The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Mingfang Zheng - One of the best experts on this subject based on the ideXlab platform.
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application of state vector formalism and Legendre Polynomial hybrid method in the longitudinal guided wave propagation analysis of composite multi layered pipes
Wave Motion, 2021Co-Authors: Jie Gao, Mingfang Zheng, Yan Lyu, Mingkun Liu, Hongye LiuAbstract:Abstract In this research, we applied a Polynomial hybrid approach for modelling longitudinal guided waves propagating in anisotropic composites multi-layered pipes. Theoretically, dispersion characteristic equations in cylindrical coordinate system were derived by introducing the state vector form of displacement and stress components. In virtue of the orthogonality completeness and recursion properties of Legendre Polynomial series, the dispersion curves of longitudinal guided waves for arbitrary multi-layered anisotropic pipes can be obtained efficiently and accurately. As an alternative serial approach, it solves the wave propagation problem of complex anisotropic cylinders, and also avoids the tedious integral operations in the traditional Legendre Polynomial method. The reliability of the numerical results of longitudinal guided waves propagating in arbitrary multi-layered anisotropic pipes was investigated based on the state matrix and Legendre Polynomial hybrid method. At first, we calculated the multi-layered pipes composed of isotropic materials (steel and aluminum) with different diameter-thickness ratios and circumferential orders, and the results are consistent with the ones from the global matrix method. Then, the numerical analysis for a triple-layered adhesive pipe was implemented. Finally, the composite multi-layered pipes with at most 16 layers, which are the T300/914 in different orientations, were studied. Meanwhile, the effect of the layer number, fiber angle and circumferential order on the propagation characteristics of longitudinal guided waves were analyzed. To demonstrate the generality of this approach, we compared the dispersion curves of flat plate case with the results from the cylindrical case using the same physical properties by making the geometrical diameter to thickness ratio infinity. Furthermore, the displacements and stress distributions were also illustrated at given frequencies.
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derivation of circumferential guided waves equations for a multilayered laminate composite hollow cylinder by state vector and Legendre Polynomial hybrid formalism
Composite Structures, 2021Co-Authors: Mingfang Zheng, Yan LyuAbstract:Abstract A new spectral method based on the hybrid formula system of the state-vector and Legendre Polynomials are used to derive the explicit expressions of circumferential guided waves in the anisotropic multilayer composite cylinders with an arbitrary lay-up. In this hybrid method, the state vector was utilized to transform the wave equation, boundary conditions, and interface continuous conditions in the cylinder coordinate system to form the dispersion equation in terms of the state matrix. Then, following the principle of the Galerkin method, projecting the dispersion state matrix equations onto the weight functions consisting of Legendre Polynomials, the system of algebraic equation is obtained. The dispersion curves and mode shape can be obtained by solving the eigenvalues and eigenvectors of the system of algebraic equations. This hybrid method uses the orthogonal and recursive properties of the Legendre Polynomial to simplify the integral expressions involved in all the matrices and yields the closed-form solutions. Numerical verification, including the cases of isotropic and anisotropic viscoelastic/elastic multilayer cylinders, was conducted to evaluate the performance of the proposed method. The results show that the proposed method overcomes the cumbersome of the traditional Legendre Polynomial method to treat the interface displacement and stress continuity. The results also confirm that the hybrid method has the exponential convergence.
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modeling guided wave propagation in functionally graded plates by state vector formalism and the Legendre Polynomial method
Ultrasonics, 2019Co-Authors: Jie Gao, Mingfang Zheng, Yan Lyu, Mingkun Liu, Hongye LiuAbstract:Abstract A numerical method is presented for the investigation of the propagation characteristic of guided waves in functionally gradient material (FGM) plates. Based on the State-vector formalism and Legendre Polynomial method, the typical non-stratified computing of dispersion curves of FGMs is realized, by introducing the univariate nonlinear regression to optimize the arbitrary gradient distribution of material component. Comparing with the conventional Matrix method, the proposed method avoids the exhausting root-locating algorithm of solving the transcendental equation by a single-variable scanning process. This method turns it into an algebraic eigenvalue problem, which mainly depends on the orthogonal completeness and strong recursive property of Legendre Polynomial series. It provides a fast and flexible approach to extracting the dispersion curves, displacement distribution and stress profile, simultaneously. Results from chrome-ceramic FGM plate are compared with those from the previous articles to confirm the feasibility and accuracy of the proposed method. Then, this approach is further applied to iron based alumina FGM. The dispersion curves with different gradient function are calculated to illustrate the influence of the gradient variation. Moreover, the influence of the cut-off order of Legendre orthogonal Polynomials on the convergence of dispersion curves is also revealed through numerical examples. Utilizing the mapping relationship between the gradient distribution and the propagation characteristics, it gives theoretical support for nondestructive evaluation and quantitative estimation of the structural characteristics of FGM plates.
