A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and vi...A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.展开更多
Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copie...Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copier paper is moving through the fusing rollers. By means of conventional shaft elements, the high gradient temperature variety causes the oscillation of the numerical solution. Based on the Daubechies scaling functions, a kind of wavelet based element is constructed for the above problem. The temperature field of the copier paper moving through the fusing rollers is simulated using the two methods. Comparison of the results shows the advantages of the wavelet finite element method, which provides a new method for improving the copier properties.展开更多
The compactly supported wavelet basis functions are introduced into the construction of interpolating function of traditional finite element method when analyzing the problems with high gradient, and the traditional i...The compactly supported wavelet basis functions are introduced into the construction of interpolating function of traditional finite element method when analyzing the problems with high gradient, and the traditional interpolating method is modified. The numerical stability of the new interpolating pattern is discussed and the convergence of the new method is also discussed by patch test analysis. The additional freedom of the new interpolating pattern is eliminated by static condensation method. Finally, the wavelet finite element formulations based on variational principles are put forward.展开更多
A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D F...A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.展开更多
Ground-penetrating radar(GPR)is a highly efficient,fast and non-destructive exploration method for shallow surfaces.High-precision numerical simulation method is employed to improve the interpretation precision of det...Ground-penetrating radar(GPR)is a highly efficient,fast and non-destructive exploration method for shallow surfaces.High-precision numerical simulation method is employed to improve the interpretation precision of detection.Second-generation wavelet finite element is introduced into the forward modeling of the GPR.As the finite element basis function,the second-generation wavelet scaling function constructed by the scheme is characterized as having multiple scales and resolutions.The function can change the analytical scale arbitrarily according to actual needs.We can adopt a small analysis scale at a large gradient to improve the precision of analysis while adopting a large analytical scale at a small gradient to improve the efficiency of analysis.This approach is beneficial to capture the local mutation characteristics of the solution and improve the resolution without changing mesh subdivision to realize the efficient solution of the forward GPR problem.The algorithm is applied to the numerical simulation of line current radiation source and tunnel non-dense lining model with analytical solutions.Result show that the solution results of the secondgeneration wavelet finite element are in agreement with the analytical solutions and the conventional finite element solutions,thereby verifying the accuracy of the second-generation wavelet finite element algorithm.Furthermore,the second-generation wavelet finite element algorithm can change the analysis scale arbitrarily according to the actual problem without subdividing grids again.The adaptive algorithm is superior to traditional scheme in grid refinement and basis function order increase,which makes this algorithm suitable for solving complex GPR forward-modeling problems with large gradient and singularity.展开更多
This paper presents the formulation of finite elements based on Deslauriers-Dubuc interpolating scaling functions, also known as Interpolets, for their use in wave propagation modeling. Unlike other wavelet families l...This paper presents the formulation of finite elements based on Deslauriers-Dubuc interpolating scaling functions, also known as Interpolets, for their use in wave propagation modeling. Unlike other wavelet families like Daubechies, Interpolets possess rational filter coefficients, are smooth, symmetric and therefore more suitable for use in numerical methods. Expressions for stiffness and mass matrices are developed based on connection coefficients, which are inner products of basis functions and their derivatives. An example in 1-D was formulated using Central Difference and Newmark schemes for time differentiation. Encouraging results were obtained even for large time steps. Results obtained in 2-D are compared with the standard Finite Difference Method for validation.展开更多
Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential ...Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems. In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees used in the spectral element method and the element sizes. Several numerical tests verify the h-p independence of the proposed preconditioning.展开更多
