Energy Finite Element Analysis Research Articles

A wave model of high frequency vibrational energy transfer in a wedge-shaped combined plate structure

Wedge shaped combined plate structure (WCPS) is broadly applied in large-sized transport equipment such as aerospace and shipping. However, with the increase of equipment operating running, it is easy to cause high-frequency vibration of structure components. Therefore, studying the energy transfer and vibration response of high-frequency vibration in WCPS is significant for the structural design of aerospace and shipping. The promising method is energy finite element analysis (EFEA). However, the energy transfer coefficient at joint of WCPS is needed in EFEA. The current studies about the energy transfer coefficients are focus on the joint between two uniform thickness plate. But it is some different that getting the energy transfer coefficient for WCPS, because the near-field solve representation for wedge-shaped plate is complicated due to the non-uniform thickness of wedge-shaped plate member in WCPS. In this research, geometric acoustic approximation and an equilibrium equation on both ends of joints were used to derive the equation of the energy transfer coefficient for the WCPS. Then by setting coupling nodes, construction of a coupling matrix to characterize discontinuity of energy density at the coupling position of the WCPS and energy density governing equation of wedge-shaped plates were integrated. In doing so, the EFEA modeling of the WCPS was developed and the energy density distribution on each node of the WCPS could be obtained. Same-sized uniformly coupled structures is analyzed, the vibration energy distribution characteristics of two types of coupling structures were compared. The results show that the energy density value of the wedge plate member attenuate more slowly than that of the uniform plate member due to the acoustic black hole aggregation effect in the wedge plate part, and there is an abrupt change in the energy density value at the joint of WCPS. As a result, the factors influencing high-frequency vibration energy transfer were investigated.

Prediction of the Transient Local Energy by Energy Finite Element Analysis

Energy finite element analysis (EFEA) has been successfully applied to steady-state response prediction over the past three decades. Compared with other energy-based methods, such as statistical energy analysis (SEA), EFEA can consider more local structural information without increasing the computational consumption too much, which makes it attractive. Inspired by the transient local energy approach (TLEA), a general transient energy balance equation was derived by assuming that the plane wave condition is satisfied. The properties of the energy balance equation were studied, and the analytical solutions with different initial conditions were provided. Utilizing the derived transient energy balance equation, transient EFEA is proposed, which has the same advantages as EFEA. A general formula is presented for the energy transmission coefficients of any number of coupled in-plane beams. The present approach was validated using a single beam and a coupled collinear beam structure under unloading conditions. The coupled collinear beams were also investigated using constant and quasi-static input power. The validation results show that TEFEA can accurately predict the local response of the structure. All of these results were compared with those of finite element analysis (FEA), simplified TEFEA (sTEFEA), transient statistical energy analysis (TSEA), and analytical formulas.

Collapse failure analysis of S13Cr-110 tubing in a high-pressure and high-temperature gas well

Due to excellent CO2 corrosion resistance and low cost, martensitic stainless steels such as super 13Cr have been widely used as tubing strings in high-pressure and high-temperature wells. However, in recent years, with the further development of the oilfield, super 13Cr tubing failure accidents keep happening in high-pressure and high-temperature gas well, resulting in the loss of well integrity and huge economic losses. So a systematic research on the failure mechanism of the super 13Cr tubing in HPHT gas well under different service conditions is vital to the reduction of the failure accidents. In this paper, a collapse failure accident of S13Cr-110 tubing in a high-pressure and high-temperature gas well was investigated by metallographic microscope, scanning electron microscope, energy dispersive spectrometer, X-ray diffraction and finite element analysis, aiming to find out the root causes and put forward useful suggestion for the establishment of the preventive measures. The results showed that the chemical composition and mechanical properties of the tubing were all in accordance with the corresponding parameter requirements, and the collapse failure was attributed to the combined effect of formation sand production, high temperature and stress corrosion cracking on the outer surface. The tubing plugging induced by the formation sand production caused the increase of pressure difference between the annulus and tubing, which was the main reason for the collapse failure. In addition, high temperature in the downhole would result in a decreasing of the tubing’s anti-collapse ability. Meanwhile, the annular environment containing Cl-, PO43-, further induced the stress corrosion cracking under service stress. The presence of the cracks on the outer surface could cause a significant decrease of the pressure-bearing capacity of tubing strings, which would finally have an obvious influence on the acceleration of the failure process.