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guided waves propagation in anisotropic hollow cylinders by Legendre Polynomial solution based on state vector formalism
Composite Structures, 2019Co-Authors: Mingfang Zheng, Yan LyuAbstract:Abstract A spectral approach was presented in the computation of dispersion curves for the general anisotropic hollow cylinders. The derivation is based on the hybrid method of the state-vector formalism and Legendre Polynomials expansion, which was previously adopted for the anisotropic plates. This method will lead to an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles. This hybrid method avoids solving the transcendental dispersion equation. A closed-form solution for the hollow cylinder, involving multiple integral expressions, is demonstrated. A stable scheme for the integration expansion was established by re-expanding the expansion operators from the first round Legendre Polynomial expansion versus the displacements. Usually, the traditional matrix methods are based on root-finding algorithms, which is difficult to implement in anisotropic tubes. In this research, the hybrid approach we proposed provides a reliable mathematical solution of wave propagations in an anisotropic hollow cylinder. Applications will be illustrated using isotropic and orthotropic hollow cylinders, in which the isotropic case agrees well with the results by global matrix method. The dispersion curves of orthotropic hollow cylinders, when the out radius set to approximate infinity, are compared to its corresponding anisotropic plate, which is obtained from our previous work. Furthermore, the displacement and stress profiles will be given and analyzed for an orthotropic tube, which has 10 mm thickness with an out radius of 50 mm.
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State-vector formalism and the Legendre Polynomial solution for modelling guided waves in anisotropic plates
Journal of Sound and Vibration, 2018Co-Authors: Mingfang ZhengAbstract:Abstract We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact solution to the problem in the form of the Legendre Polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre Polynomials. The Legendre Polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre Polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.
Yan Lyu - One of the best experts on this subject based on the ideXlab platform.
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application of state vector formalism and Legendre Polynomial hybrid method in the longitudinal guided wave propagation analysis of composite multi layered pipes
Wave Motion, 2021Co-Authors: Jie Gao, Mingfang Zheng, Yan Lyu, Mingkun Liu, Hongye LiuAbstract:Abstract In this research, we applied a Polynomial hybrid approach for modelling longitudinal guided waves propagating in anisotropic composites multi-layered pipes. Theoretically, dispersion characteristic equations in cylindrical coordinate system were derived by introducing the state vector form of displacement and stress components. In virtue of the orthogonality completeness and recursion properties of Legendre Polynomial series, the dispersion curves of longitudinal guided waves for arbitrary multi-layered anisotropic pipes can be obtained efficiently and accurately. As an alternative serial approach, it solves the wave propagation problem of complex anisotropic cylinders, and also avoids the tedious integral operations in the traditional Legendre Polynomial method. The reliability of the numerical results of longitudinal guided waves propagating in arbitrary multi-layered anisotropic pipes was investigated based on the state matrix and Legendre Polynomial hybrid method. At first, we calculated the multi-layered pipes composed of isotropic materials (steel and aluminum) with different diameter-thickness ratios and circumferential orders, and the results are consistent with the ones from the global matrix method. Then, the numerical analysis for a triple-layered adhesive pipe was implemented. Finally, the composite multi-layered pipes with at most 16 layers, which are the T300/914 in different orientations, were studied. Meanwhile, the effect of the layer number, fiber angle and circumferential order on the propagation characteristics of longitudinal guided waves were analyzed. To demonstrate the generality of this approach, we compared the dispersion curves of flat plate case with the results from the cylindrical case using the same physical properties by making the geometrical diameter to thickness ratio infinity. Furthermore, the displacements and stress distributions were also illustrated at given frequencies.