The practice of exploration and production has proved that explosives are excited in different surrounding rocks and the seismic wavelets collected have different characteristics. In this paper, by establishing a nume...The practice of exploration and production has proved that explosives are excited in different surrounding rocks and the seismic wavelets collected have different characteristics. In this paper, by establishing a numerical model of the explosion in the well, using finite element analysis technology for numerical simulation, the simulation calculated the stress structure in the near-source area of the earthquake excitation, and extracted the seismic wavelet. The results show that the simulation seismic wavelet characteristics of different thin interbedded sand and mudstone structures have changed significantly. Through excitation simulation, the amplitude and spectrum information of seismic wavelets can be compared and analyzed, and the excitation parameters can be optimized. .展开更多
The present work proposed a new method for the modeling by the finite element method of the acoustic propagation problems in infinite axisymmetric cylindrical guides lined with locally reacting absorbent materials wit...The present work proposed a new method for the modeling by the finite element method of the acoustic propagation problems in infinite axisymmetric cylindrical guides lined with locally reacting absorbent materials without flow. The method deals with the development of an efficient transparent boundary condition based on DtN operators. The method developed in this study is successfully applied to a straight axisymmetric lined guide by imposing a mode on one of the artificial boundaries of the truncated guide. The results are in good agreement with analytical solutions. Applying the method for a non-uniform axisymmetric lined guide which is a complex case, proved its effectiveness and the results compared to those of PML layers are in very good agreement.展开更多
We’ll consider the model of two-phase compressible miscible displacement in porous media which includes molecular diffusion and dispersion in one dimensional space. Time-discretization procedure is established and an...We’ll consider the model of two-phase compressible miscible displacement in porous media which includes molecular diffusion and dispersion in one dimensional space. Time-discretization procedure is established and analysed. The optimal error estimate in L2 norm is proved by introducing a new interpolation operator R.展开更多
The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differe...The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differential equation into a system of algebraic equations by application of the method of weighted residuals in conjunction with a finite element ansatz. However, this procedure is restricted to even-ordered differential equations and leads to symmetric system matrices as a key property of the finite element method. This paper aims in a generalization of the finite element method towards the solution of first-order differential equations. This is achieved by an approach which replaces the first-order derivative by fractional powers of operators making use of the square root of a Sturm-Liouville operator. The resulting procedure incorporates a finite element formulation and leads to a symmetric but dense system matrix. Finally, the scheme is applied to the barometric equation where the results are compared with the analytical solution and other numerical approaches. It turns out that the resulting numerical scheme shows excellent convergence properties.展开更多
Based on B-spline wavelet on the interval （BSWI）, two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately t...Based on B-spline wavelet on the interval （BSWI）, two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.展开更多
A high-precision identification method for steam turbine rotor crack is presented. By providing me nrst three measured natural frequencies, contours for the specified natural frequency are plotted in the same coordi- ...A high-precision identification method for steam turbine rotor crack is presented. By providing me nrst three measured natural frequencies, contours for the specified natural frequency are plotted in the same coordi- nate, and the intersection of the three curves predicts the crack location and size. The cracked rotor system is mod- eled using B-spline wavelet on the interval （BSWI） finite element method, and a method based on empirical mode decomposition （EMD） and Laplace wavelet is implemented to improve the identification precision of the first three measured natural frequencies. Compared with the classical nondestructive testing, the presented method shows its effectiveness and reliability. It is feasible to apply this method to the online health monitoring for rotor structure.展开更多
Rotor blade is one of the most significant components of helicopters. But due to its highspeed rotation characteristics, it is difficult to collect the vibration signals during the flight stage.Moreover, sensors are h...Rotor blade is one of the most significant components of helicopters. But due to its highspeed rotation characteristics, it is difficult to collect the vibration signals during the flight stage.Moreover, sensors are highly susceptible to damage resulting in the failure of the measurement.In order to make signal predictions for the damaged sensors, an operational modal analysis(OMA) together with the virtual sensing(VS) technology is proposed in this paper. This paper discusses two situations, i.e., mode shapes measured by all sensors(both normal and damaged) can be obtained using OMA, and mode shapes measured by some