Energy Flow Analysis Model of High-Frequency Vibration Response for Plates with Free Layer Damping Treatment

The energy flow analysis (EFA) model is developed for predicting the vibrational response of plates with free layer damping (FLD) treatment under high-frequency excitation. For the plate with fully free layer damping (FFLD) treatment, the energy density equation of the laminated plate with high damping is deduced by combining the equivalent complex stiffness method with the EFA theory. For the plate with partially free layer damping (PFLD) treatment, the relationship between energy density and energy intensity is obtained based on the wave theory of coupled plate by analyzing the energy transfer relationship at the damping boundary. The high-frequency energy density response of the structure with FLD treatment is solved through the energy finite element analysis (EFEA) method. To verify the developed EFEA model, several numerical analyses are performed for the plate with FFLD and PFLD treatments. The numerical results demonstrate that the obtained EFEA solutions consistently converge to the time-averaged modal analytical solutions at various analysis frequencies. Finally, the influences of the loss factor and the thickness of the damping layer on the resulting energy density are investigated in detail.

Research status and development trend of energy finite element analysis: a review

Compared with finite element method (FEA) and statistical energy method (SEA), the energy finite element method (EFEA) is a promising and more suitable method to predict the high-frequency vibration response and radiated noise of mechanical structures, due to its advantages of both computational efficiency and ability to get detail information. In recent years, researchers have made great progress in EFEA, due to the urgency of engineering application. This paper aims to comprehensively summarize historical and latest development of energy finite element analysis from two aspects of theory and engineering, to furtherly promote its application in the engineering field. Firstly, the development history of EFEA in basic structures is summarized, and the theoretical development direction of energy finite element in recent years is further analyzed. After that, the application of EFEA in aerospace, ship and vehicle engineering are summarized. Finally, the problems that need to be furtherly studied in EFEA are presented, and it is pointed out that it is an urgent research work to continue to improve the energy finite element analysis theory and software and apply it to engineering.

Investigation on Distributed Vibration Damping of Bridge Based on Energy Harvesting Technique and Finite Element Analysis

Based on the vibration control method and energy harvesting principle in the bridge field, this paper proposes a distributed vibration reduction and energy harvesting method for bridges. Firstly, the analytical solutions of the induced electromotive force, output power and magnetic damping generated by a coil in a magnetic field were deduced through an electromagnetic theory analysis. In addition, the structural vibration equation under the magnetic damping was deduced. Then, a new method of joint simulation and modeling analysis of vibration and energy output was proposed. Finally, the structural vibration reduction and energy output power were analyzed and calculated. The main research results are as follows: by calculating the instantaneous power of the energy collection of the designed circuit, the average instantaneous power collected by the design method is 1.093 × 10−9 W; the initial vibration signal of the target node is obtained through analysis, and the vibration signal of the node before and after applying the electromagnetic damping force is transformed. For the energy analysis, the energy of the acceleration curve before and after the node was calculated to be 3.1048 × 108 and 3.1044 × 108, respectively, and the reduction rate of the node vibration energy was 0.01% and 0.02%, respectively. Thus, the feasibility and vibration reduction effect of the designed bridge distributed vibration reduction and energy harvesting method is verified when the electromagnetic damping force is small. This method can provide new ideas for bridge structure vibration reduction and energy harvesting research and is of great significance to the infrastructure construction and utilization of renewable energy.

A Linear-Arc Composite Beam Piezoelectric Energy Harvester Modeling and Finite Element Analysis.