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derivation of circumferential guided waves equations for a multilayered laminate composite hollow cylinder by state vector and Legendre Polynomial hybrid formalism
Composite Structures, 2021Co-Authors: Mingfang Zheng, Yan LyuAbstract:Abstract A new spectral method based on the hybrid formula system of the state-vector and Legendre Polynomials are used to derive the explicit expressions of circumferential guided waves in the anisotropic multilayer composite cylinders with an arbitrary lay-up. In this hybrid method, the state vector was utilized to transform the wave equation, boundary conditions, and interface continuous conditions in the cylinder coordinate system to form the dispersion equation in terms of the state matrix. Then, following the principle of the Galerkin method, projecting the dispersion state matrix equations onto the weight functions consisting of Legendre Polynomials, the system of algebraic equation is obtained. The dispersion curves and mode shape can be obtained by solving the eigenvalues and eigenvectors of the system of algebraic equations. This hybrid method uses the orthogonal and recursive properties of the Legendre Polynomial to simplify the integral expressions involved in all the matrices and yields the closed-form solutions. Numerical verification, including the cases of isotropic and anisotropic viscoelastic/elastic multilayer cylinders, was conducted to evaluate the performance of the proposed method. The results show that the proposed method overcomes the cumbersome of the traditional Legendre Polynomial method to treat the interface displacement and stress continuity. The results also confirm that the hybrid method has the exponential convergence.
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modeling guided wave propagation in functionally graded plates by state vector formalism and the Legendre Polynomial method
Ultrasonics, 2019Co-Authors: Jie Gao, Mingfang Zheng, Yan Lyu, Mingkun Liu, Hongye LiuAbstract:Abstract A numerical method is presented for the investigation of the propagation characteristic of guided waves in functionally gradient material (FGM) plates. Based on the State-vector formalism and Legendre Polynomial method, the typical non-stratified computing of dispersion curves of FGMs is realized, by introducing the univariate nonlinear regression to optimize the arbitrary gradient distribution of material component. Comparing with the conventional Matrix method, the proposed method avoids the exhausting root-locating algorithm of solving the transcendental equation by a single-variable scanning process. This method turns it into an algebraic eigenvalue problem, which mainly depends on the orthogonal completeness and strong recursive property of Legendre Polynomial series. It provides a fast and flexible approach to extracting the dispersion curves, displacement distribution and stress profile, simultaneously. Results from chrome-ceramic FGM plate are compared with those from the previous articles to confirm the feasibility and accuracy of the proposed method. Then, this approach is further applied to iron based alumina FGM. The dispersion curves with different gradient function are calculated to illustrate the influence of the gradient variation. Moreover, the influence of the cut-off order of Legendre orthogonal Polynomials on the convergence of dispersion curves is also revealed through numerical examples. Utilizing the mapping relationship between the gradient distribution and the propagation characteristics, it gives theoretical support for nondestructive evaluation and quantitative estimation of the structural characteristics of FGM plates.
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guided waves propagation in anisotropic hollow cylinders by Legendre Polynomial solution based on state vector formalism
Composite Structures, 2019Co-Authors: Mingfang Zheng, Yan LyuAbstract:Abstract A spectral approach was presented in the computation of dispersion curves for the general anisotropic hollow cylinders. The derivation is based on the hybrid method of the state-vector formalism and Legendre Polynomials expansion, which was previously adopted for the anisotropic plates. This method will lead to an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles. This hybrid method avoids solving the transcendental dispersion equation. A closed-form solution for the hollow cylinder, involving multiple integral expressions, is demonstrated. A stable scheme for the integration expansion was established by re-expanding the expansion operators from the first round Legendre Polynomial expansion versus the displacements. Usually, the traditional matrix methods are based on root-finding algorithms, which is difficult to implement in anisotropic tubes. In this research, the hybrid approach we proposed provides a reliable mathematical solution of wave propagations in an anisotropic hollow cylinder. Applications will be illustrated using isotropic and orthotropic hollow cylinders, in which the isotropic case agrees well with the results by global matrix method. The dispersion curves of orthotropic hollow cylinders, when the out radius set to approximate infinity, are compared to its corresponding anisotropic plate, which is obtained from our previous work. Furthermore, the displacement and stress profiles will be given and analyzed for an orthotropic tube, which has 10 mm thickness with an out radius of 50 mm.