sensors(only including normal) can be obtained using OMA. For the second situation, it is necessary to use finite element(FE) analysis to supplement the missing mode shapes of damaged sensor. In order to improve the correlation between the FE model and the real structure, the FE mode shapes are corrected using the local correspondence(LC) principle and mode shapes measured by some sensors(only including normal).Then, based on the VS technology, the vibration signals of the damaged sensors during the flight stage can be accurately predicted using the identified mode shapes(obtained based on OMA and FE analysis) and the normal sensors signals. Given the high degrees of freedom(DOFs) in the FE mode shapes, this approach can also be used to predict vibration data at locations without sensors. The effectiveness and robustness of the proposed method is verified through finite element simulation, experiment as well as the actual flight test. The present work can be further used in the fault diagnosis and damage identification for rotor blade of helicopters.展开更多
In this paper,we develop and analyze a weak Galerkin(WG)finite element method for solving a H(curl)-elliptic problem.With the aid of the weak curl operator and a stabilizer term,we first design a WG discretization.The...In this paper,we develop and analyze a weak Galerkin(WG)finite element method for solving a H(curl)-elliptic problem.With the aid of the weak curl operator and a stabilizer term,we first design a WG discretization.Then,by using an auxiliary problem and establishing an error equation,we achieve the optimal order error estimates in both the energy norm and L^(2)norm for the WG method.At last,we report some numerical experiments to confirm the theoretical results.展开更多
A new discontinuous Galerkin(DG)method is proposed and analyzed for the Maxwell eigenproblem,featuring a local reconstruction of the curl operator in a discontinuous finite element space.The proposed method can be pen...A new discontinuous Galerkin(DG)method is proposed and analyzed for the Maxwell eigenproblem,featuring a local reconstruction of the curl operator in a discontinuous finite element space.The proposed method can be penalty-free or penalty-factor-free,depending on which discontinuous finite element space the curl operator is locally reconstructed in.The new DG method is recast into a saddlepoint problem so that it can be analyzed from the Babuska-Osborn theory for the finite element approximation of the spectrum of the compact operator,and the convergence and the optimal error estimates are then obtained;the discrete eigenmodes are spurious-free and spectral-correct.We provide numerical results to illustrate the proposed method.展开更多
This paper presents a novel parallel implementation technology for wave-based structural health monitoring (SHM) in laminated composite plates. The wavelet-based B-spline wavelet on he interval (BSWI) element is cons...This paper presents a novel parallel implementation technology for wave-based structural health monitoring (SHM) in laminated composite plates. The wavelet-based B-spline wavelet on he interval (BSWI) element is constructed according to Hamilton’s principle, and the element by element algorithm is parallelly executed on graphics processing unit (GPU) using compute unified device architecture (CUDA) to get the responses in full wave field accurately. By means of the Fourier spectral analysis method,the Mindlin plate theory is selected for wave modeling of laminated composite plates while the Kirchhoff plate theory predicts unreasonably phase and group velocities. Numerical examples involving wave propagation in laminated composite plates without and with crack are performed and discussed in detail. The parallel implementation on GPU is accelerated 146 times comparing with the same wave motion problem executed on central processing unit (CPU). The validity and accuracy of the proposed parallel implementation are also demonstrated by comparing with conventional finite element method (FEM) and the computation time has been reduced from hours to minutes. The damage size and location have been successfully determined according to wave propagation results based on delay-and-sum (DAS). The results show that the proposed parallel implementation of wavelet finite element method (WFEM) is very appropriate and efficient for wave-based SHM in laminated composite plates.展开更多
This paper is a generalization of some recent results concerned with the lower bound property of eigenvalues produced by both the enriched rotated Q_(1) and Crouzeix-Raviart elements of the Stokes eigenvalue problem.T...This paper is a generalization of some recent results concerned with the lower bound property of eigenvalues produced by both the enriched rotated Q_(1) and Crouzeix-Raviart elements of the Stokes eigenvalue problem.The main ingredient are a novel and sharp L^(2) error estimate of discrete eigenfunctions,and a new error analysis of nonconforming finite element methods.展开更多
基金This work was supported by the National Natural Science Foundation of China(Nos.51405370&51421004)the National Key Basic Research Program of China(No.2015CB057400)+2 种基金the project supported by Natural Science Basic Plan in Shaanxi Province of China(No.2015JQ5184)the Fundamental Research Funds for the Central Universities(xjj2014014)Shaanxi Province Postdoctoral Research Project.
