate are analytically obtained. Due to the complexity of the analytical form of the wavenumbers for the bonded region of the specimen, which makes the calculation of eigenfrequencies intractable, a series approximation method is used. The results of the proposed analytical solution are verified using a 2D Finite Element Model. The results show the dependency of the Strain Energy Release Rate and the mode mixity on the eigenfrequencies and the eigenmodes of the specimen rendering the value of the mode mixity highly inconsistent through time.

Structural Damage Detection Using Convolutional Neural Networks Based on Modal Strain Energy and Population of Structures

A convolutional neural network (CNN)-based structural damage detection (SDD) method using populations of structures and modal strain energy (MSE) is proposed. In this study, sufficient samples of the CNN are provided by numerical simulations, and the size of the model can be changed by modifying the coordinates of some nodes, thereby establishing a series of numerical models (i.e., a population). Finally, three groups are investigated, the effects of multiple indices on damage detection based on population are compared. The results demonstrate that the MSE as a damage index is superior to the other indices.

A Hybrid Method for Vibration-Based Bridge Damage Detection

Damage detection algorithms employing the conventional acceleration measurements and the associated modal features may underperform due to the limited number of sensors used in the monitoring and the smoothing effect of spline functions used to increase the spatial resolution. The effectiveness of such algorithms could be increased if a more accurate estimate of mode shapes were provided. This study presents a hybrid structural health monitoring method for vibration-based damage detection of bridge-type structures. The proposed method is based on the fusion of data from conventional accelerometers and computer vision-based measurements. The most commonly used mode shape-based damage measures, namely, the mode shape curvature method, the modal strain energy method, and the modal flexibility method, are used for damage detection. The accuracy of these parameters used together with the conventional sparse sensor setups and the proposed hybrid approach is investigated in numerical case studies, with damage scenarios simulated on a simply-supported bridge. The simulations involve measuring the acceleration response of the bridge to ambient vibrations and train crossings and then processing the data to determine the modal frequencies and mode shapes. The efficiency and accuracy of the proposed hybrid health monitoring methodology are demonstrated in case studies involving scenarios in which conventional acceleration measurements fail to detect and locate damage. The robustness of the proposed method against various levels of noise is shown as well. In the studies considered, damage as small as 10% decrease in flexural stiffness of the bridge and localized in less than 1% of the span-length of the bridge is reliably detected even with very high levels of measurement noise. Finally, a modified modal flexibility damage parameter is derived and used to alleviate the shortcomings of the modal flexibility damage parameter.

Inverse Analysis of Structural Damage Based on the Modal Kinetic and Strain Energies with the Novel Oppositional Unified Particle Swarm Gradient-Based Optimizer

Structural damage inspection is a key structural engineering technique that strives for ensuring structural safety. In this regard, one of the major intelligent approaches is the inverse analysis of structural damage using evolutionary computation. By considering the recent advances in this field, an efficient hybrid objective function that combines the global modal kinetic and modal strain energies is introduced. The newly developed objective function aims to extract maximum dynamic information from the structure and overcome noisy conditions. Moreover, the original methods are usually vulnerable to the associated high multimodality and uncertainty of the inverse problem. Therefore, the oppositional learning (OL) for population initialization and convergence acceleration is first adopted. Thereafter, the unified particle swarm algorithm (UPSO) mechanism is combined with another newly developed algorithm, the gradient-based optimizer (GBO). The new algorithm, called the oppositional unified particle swarm gradient-based optimizer (OL-UPSGBO), with the convergence acceleration feature of (OL), enhances balanced exploration-exploitation of UPSO, and the local escaping operator of GBO is designed to specifically deal with the complex inverse analysis of structural damage problems. To authenticate the performance of the OL-UPSGBO, the complex benchmark set of CEC 2017 is adopted to compare the OL-UPSGBO with several original metaheuristics. Furthermore, the developed approach for structural damage identification is tested using several damage scenarios in a multi-story frame structure. Results show that the developed approach shows superior performance and robust behavior when tackling the inverse analysis of structural damage.

A hybrid IMSE-FE-BE method coupled with RSM for vibro-acoustic analysis and optimization of an I-shaped steel beam damped with constrained layer damping

In this paper, a method for calculating vibration and noise from the I-shaped steel beam damped with constrained layer damping (CLD) was proposed based on iterative modal strain energy (IMSE) method and finite element (FE)-boundary element method (BEM). Then, a series of hammer tests were carried out to obtain the typical vibro-acoustic response samples of a CLD-damped beam. It is shown that the calculated noise and vibration agreed well with the measured results, indicating that the proposed method is effective and accurate. Then, the response surface methodology (RSM) was used to analyze the influence of CLD-structural parameters on the sound radiation characteristics and natural frequency of the damped beam. With the objective of minimizing the acoustic radiation power, a program for finding the optimal CLD-structural parameters was developed based on interior penalty function method (IPFM). Finally, the acoustic response comparisons between the original bare beam and the optimized CLD-damped beam were performed. It shows that the overall sound power level was decreased from 98.12 dB to 80.47 dB, and the overall sound pressure level at measuring point S3-3 was reduced from 78.86 dB to 61.07 dB, demonstrating that the optimization of CLD-structural parameters can significantly improve the acoustic performance of CLD-structures.