J. E. Lefebvre - One of the best experts on this subject based on the ideXlab platform.
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free ultrasonic waves in multilayered piezoelectric plates an improvement of the Legendre Polynomial approach for multilayered structures with very dissimilar materials
Composites Part B-engineering, 2013Co-Authors: J. E. Lefebvre, Y Q GuoAbstract:Abstract In 1999, Legendre Polynomial approach has been proposed to solve wave propagation in the multilayered piezoelectric plate. However, it can deal with the multilayered plate only when the material properties of two adjacent layers do not change significantly. In this paper, an improvement of the Legendre Polynomial approach is promoted to solve wave propagation in multilayered piezoelectric plates whatever the dissimilarities of the layer material properties. Detailed formulations are given to highlight the differences from the conventional Legendre Polynomial approach. The validity of the proposed improved approach is illustrated through a numerical comparison between the improved method’s results and the exact solution obtained from the reverberation-ray matrix method. It is shown that the conventional orthogonal Polynomial approach cannot conceptually calculate accurately, neither the discontinuous distribution of the normal electric field nor the continuous distributions of the normal stress and normal electric displacement, even in multilayered plates with similar layer material properties while the proposed improved Polynomial approach overcomes these major drawbacks. Finally, the influences of the stacking sequences and volume fractions on dispersion curves are illustrated. It is also found that the stress and electric displacement of high frequency waves always distribute on the layer with lower wave speed.
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wave propagation in multilayered piezoelectric spherical plates
Acta Mechanica, 2013Co-Authors: J. E. Lefebvre, Y Q GuoAbstract:This paper proposes an improvement of the Legendre Polynomial series method to solve the harmonic wave propagation in multilayered piezoelectric spherical plates, which are used in point-focusing transducers. The conventional Legendre Polynomial method can deal with the multilayered structures only when the material properties of two adjacent layers do not change significantly and cannot obtain correctly normal stress and normal electric displacement shapes unlike the proposed improved orthogonal Polynomial approach which overcomes these drawbacks. Detailed formulations are given to highlight its differences from the conventional Legendre Polynomial approach. Through the comparisons of numerical results given by an exact solution (obtained from the reverberation-ray matrix method), and by the conventional Polynomial approach and the improved Polynomial approach, the validity of the proposed approach is illustrated. The influences of the radius-to-thickness ratio on dispersion curves, stress and electric displacement distributions are discussed. It is found that three factors determine the distribution of mechanical energy and electric energy at higher frequencies: radius-to-thickness ratio, wave speed, and position of the component material.
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guided waves in multilayered hollow cylinders the improved Legendre Polynomial method
Composite Structures, 2013Co-Authors: J. E. LefebvreAbstract:Abstract Legendre Polynomial series method has been proposed to solve the wave propagation in multilayered flat plates for more than 10 years. But it has never been used for curved waveguides. This method has intrinsic limitations: it can deal only with low contrast multilayered structures and is unable to restitute correct continuous normal stress distributions. This paper proposes an improvement of the Legendre Polynomial method to overcome these drawbacks and uses it to solve the guided wave propagation in general multilayered hollow cylinders i.e. with or without very dissimilar material properties. Detailed formulations are given to show the differences between the improved orthogonal Polynomial method and the conventional one. Through a numerical comparison among the exact solution (from the transfer matrix method), the improved Polynomial approach and the conventional Polynomial approach, the validity of the improved Polynomial approach is illustrated. Then, the flexural guided wave dispersion curves and stress distributions are analyzed. The influences of the flexural orders and of the radius to thickness ratio on flexural longitudinal wave and flexural torsional wave are discussed.
