The Experts below are selected from a list of 99 Experts worldwide ranked by ideXlab platform
M.w. Abd El Maguid Ahmed - One of the best experts on this subject based on the ideXlab platform.
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ISCAS - Discrete fractional Fourier transform based on the eigenvectors of Grünbaum tridiagonal matrix
2008 IEEE International Symposium on Circuits and Systems, 2008Co-Authors: Magdy Tawfik Hanna, Nabila Philip Attalla Seif, M.w. Abd El Maguid AhmedAbstract:The development of the discrete fractional Fourier transform (DFRFT) necessitates the availability of a complete set of orthonormal eigenvectors of the DFT matrix F. An eigenanalysis is performed for the original Grunbaum tridiagonal matrix T - which commutes with matrix F - having only one Eigenvalue of multiplicity two and simple remaining Eigenvalues. The two easily obtainable eigenvectors of T corresponding to its Repeated Eigenvalue - which are not eigenvectors of F - are exploited for analytically generating two orthonormal eigenvectors common to both T and F.
Magdy Tawfik Hanna - One of the best experts on this subject based on the ideXlab platform.
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fractional discrete fourier transform of type iv based on the eigenanalysis of a nearly tridiagonal matrix
Digital Signal Processing, 2012Co-Authors: Magdy Tawfik HannaAbstract:A fully-fledged definition for the fractional discrete Fourier transform of type IV (FDFT-IV) is presented and shown to outperform the simple definition of the FDFT-IV which is proved to be just a linear combination of the signal, its DFT-IV and their flipped versions. This definition heavily depends on the availability of orthonormal eigenvectors of the DFT-IV matrix G. An eigenanalysis is performed of a nearly tridiagonal matrix S which commutes with matrix G. An involutary unitary matrix P is defined and used for performing a similarity transformation that reduces S to a block diagonal form where the two diagonal blocks are exactly tridiagonal matrices. Moreover the elements of those two diagonal blocks are derived in order to circumvent the need for performing the two matrix multiplications involved in the similarity transformation. Orthonormal even and odd symmetric eigenvectors for S are generated - in terms of the eigenvectors of the two diagonal blocks - and proved to always be eigenvectors of G irrespective of the multiplicities of the Eigenvalues of S. The relevance of the method contributed here is manifested in the case of a Repeated Eigenvalue of S with multiplicity 2 where a direct application of a general eigenanalysis procedure in any software package will not produce a pair of even and odd symmetric eigenvectors corresponding to this Repeated Eigenvalue. It should be mentioned that the almost tridiagonal matrix S which commutes with the DFT-IV matrix G being dealt with here is distinct from matrix S which commutes with the DFT matrix F dealt with in a previous paper Hanna et al. (2008) [7].
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ISCAS - Discrete fractional Fourier transform based on the eigenvectors of Grünbaum tridiagonal matrix
2008 IEEE International Symposium on Circuits and Systems, 2008Co-Authors: Magdy Tawfik Hanna, Nabila Philip Attalla Seif, M.w. Abd El Maguid AhmedAbstract:The development of the discrete fractional Fourier transform (DFRFT) necessitates the availability of a complete set of orthonormal eigenvectors of the DFT matrix F. An eigenanalysis is performed for the original Grunbaum tridiagonal matrix T - which commutes with matrix F - having only one Eigenvalue of multiplicity two and simple remaining Eigenvalues. The two easily obtainable eigenvectors of T corresponding to its Repeated Eigenvalue - which are not eigenvectors of F - are exploited for analytically generating two orthonormal eigenvectors common to both T and F.
Stanley Osher - One of the best experts on this subject based on the ideXlab platform.
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Efficient Characteristic Projection in Upwind Difference Schemes for Hyperbolic Systems
Journal of Computational Physics, 1998Co-Authors: Ronald Fedkiw, Barry Merriman, Stanley OsherAbstract:The standard construction of upwind difference schemes for hyperbolic systems of conservation laws requires the full eigensystem of the Jacobian matrix. This system is used to define the transformation into and out of the characteristic scalar fields, where upwind differencing is meaningful. When the Jacobian has a Repeated Eigenvalue, the associated normalized eigenvectors are not uniquely determined, and an arbitrary choice of eigenvectors must be made to span the characteristic subspace. In this report we point out that it is possible to avoid this arbitrary choice entirely. Instead, a complementary projection technique can be used to formulate upwind differencing without specifying a basis. For systems with Eigenvalues of high multiplicity, this approach simplifies the analytical and programming effort and reduces the computational cost. Numerical experiments show no significant difference in computed results between this formulation and the traditional one, and thus we recommend its use for these types of problems. This complementary projection method has other applications. For example, it can be used to extend upwind schemes to some weakly hyperbolic systems. These lack complete eigensystems, so the traditional form of characteristic upwinding is not possible.
Bo Wang - One of the best experts on this subject based on the ideXlab platform.