To improve the output performance of the piezoelectric energy harvester, this paper proposed the design of a linear-arc composite beam piezoelectric energy harvester (PEH-C). First the nonlinear restoring force model of a composite beam was obtained by the numerical simulation method. Afterwards, the corresponding coupled governing equations were derived by using the generalized Hamilton principle, laying the foundation for subsequent in-depth research. After this, a finite element simulation was performed in the COMSOL software to simulate the output voltage, stress distribution, and resonance frequency of the PEH-C under different curvatures. In this way, the effect of curvature change on the PEH-C was analyzed. Finally, the PEH-C with a curvature of 40 was prepared, and an experimental platform was built to verify the correctness of the relevant analysis. The results showed that the resonant frequency of the PEH-C can be changed by changing the curvature, and that the stress on the composite beam will increase after the arc segment is introduced. When the curvature of the PEH-C was 40 , the open-circuit output voltage was 44.3% higher than that of the straight beam.

Failure analysis of smoke lampblack machine crack

The smoke lampblack machine cracked in use. Through macro and micro morphology observation, energy spectrum detection, metallographic examination and finite element simulation calculation and analysis, the failure nature and reason of the smoke lampblack machine were determined. The results showed that the cracking property was corrosion fatigue, and the cracking of the smoke lampblack machine was caused by the damage of the protective layer in the vibration environment. It was suggested that the surface protection of smoke lampblack machine should be strengthened and the structural design of stress concentration should be improved.

Energy Flow Analysis of High-Frequency Flexural Vibration of Wedge Beam Structures

Wedge members with variable thickness are widely used in ship structures, aerospace structures, and building structures. Considering their application scenarios, their high-frequency vibration characteristics have important research value. Energy finite element analysis (EFEA) is a powerful tool to predict high-frequency vibration response. EFEA is essentially applying finite element analysis to solve the energy density governing equation. However, the equation for wedge beam is missing. Energy flow analysis aims to obtain energy density governing equation. The energy flow model of wedge beam with variable thickness is established in this paper. Firstly, according to the geometric acoustic approximation method, the general displacement solution of the bending deformation equation for a wedge beam is deduced. Furthermore, the wave dispersion relation of bending deformation of wedge beam is derived. Then, the relationship between the time-averaged vibration energy density and energy flow of the wedge beam is also derived. Also, the governing equation taking energy density as a variable of the wedge beam structure is derived through the energy balance relationship in the microelement body. The governing equation is numerically solved, and the energy density distribution on the wedge beam structure is calculated. Finally, the energy density distribution of uniform beam and wedge beam under the same excitation is analyzed and summarized; the influence of different excitation frequencies and power exponent of thickness change on the performance of wedge beam structure is also summarized. Geometrically, the wedge beam satisfies the one-dimensional acoustic black hole structure. The calculation results show that the energy density on the beam structure increases with the decrease of thickness and reaches its maximum near the tip. The wedge acoustic black hole beam structure has a good energy absorption effect with a frequency between 250 Hz and 2000 Hz. With the further increase of excitation frequency, the energy absorption effect of the wedge beam structure has dropped significantly.

Study on cracking process of hot pressed tee based on Fick's second law

The microstructure, composition, hardness, stress and crack morphology of cracked tee in petrochemical plant were analyzed by optical microscope, scanning electron microscope, energy spectrum analysis and finite element analysis. The carbon content of decarburized layer was calculated by Fick's second law combined with Gauss error function. The accident tee was cracked due to decarburization. The decarburization stage is determined by morphology and composition analysis. The results show that the hardness near the crack is low, only a large amount of ferrite is left in the metallographic structure, and the content of pearlite is very little, which indicates that decarburization occurs during the manufacturing of the tee. Fick's second law combined with Gauss Error Function calculation proves that the carbon content is very low, resulting in the decrease of hardness. Through the finite element calculation, the stress near the crack is the largest. In addition, the crack is covered with a layer of uniform oxide, which proves that the crack occurrs in the early stage of pressing, decarburization and oxidation in the subsequent heat treatment process. Finally, the stress concentration occurres near the open crack, resulting in liquid leakage under the action of external liquid pressure in the process of hydrostatic test. This paper provides a method for researchers to calculate the carbon content of decarburization and judge the decarburization time.