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Wave propagation in the circumferential direction of general multilayered piezoelectric cylindrical plates
IEEE transactions on ultrasonics ferroelectrics and frequency control, 2012Co-Authors: J. E. Lefebvre, Y. G. Guo, L. ElmaimouniAbstract:The Legendre Polynomial approach has been proposed to solve wave propagation in multilayered flat plates and functionally graded structures for more than ten years, but it can deal with a multilayered plate only when the material properties of two adjacent layers do not change significantly. In this paper, an improvement of the Legendre Polynomial approach is proposed to solve wave propagation in what, from now on, we will call general multilayered piezoelectric cylindrical plates, to mean indifferently with or without very dissimilar materials. Detailed formulations are given to highlight the differences from the conventional Legendre Polynomial approach. Through numerical comparisons among the exact solution (from the reverberation-ray matrix), the conventional Polynomial approach, and the improved Polynomial approach, the validity of the proposed approach is illustrated. Then, the influences of the radius-to-thickness ratio on the dispersion curves, the stress, and electric displacement distributions are discussed. It is shown that the conventional orthogonal Polynomial approach cannot obtain correct continuous normal stress and normal electric displacement shapes, unlike the improved orthogonal Polynomial approach, which overcomes these drawbacks. It is also found that three factors determine the distribution of mechanical energy and electric energy at higher frequencies: the radius-to-thickness ratio, the wave speed of component material, and the position of the component material.
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Legendre Polynomial modeling of composite bulk acoustic wave resonators
Journal of Applied Physics, 2008Co-Authors: A Raherison, J. E. Lefebvre, F E Ratolojanahary, L. ElmaimouniAbstract:The Legendre Polynomial method has been extended to the modeling of bulk acoustic wave (BAW) resonators. Modifications have been made to the formulation in order to account for large differences in the physical properties of adjoining layers and to take into account the electric source. A unique formalism has been obtained which allows for both harmonic and modal analyses. Resonance and antiresonance frequencies, electric input impedance, electromechanical coupling coefficients, and quality factors have been obtained for an aluminum/zinc oxide/aluminum (Al∕ZnO∕Al) BAW resonator. The results are in excellent agreement with analytical results.
Hongye Liu - One of the best experts on this subject based on the ideXlab platform.
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application of state vector formalism and Legendre Polynomial hybrid method in the longitudinal guided wave propagation analysis of composite multi layered pipes
Wave Motion, 2021Co-Authors: Jie Gao, Mingfang Zheng, Yan Lyu, Mingkun Liu, Hongye LiuAbstract:Abstract In this research, we applied a Polynomial hybrid approach for modelling longitudinal guided waves propagating in anisotropic composites multi-layered pipes. Theoretically, dispersion characteristic equations in cylindrical coordinate system were derived by introducing the state vector form of displacement and stress components. In virtue of the orthogonality completeness and recursion properties of Legendre Polynomial series, the dispersion curves of longitudinal guided waves for arbitrary multi-layered anisotropic pipes can be obtained efficiently and accurately. As an alternative serial approach, it solves the wave propagation problem of complex anisotropic cylinders, and also avoids the tedious integral operations in the traditional Legendre Polynomial method. The reliability of the numerical results of longitudinal guided waves propagating in arbitrary multi-layered anisotropic pipes was investigated based on the state matrix and Legendre Polynomial hybrid method. At first, we calculated the multi-layered pipes composed of isotropic materials (steel and aluminum) with different diameter-thickness ratios and circumferential orders, and the results are consistent with the ones from the global matrix method. Then, the numerical analysis for a triple-layered adhesive pipe was implemented. Finally, the composite multi-layered pipes with at most 16 layers, which are the T300/914 in different orientations, were studied. Meanwhile, the effect of the layer number, fiber angle and circumferential order on the propagation characteristics of longitudinal guided waves were analyzed. To demonstrate the generality of this approach, we compared the dispersion curves of flat plate case with the results from the cylindrical case using the same physical properties by making the geometrical diameter to thickness ratio infinity. Furthermore, the displacements and stress distributions were also illustrated at given frequencies.