文摘A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.
文摘Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copier paper is moving through the fusing rollers. By means of conventional shaft elements, the high gradient temperature variety causes the oscillation of the numerical solution. Based on the Daubechies scaling functions, a kind of wavelet based element is constructed for the above problem. The temperature field of the copier paper moving through the fusing rollers is simulated using the two methods. Comparison of the results shows the advantages of the wavelet finite element method, which provides a new method for improving the copier properties.
文摘The compactly supported wavelet basis functions are introduced into the construction of interpolating function of traditional finite element method when analyzing the problems with high gradient, and the traditional interpolating method is modified. The numerical stability of the new interpolating pattern is discussed and the convergence of the new method is also discussed by patch test analysis. The additional freedom of the new interpolating pattern is eliminated by static condensation method. Finally, the wavelet finite element formulations based on variational principles are put forward.
基金supported by the National Natural Science Foundation of China (51109029,51178081,51138001,and 51009020)the State Key Development Program for Basic Research of China (2013CB035905)
文摘A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.
基金supported by the National Natural Science Foundation of China(Nos.41574116 and 41774132)Hunan Provincial Innovation Foundation for Postgraduate(Grant Nos.CX2017B052)the Fundamental Research Funds for the Central Universities of Central South University(Nos.2018zzts693)。
文摘Ground-penetrating radar(GPR)is a highly efficient,fast and non-destructive exploration method for shallow surfaces.High-precision numerical simulation method is employed to improve the interpretation precision of detection.Second-generation wavelet finite element is introduced into the forward modeling of the GPR.As the finite element basis function,the second-generation wavelet scaling function constructed by the scheme is characterized as having multiple scales and resolutions.The function can change the analytical scale arbitrarily according to actual needs.We can adopt a small analysis scale at a large gradient to improve the precision of analysis while adopting a large analytical scale at a small gradient to improve the efficiency of analysis.This approach is beneficial to capture the local mutation characteristics of the solution and improve the resolution without changing mesh subdivision to realize the efficient solution of the forward GPR problem.The algorithm is applied to the numerical simulation of line current radiation source and tunnel non-dense lining model with analytical solutions.Result show that the solution results of the secondgeneration wavelet finite element are in agreement with the analytical solutions and the conventional finite element solutions,thereby verifying the accuracy of the second-generation wavelet finite element algorithm.Furthermore,the second-generation wavelet finite element algorithm can change the analysis scale arbitrarily according to the actual problem without subdividing grids again.The adaptive algorithm is superior to traditional scheme in grid refinement and basis function order increase,which makes this algorithm suitable for solving complex GPR forward-modeling problems with large gradient and singularity.
文摘This paper presents the formulation of finite elements based on Deslauriers-Dubuc interpolating scaling functions, also known as Interpolets, for their use in wave propagation modeling. Unlike other wavelet families like Daubechies, Interpolets possess rational filter coefficients, are smooth, symmetric and therefore more suitable for use in numerical methods. Expressions for stiffness and mass matrices are developed based on connection coefficients, which are inner products of basis functions and their derivatives. An example in 1-D was formulated using Central Difference and Newmark schemes for time differentiation. Encouraging results were obtained even for large time steps. Results obtained in 2-D are compared with the standard Finite Difference Method for validation.
文摘Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems. In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees used in the spectral element method and the element sizes. Several numerical tests verify the h-p independence of the proposed preconditioning.