Damping of rubberized recycled aggregate concrete and damping estimation of its elements by finite element analysis

Concrete structures inevitably suffer from dynamic loadings, causing damage and uncomfortable vibration. Improving the damping of concrete to passively absorb the vibration energy is beneficial to mitigate the hazards and improve comfort. However, at least two challenges must be completed before applying this strategy, namely, preparing effective energy dissipating concrete and estimating the damping parameter of its elements and structures. In this study, rubberized recycled aggregate concrete (RRAC), prepared with coarse recycled concrete aggregate (RCA) and recycled rubber aggregate (RRA) instead of natural aggregate, is experimentally validated to show higher damping. Besides, a universal function of energy dissipation over strain amplitude is established for concrete containing natural aggregate, RCA, and RRA. Based on the found strain–energy dissipation function and finite element analysis, an iterative method of estimating the inner damping ratio of RRAC elements from the material damping is proposed and validated. Through the proposed method, the effects of loading amplitude, loading frequency, and stress history on the nonlinear damping behaviors of RRAC beams are numerically analyzed. The experiment result and the proposed damping determination method can encourage the application of recycled building materials in structural engineering, especially in projects with requirements of vibration control.

Analysis of transient response of the human foot based on the finite element method.

The foot is an important part of the human body. Its functions are mainly walking and load-bearing. It also keeps the human body stable and absorbs ground vibrations to protect important human organs. Many researchers use finite element methods to study the biomechanics of the foot. However, current studies on the finite element of the foot are based on the stress and displacement response analysis of the foot under static or quasi-static conditions, ignoring the movement process of the foot and the impact of vibration. Moreover, the joint application of energy method and finite element analysis in foot biomechanics is rarely reported. In this paper, to obtain the foot energy transfer process, the transient response of the foot under neutral position is analyzed based on the energy method. The results show that: (1) In this model, the energy analysis follows the conservation of energy, which indicates that the transient response analysis has obtained a reasonable response. (2) When the foot touches the ground, the strain energy of the calcaneus, second metatarsal and third metatarsal is relatively large, which is consistent with the main stress concentration area of the plantar. (3) The gravity of the human body is mainly transmitted through the talus to the calcaneus, while the effect of transmittal through the scaphoid to the cuneiform bone and metatarsal is weak. This study can not only more clearly and intuitively reflect the energy transfer and source of various skeletal foreheads in the foot, but also provide a new research idea for the study of foot biomechanics.

High-frequency random vibrations of a stiffened plate with a cutout using energy finite element and experimental methods

In this paper, by employing the energy finite element analysis, the high-frequency vibrations of a stiffened plate having a cutout, subjected to random vibrations, have been analyzed, and the obtained results have been validated by use of experimental methods. By using equations for joining of structures, energy finite element analysis computer codes were developed for the coupling of beam-plate elements. Finally, a plate containing a cutout and three stiffeners was fabricated and subjected to high-frequency random vibration tests. The results of the prepared codes were compared with the results of experiments. These comparisons indicated that at high frequencies, the energy finite element analysis can be used as an effective tool in the analysis of high-frequency vibrations.

Classical modal analysis and asymptotic modal analysis of structural and acoustic systems

The Classical Modal Analysis (CMA) method is commonly used to solve for the vibroacoustic response of large scale structural and acoustic systems. In this method, the modal equations of motion are developed and solved for the modal coefficients to form a modal series solution to predict the structural and acoustic responses. The CMA method generally works well in the low-to-medium frequency range. However, at high frequencies, the large number of modes required in the summation limits the usefulness of the CMA method and alternative methods, such as Statistical Energy Analysis (SEA) and Energy Finite Element Analysis (EFEA) have been developed. As an alternative to SEA and EFEA, the Asymptotic Modal Analysis (AMA) method has been developed in which the modal series summation in the CMA method is asymptotically approximated based on the overall frequency and band averaging of the modal series. The AMA method thereby predicts the band averaged frequency response in the high frequency range and also has the advantage of providing the spatial distribution of the response based on the summed modes in the frequency band. In this paper, an example of coupled cavity-plate system subject to external random white noise pressure load excitation is developed to illustrate the CMA and AMA methods and to address their accuracy.