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modeling guided wave propagation in functionally graded plates by state vector formalism and the Legendre Polynomial method
Ultrasonics, 2019Co-Authors: Jie Gao, Mingfang Zheng, Yan Lyu, Mingkun Liu, Hongye LiuAbstract:Abstract A numerical method is presented for the investigation of the propagation characteristic of guided waves in functionally gradient material (FGM) plates. Based on the State-vector formalism and Legendre Polynomial method, the typical non-stratified computing of dispersion curves of FGMs is realized, by introducing the univariate nonlinear regression to optimize the arbitrary gradient distribution of material component. Comparing with the conventional Matrix method, the proposed method avoids the exhausting root-locating algorithm of solving the transcendental equation by a single-variable scanning process. This method turns it into an algebraic eigenvalue problem, which mainly depends on the orthogonal completeness and strong recursive property of Legendre Polynomial series. It provides a fast and flexible approach to extracting the dispersion curves, displacement distribution and stress profile, simultaneously. Results from chrome-ceramic FGM plate are compared with those from the previous articles to confirm the feasibility and accuracy of the proposed method. Then, this approach is further applied to iron based alumina FGM. The dispersion curves with different gradient function are calculated to illustrate the influence of the gradient variation. Moreover, the influence of the cut-off order of Legendre orthogonal Polynomials on the convergence of dispersion curves is also revealed through numerical examples. Utilizing the mapping relationship between the gradient distribution and the propagation characteristics, it gives theoretical support for nondestructive evaluation and quantitative estimation of the structural characteristics of FGM plates.
Jie Gao - One of the best experts on this subject based on the ideXlab platform.
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application of state vector formalism and Legendre Polynomial hybrid method in the longitudinal guided wave propagation analysis of composite multi layered pipes
Wave Motion, 2021Co-Authors: Jie Gao, Mingfang Zheng, Yan Lyu, Mingkun Liu, Hongye LiuAbstract:Abstract In this research, we applied a Polynomial hybrid approach for modelling longitudinal guided waves propagating in anisotropic composites multi-layered pipes. Theoretically, dispersion characteristic equations in cylindrical coordinate system were derived by introducing the state vector form of displacement and stress components. In virtue of the orthogonality completeness and recursion properties of Legendre Polynomial series, the dispersion curves of longitudinal guided waves for arbitrary multi-layered anisotropic pipes can be obtained efficiently and accurately. As an alternative serial approach, it solves the wave propagation problem of complex anisotropic cylinders, and also avoids the tedious integral operations in the traditional Legendre Polynomial method. The reliability of the numerical results of longitudinal guided waves propagating in arbitrary multi-layered anisotropic pipes was investigated based on the state matrix and Legendre Polynomial hybrid method. At first, we calculated the multi-layered pipes composed of isotropic materials (steel and aluminum) with different diameter-thickness ratios and circumferential orders, and the results are consistent with the ones from the global matrix method. Then, the numerical analysis for a triple-layered adhesive pipe was implemented. Finally, the composite multi-layered pipes with at most 16 layers, which are the T300/914 in different orientations, were studied. Meanwhile, the effect of the layer number, fiber angle and circumferential order on the propagation characteristics of longitudinal guided waves were analyzed. To demonstrate the generality of this approach, we compared the dispersion curves of flat plate case with the results from the cylindrical case using the same physical properties by making the geometrical diameter to thickness ratio infinity. Furthermore, the displacements and stress distributions were also illustrated at given frequencies.
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modeling guided wave propagation in functionally graded plates by state vector formalism and the Legendre Polynomial method
Ultrasonics, 2019Co-Authors: Jie Gao, Mingfang Zheng, Yan Lyu, Mingkun Liu, Hongye LiuAbstract:Abstract A numerical method is presented for the investigation of the propagation characteristic of guided waves in functionally gradient material (FGM) plates. Based on the State-vector formalism and Legendre Polynomial method, the typical non-stratified computing of dispersion curves of FGMs is realized, by introducing the univariate nonlinear regression to optimize the arbitrary gradient distribution of material component. Comparing with the conventional Matrix method, the proposed method avoids the exhausting root-locating algorithm of solving the transcendental equation by a single-variable scanning process. This method turns it into an algebraic eigenvalue problem, which mainly depends on the orthogonal completeness and strong recursive property of Legendre Polynomial series. It provides a fast and flexible approach to extracting the dispersion curves, displacement distribution and stress profile, simultaneously. Results from chrome-ceramic FGM plate are compared with those from the previous articles to confirm the feasibility and accuracy of the proposed method. Then, this approach is further applied to iron based alumina FGM. The dispersion curves with different gradient function are calculated to illustrate the influence of the gradient variation. Moreover, the influence of the cut-off order of Legendre orthogonal Polynomials on the convergence of dispersion curves is also revealed through numerical examples. Utilizing the mapping relationship between the gradient distribution and the propagation characteristics, it gives theoretical support for nondestructive evaluation and quantitative estimation of the structural characteristics of FGM plates.