文摘The practice of exploration and production has proved that explosives are excited in different surrounding rocks and the seismic wavelets collected have different characteristics. In this paper, by establishing a numerical model of the explosion in the well, using finite element analysis technology for numerical simulation, the simulation calculated the stress structure in the near-source area of the earthquake excitation, and extracted the seismic wavelet. The results show that the simulation seismic wavelet characteristics of different thin interbedded sand and mudstone structures have changed significantly. Through excitation simulation, the amplitude and spectrum information of seismic wavelets can be compared and analyzed, and the excitation parameters can be optimized. .
文摘The present work proposed a new method for the modeling by the finite element method of the acoustic propagation problems in infinite axisymmetric cylindrical guides lined with locally reacting absorbent materials without flow. The method deals with the development of an efficient transparent boundary condition based on DtN operators. The method developed in this study is successfully applied to a straight axisymmetric lined guide by imposing a mode on one of the artificial boundaries of the truncated guide. The results are in good agreement with analytical solutions. Applying the method for a non-uniform axisymmetric lined guide which is a complex case, proved its effectiveness and the results compared to those of PML layers are in very good agreement.
基金This work was supported by National Science Foundation and China State Major Key Project for Basic Research
文摘We’ll consider the model of two-phase compressible miscible displacement in porous media which includes molecular diffusion and dispersion in one dimensional space. Time-discretization procedure is established and analysed. The optimal error estimate in L2 norm is proved by introducing a new interpolation operator R.
文摘The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differential equation into a system of algebraic equations by application of the method of weighted residuals in conjunction with a finite element ansatz. However, this procedure is restricted to even-ordered differential equations and leads to symmetric system matrices as a key property of the finite element method. This paper aims in a generalization of the finite element method towards the solution of first-order differential equations. This is achieved by an approach which replaces the first-order derivative by fractional powers of operators making use of the square root of a Sturm-Liouville operator. The resulting procedure incorporates a finite element formulation and leads to a symmetric but dense system matrix. Finally, the scheme is applied to the barometric equation where the results are compared with the analytical solution and other numerical approaches. It turns out that the resulting numerical scheme shows excellent convergence properties.
基金Project supported by the National Natural Science Foundation of China (Nos. 50335030, 50505033 and 50575171)National Basic Research Program of China (No. 2005CB724106)Doctoral Program Foundation of University of China(No. 20040698026)
文摘Based on B-spline wavelet on the interval （BSWI）, two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.
基金National Natural Science Foundation of China(No.51225501No.51035007)Program for Changjiang Scholars and Innovative Research Team in University
文摘A high-precision identification method for steam turbine rotor crack is presented. By providing me nrst three measured natural frequencies, contours for the specified natural frequency are plotted in the same coordi- nate, and the intersection of the three curves predicts the crack location and size. The cracked rotor system is mod- eled using B-spline wavelet on the interval （BSWI） finite element method, and a method based on empirical mode decomposition （EMD） and Laplace wavelet is implemented to improve the identification precision of the first three measured natural frequencies. Compared with the classical nondestructive testing, the presented method shows its effectiveness and reliability. It is feasible to apply this method to the online health monitoring for rotor structure.
基金supported by grants from the High-Level Oversea Talent Introduction Plan,Chinathe Special Fund for Basic Scientific Research in Central Universities of China-Doctoral Research and Innovation Fund Project,China(No.3072023CFJ0206).
文摘Rotor blade is one of the most significant components of helicopters. But due to its highspeed rotation characteristics, it is difficult to collect the vibration signals during the flight stage.Moreover, sensors are highly susceptible to damage resulting in the failure of the measurement.In order to make signal predictions for the damaged sensors, an operational modal analysis(OMA) together with the virtual sensing(VS) technology is proposed in this paper. This paper discusses two situations, i.e., mode shapes measured by all sensors(both normal and damaged) can be obtained using OMA, and mode shapes measured by some sensors(only including normal) can be obtained using OMA. For the second situation, it is necessary to use finite element(FE) analysis to supplement the missing mode shapes of damaged sensor. In order to improve the correlation between the FE model and the real structure, the FE mode shapes are corrected using the local correspondence(LC) principle and mode shapes measured by some sensors(only including normal).Then, based on the VS technology, the vibration signals of the damaged sensors during the flight stage can be accurately predicted using the identified mode shapes(obtained based on OMA and FE analysis) and the normal sensors signals. Given the high degrees of freedom(DOFs) in the FE mode shapes, this approach can also be used to predict vibration data at locations without sensors. The effectiveness and robustness of the proposed method is verified through finite element simulation, experiment as well as the actual flight test. The present work can be further used in the fault diagnosis and damage identification for rotor blade of helicopters.