Fracture failure analysis of DY08Aluminum alloy elastic coupling

The failure reasons of a DY08 aluminum alloy elastic coupling connecting the motor of the multi-functional test bench with the experimental device was investigated in this paper based on the fact that the lifespan of coupling was not reached. By the means of chemical composition analysis, mechanical properties test, macroscopic examinations, scanning electron microscopic analysis, fracture energy spectrum analysis, metallographic analysis and finite element analysis, fracture modes of the coupling are described as fatigue fracture failure due to machining defects. Residual machining defects were found on the inside surface of the coupling, which caused the initial crack generation. Stress concentration is generated at the machining defect, causing the crack to expand continuously along the radial direction. Microstructural analysis of the metallographic sample revealed secondary phase present in the alloy's microstructure. Therefore, secondary phase energy spectrum analysis of fracture surface was carried out, and found that the secondary phase contains Mg and Si elements. In addition, the Si element content in the fracture micro-region exceeds the material standard, we deduced that it forms MgSi secondary compound phase with the Mg element, which increases the strength matrix material. It is shows that the hardness of fracture single micro-areas is significantly higher than other measured points. Furthermore, a finite element analysis was conducted to simulate the coupling in service; the result showed that the coupling does not exceed the strength limit of the material under the rated torque, which indicates that the material strength is qualified.

Structural-Acoustic Modeling and Optimization of a Submarine Pressure Hull

<div class="section abstract"><div class="htmlview paragraph">The Energy Finite Element Analysis (EFEA) has been validated in the past through comparison with test data for computing the structural vibration and the radiated noise for Naval systems in the mid to high frequency range. A main benefit of the method is that it enables fast computations for full scale models. This capability is exploited by using the EFEA for a submarine pressure hull design optimization study. A generic but representative pressure hull is considered. Design variables associated with the dimensions of the king frames, the thickness of the pressure hull in the vicinity of the excitation (the latter is considered to be applied on the king frames of the machinery room), the dimensions of the frames, and the damping applied on the hull are adjusted during the optimization process in order to minimize the radiated noise in the frequency range from 1,000Hz to 16,000Hz. Constraints on the total amount of damping that can be used are considered (resource driven constraints) and structural collapse constraints are also taken into account in order to avoid degrading the structural integrity of the pressure hull. Two different optimization strategies are exercised. First a concurrent multidisciplinary analysis is performed; optimal configurations for structural performance and for acoustic radiation are identified and the results are used for producing a single design with optimized performance in both disciplines. Then, an analysis based on set-based design principles is performed. The latter identifies several alternative and diverse hull configurations that provide similar levels of performance with respect to the radiated noise. Having several alternative solutions of nearly equal performance provides insight into the design trade-offs when configuring the pressure hull. The results from both optimization strategies are analyzed and discussed.</div></div>

Prediction and energy contribution analysis of interior noise in a high-speed train based on modified energy finite element analysis