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Fast buckling load numerical prediction method for imperfect shells under axial compression based on POD and vibration correlation technique
Composite Structures, 2020Co-Authors: Kuo Tian, Peng Hao, Yu Sun, Lei Huang, Bo WangAbstract:Abstract Vibration correlation technique (VCT) is an effective non-destructive buckling experimental technique for shell structures. In this study, VCT is studied from the point-of-view of being a buckling load numerical prediction method by numerically simulating the experimental procedure of VCT. Firstly, the formulas of VCT are introduced for axially loaded cylindrical shells and conical shells under the clamped–clamped boundary condition. According to the VCT formulas, the numerical procedure of VCT is provided. In order to accelerate the Repeated Eigenvalue analysis of VCT, the proper orthogonal decomposition (POD) method is integrated into VCT, and the POD-VCT is developed. Extensive examples are presented to verify the effectiveness of the proposed method, including unstiffened cylindrical shell with real measured imperfection, unstiffened conical shell with single perturbation load imperfection, composite cylindrical shell with eigenmode imperfection, and hierarchical stiffened cylindrical shell with combined imperfection. In comparison to buckling test results, high-fidelity explicit dynamic method and VCT method, the high prediction accuracy and efficiency of the proposed POD-VCT are fully demonstrated. Additionally, example results indicate the strong applicability of the proposed POD-VCT for various types of structural configurations, materials and imperfections. Above all, the POD-VCT is verified to be a fast buckling load numerical prediction method for imperfect shells.
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Finite element model updating for Repeated Eigenvalue structures via the reduced-order model using incomplete measured modes
Mechanical Systems and Signal Processing, 2020Co-Authors: Kuo Tian, Peng Hao, Bo Wang, Wang BinAbstract:Abstract In order to obtain a precise dynamic structural FE model for dynamic analysis, FE model updating is usually used to correct uncertainty parameters for an initial FE model using incomplete measured data. Despite numerous studies concerning FE model updating, the computational cost is still a challenging issue for the Repeated Eigenvalue structures. Firstly, an improved modal assurance criterion is proposed to evaluate the similarity of mode shapes for the Repeated Eigenvalue structures in this paper. And then, a novel ROM-based FE model updating framework consisting of an off-line phase and an on-line phase is proposed. In the off-line phase, a reduced-order basis is constructed by extracting primary components of a snapshot matrix using a proper orthogonal decomposition technique. The snapshot matrix represents a collection of static displacement vectors of the FE model under radial nodal loads, which are determined by incomplete measured mode shapes. In the on-line phase, FE model updating is performed via a reduced-order model with much cheaper computational cost. Finally, a numerical example and an experimental example demonstrate the accuracy and efficiency of the proposed framework. The results indicate that the proposed ROM-based FE model updating framework is more efficient and stable than the FOM-based FE model updating framework.
Kuo Tian - One of the best experts on this subject based on the ideXlab platform.
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Fast buckling load numerical prediction method for imperfect shells under axial compression based on POD and vibration correlation technique
Composite Structures, 2020Co-Authors: Kuo Tian, Peng Hao, Yu Sun, Lei Huang, Bo WangAbstract:Abstract Vibration correlation technique (VCT) is an effective non-destructive buckling experimental technique for shell structures. In this study, VCT is studied from the point-of-view of being a buckling load numerical prediction method by numerically simulating the experimental procedure of VCT. Firstly, the formulas of VCT are introduced for axially loaded cylindrical shells and conical shells under the clamped–clamped boundary condition. According to the VCT formulas, the numerical procedure of VCT is provided. In order to accelerate the Repeated Eigenvalue analysis of VCT, the proper orthogonal decomposition (POD) method is integrated into VCT, and the POD-VCT is developed. Extensive examples are presented to verify the effectiveness of the proposed method, including unstiffened cylindrical shell with real measured imperfection, unstiffened conical shell with single perturbation load imperfection, composite cylindrical shell with eigenmode imperfection, and hierarchical stiffened cylindrical shell with combined imperfection. In comparison to buckling test results, high-fidelity explicit dynamic method and VCT method, the high prediction accuracy and efficiency of the proposed POD-VCT are fully demonstrated. Additionally, example results indicate the strong applicability of the proposed POD-VCT for various types of structural configurations, materials and imperfections. Above all, the POD-VCT is verified to be a fast buckling load numerical prediction method for imperfect shells.
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Finite element model updating for Repeated Eigenvalue structures via the reduced-order model using incomplete measured modes
Mechanical Systems and Signal Processing, 2020Co-Authors: Kuo Tian, Peng Hao, Bo Wang, Wang BinAbstract:Abstract In order to obtain a precise dynamic structural FE model for dynamic analysis, FE model updating is usually used to correct uncertainty parameters for an initial FE model using incomplete measured data. Despite numerous studies concerning FE model updating, the computational cost is still a challenging issue for the Repeated Eigenvalue structures. Firstly, an improved modal assurance criterion is proposed to evaluate the similarity of mode shapes for the Repeated Eigenvalue structures in this paper. And then, a novel ROM-based FE model updating framework consisting of an off-line phase and an on-line phase is proposed. In the off-line phase, a reduced-order basis is constructed by extracting primary components of a snapshot matrix using a proper orthogonal decomposition technique. The snapshot matrix represents a collection of static displacement vectors of the FE model under radial nodal loads, which are determined by incomplete measured mode shapes. In the on-line phase, FE model updating is performed via a reduced-order model with much cheaper computational cost. Finally, a numerical example and an experimental example demonstrate the accuracy and efficiency of the proposed framework. The results indicate that the proposed ROM-based FE model updating framework is more efficient and stable than the FOM-based FE model updating framework.