基金supported by the National Natural Science Foundation of China(No.12071160)supported by the National Natural Science Foundation of China(No.12101250)+1 种基金the Science and Technology Projects in Guangzhou(No.202201010644)supported by the National Natural Science Foundation of China(No.12101147).
文摘In this paper,we develop and analyze a weak Galerkin(WG)finite element method for solving a H(curl)-elliptic problem.With the aid of the weak curl operator and a stabilizer term,we first design a WG discretization.Then,by using an auxiliary problem and establishing an error equation,we achieve the optimal order error estimates in both the energy norm and L^(2)norm for the WG method.At last,we report some numerical experiments to confirm the theoretical results.
基金supported by the National Natural Science Foundation of China(Grants no:12401482)the second author H.Duan was also supported by the National Natural Science Foundation of China(Grants nos:12371371,12261160361,11971366).
文摘A new discontinuous Galerkin(DG)method is proposed and analyzed for the Maxwell eigenproblem,featuring a local reconstruction of the curl operator in a discontinuous finite element space.The proposed method can be penalty-free or penalty-factor-free,depending on which discontinuous finite element space the curl operator is locally reconstructed in.The new DG method is recast into a saddlepoint problem so that it can be analyzed from the Babuska-Osborn theory for the finite element approximation of the spectrum of the compact operator,and the convergence and the optimal error estimates are then obtained;the discrete eigenmodes are spurious-free and spectral-correct.We provide numerical results to illustrate the proposed method.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51421004 & 51405369)the National Key Basic Research Program of China (Grant No. 2015CB057400)+1 种基金the China Postdoctoral Science Foundation (Grant No. 2014M560766)the China Scholarship Council,and the Fundamental Research Funds for the Central Universities(Grant No. xjj2014107)
文摘This paper presents a novel parallel implementation technology for wave-based structural health monitoring (SHM) in laminated composite plates. The wavelet-based B-spline wavelet on he interval (BSWI) element is constructed according to Hamilton’s principle, and the element by element algorithm is parallelly executed on graphics processing unit (GPU) using compute unified device architecture (CUDA) to get the responses in full wave field accurately. By means of the Fourier spectral analysis method,the Mindlin plate theory is selected for wave modeling of laminated composite plates while the Kirchhoff plate theory predicts unreasonably phase and group velocities. Numerical examples involving wave propagation in laminated composite plates without and with crack are performed and discussed in detail. The parallel implementation on GPU is accelerated 146 times comparing with the same wave motion problem executed on central processing unit (CPU). The validity and accuracy of the proposed parallel implementation are also demonstrated by comparing with conventional finite element method (FEM) and the computation time has been reduced from hours to minutes. The damage size and location have been successfully determined according to wave propagation results based on delay-and-sum (DAS). The results show that the proposed parallel implementation of wavelet finite element method (WFEM) is very appropriate and efficient for wave-based SHM in laminated composite plates.
基金The author would like to thank Prof.Shangyou Zhang for helping the numerical experiments.The author was supported by the NSFC under Grants Nos.11571023 and 11401015.
文摘This paper is a generalization of some recent results concerned with the lower bound property of eigenvalues produced by both the enriched rotated Q_(1) and Crouzeix-Raviart elements of the Stokes eigenvalue problem.The main ingredient are a novel and sharp L^(2) error estimate of discrete eigenfunctions,and a new error analysis of nonconforming finite element methods.