Abstract Compared with traditional finite element analysis and statistical energy analysis, the energy finite element analysis (EFEA) has the advantages of small computations and solving local responses in large-scale complex structures. In this paper, the structural sound insulation effect is introduced to EFEA for predicting and analyzing interior noise responses of extruded structures in a high-speed train. Firstly, the carriage structure and cavity models are established based on EFEA theory, and model parameters are obtained through experiments and effective simulations. Mechanical and acoustic excitation sources of the high-speed train are extracted through multi-body dynamic simulation, acoustic finite element method and nonlinear acoustic solution. The reliability of predicted excitations is validated by verifying the amplitude peak frequency bands. The interior noise responses at several observations are obtained and in good agreement with on-site test results, and the EFEA prediction model of interior noise is verified accurately. Secondly, the energy contribution of exterior excitation sources to interior noise responses is analyzed based on EFEA model. The results indicate that acoustic excitations dominate the acoustic energy in the frequency bands above 800 Hz, and the energy contribution of mechanical excitations and acoustic excitations is relatively close in the frequency bands below 600 Hz. The contribution of aerodynamic noise excitations is predominantly concentrated in the frequency bands below 500 Hz, while that of wheel-rail noise excitations is concentrated in the frequency bands above 800 Hz. In the frequency bands below 1250 Hz, the energy contribution of rail noise excitations is much more important than that of wheel noise excitations, while their contribution gets gradually close in the frequency bands above 1600 Hz. Besides, the acoustic excitations at the bottom of the carriage are quite important sources. Finally, wheel-rail noise excitations are optimized with spoke-shielding damping wheels and dynamic vibration absorbers, and the sound pressure level in the amplitude peak bands is reduced by about 8 dB. The interior noise responses are reduced by about 3–5 dB in the frequency bands above 800 Hz, and total loudness, sharpness and roughness at different locations are decreasing by more than 1 sone, 0.05 acum and 0.03 asper respectively. Therefore, wheel-rail noise optimizations have good reduction effects on interior noise responses in the high frequency bands.

Application of the energy finite element analysis to vibration of beams with stepped thickness and variable cross-section

Energy finite element analysis (EFEA) has been developed to compute the energy distribution of vibrating structures. The method adopts the energy density as the basic variable of differential equation. The energy density can be used to analyze the behavior of vibrating beams. Firstly, an EFEA equation is obtained from the classical displacement equation. In the applications of uniform and non-uniform beams, the EFEA results are compared with the analytical and FEA results. Secondly, a junction formulation solving the discontinuity problem of energy density at the junction of two beams with stepped thickness is proposed. The EFEA equation combined with junction formulation is used to solve the energy transmission problem of the coupling beams with stepped thickness and variable cross-section. The smoothed results of coupling beams are achieved, and the differences of energy density at the junctions are analyzed. The feasibility of the EFEA approach is validated by using several design examples under the various frequencies and structural damping loss factors.

An improved approach for analysis of coupled structures in Energy Finite Element Analysis using the coupling loss factor

An alternative and improved approach for the analysis of coupled structures in Energy Finite Element Analysis (EFEA) is presented, which is termed as iEFEA in this paper. The conventional EFEA uses the power transfer coefficients (PTCs) to establish the power coupling relation on discontinuous joints, where PTCs are usually derived and processed by the wave transmission approach based on the diffuse wavefield assumption. However, the PTCs in conventional EFEA cannot capture wave filtering effects and only provide accurate predictions when the damping effect is weak. Inspired by the power coupling concept of Statistical Energy Analysis (SEA), an alternative approach using the coupling loss factors (CLFs) and considering the direct wavefield is developed. The present approach is implemented by Finite Element Method (FEM), and thus it inherits the advantages of FEM on handling geometrical complexity and material complexity. The applications of the present approach on coupled beams and coupled plates are demonstrated. The validation simulations show the accuracy and reliability of the present approach.

Applications of the hybrid finite element method

The hybrid finite element analysis (Hybrid FEA) method is based on combining conventional finite element analysis (FEA) with energy finite element analysis (EFEA) for expediting the FEA computations when very dense models are needed. The difficulty in using conventional FEA at higher frequencies originates from requiring a very large number of elements in order to capture the flexible wavelength of the panel members which are present in a structure. In the Hybrid FEA the conventional FEA model is modified by de-activating the bending behavior of the flexible panels in the FEA computations and introducing instead a large number of dynamic impedance elements for representing the omitted bending behavior. The excitation is considered to be applied on the conventional FEA model and the vibration analysis is conducted. The power flow through the dynamic impedance elements is computed and applied as excitation to the EFEA model of the flexible panels. The EFEA analysis computes the vibration of the flexible panels. In the past, the Hybrid FEA has been utilized successfully for evaluating the vibration is production automotive and rotorcraft structures. A brief theoretical background will be reviewed, the practical aspects of the method will be discussed, and results from previous correlation studies will be presented.