This research explores the dynamic behaviour of horn-shaped single-walled carbon nanotubes(HS-SWCNTs)conveying viscous nanofluid with pulsating the influence of a longitudinal magnetic field.The analysis utilizes Eule...This research explores the dynamic behaviour of horn-shaped single-walled carbon nanotubes(HS-SWCNTs)conveying viscous nanofluid with pulsating the influence of a longitudinal magnetic field.The analysis utilizes Euler-Bernoulli beam model,considering the variable cross section,and incorporating Eringen’s nonlocal theory to formulate the governing partial differential equation of motion.The instability domain of HS-SWCNTs is estimated using Galerkin’s approach.Numerical analysis is performed using the Haar wavelet method.The critical buckling load obtained in this study is compared with previous research to validate the proposed model.The results highlight the effectiveness of the proposed model in assessing the vibrational characteristics of a complex multi-physics system involving HS-SWCNTs.Dispersion graphs and tables are presented to visualize the numerical findings pertaining to various system parameters,including the nonlocal parameter,magnetic flux,Knudsen number,and viscous factor.展开更多
An r-adaptive boundary element method（BEM） based on unbalanced Haar wavelets（UBHWs） is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To a...An r-adaptive boundary element method（BEM） based on unbalanced Haar wavelets（UBHWs） is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To accelerate the convergence of the adaptive process,the grading function and optimization iteration methods are successively employed.Numerical results of two representative examples clearly show that,first,the combined iteration method can accelerate the convergence;moreover,by using UBHWs,the memory usage for storing the system matrix of the r-adaptive BEM can be reduced by a factor of about 100 for problems with more than 15 thousand unknowns,while the error and convergence property of the original BEM can be retained.展开更多
Objective of our paper is to present the Haar wavelet based solutions of boundary value problems by Haar collocation method and utilizing Quasilinearization technique to resolve quadratic nonlinearity in y. More accur...Objective of our paper is to present the Haar wavelet based solutions of boundary value problems by Haar collocation method and utilizing Quasilinearization technique to resolve quadratic nonlinearity in y. More accurate solutions are obtained by wavelet decomposition in the form of a multiresolution analysis of the function which represents solution of boundary value problems. Through this analysis, solutions are found on the coarse grid points and refined towards higher accuracy by increasing the level of the Haar wavelets. A distinctive feature of the proposed method is its simplicity and applicability for a variety of boundary conditions. Numerical tests are performed to check the applicability and efficiency. C++ program is developed to find the wavelet solution.展开更多
In this work, by choosing an orthonormal basis for the Hilbert space L^2[0, 1], an approximation method for finding approximate solutions of the equation （I ＋ K）x = y is proposed, called Haar wavelet approximation ...In this work, by choosing an orthonormal basis for the Hilbert space L^2[0, 1], an approximation method for finding approximate solutions of the equation （I ＋ K）x = y is proposed, called Haar wavelet approximation method （HWAM）. To prove the applicabifity of the HWAM, a more general applicability theorem on an approximation method （AM） for an operator equation Ax = y is proved first. As an application, applicability of the HWAM is obtained. Fhrthermore, four steps to use the HWAM are listed and three numerical examples are given in order to illustrate the effectiveness of the method.展开更多
Investigation on vibration of laminated composite beam(LCB)is an important issue owing to its wide use as fundamental component.In the present work,we study the free vibration of arbitrarily LCB with generalized elast...Investigation on vibration of laminated composite beam(LCB)is an important issue owing to its wide use as fundamental component.In the present work,we study the free vibration of arbitrarily LCB with generalized elastic boundary condition(BC)by using Haar wavelet discretization method(HWDM).Timoshenko beam theory is utilized to model the free vibration of LCB.The LCB is first split into several segments,and then the displacement for each segment is obtained from the Haar wavelet series and their integral.Hamilton’s principle is applied to construct governing equations and the artificial spring boundary technique is adopted to obtain the general elastic boundary and continuity conditions at two ends of LCB.The vibration characteristics of beam with different fiber orientations and lamina numbers is investigated and its displacements are compared with those in previous works.Numerical results are shown graphically and demonstrate the validation of our method.展开更多
文摘This research explores the dynamic behaviour of horn-shaped single-walled carbon nanotubes(HS-SWCNTs)conveying viscous nanofluid with pulsating the influence of a longitudinal magnetic field.The analysis utilizes Euler-Bernoulli beam model,considering the variable cross section,and incorporating Eringen’s nonlocal theory to formulate the governing partial differential equation of motion.The instability domain of HS-SWCNTs is estimated using Galerkin’s approach.Numerical analysis is performed using the Haar wavelet method.The critical buckling load obtained in this study is compared with previous research to validate the proposed model.The results highlight the effectiveness of the proposed model in assessing the vibrational characteristics of a complex multi-physics system involving HS-SWCNTs.Dispersion graphs and tables are presented to visualize the numerical findings pertaining to various system parameters,including the nonlocal parameter,magnetic flux,Knudsen number,and viscous factor.
基金Supported by the National Natural Science Foundation of China (10674109)the Doctorate Foundation of Northwestern Polytechnical University (CX200601)
文摘An r-adaptive boundary element method（BEM） based on unbalanced Haar wavelets（UBHWs） is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To accelerate the convergence of the adaptive process,the grading function and optimization iteration methods are successively employed.Numerical results of two representative examples clearly show that,first,the combined iteration method can accelerate the convergence;moreover,by using UBHWs,the memory usage for storing the system matrix of the r-adaptive BEM can be reduced by a factor of about 100 for problems with more than 15 thousand unknowns,while the error and convergence property of the original BEM can be retained.
文摘Objective of our paper is to present the Haar wavelet based solutions of boundary value problems by Haar collocation method and utilizing Quasilinearization technique to resolve quadratic nonlinearity in y. More accurate solutions are obtained by wavelet decomposition in the form of a multiresolution analysis of the function which represents solution of boundary value problems. Through this analysis, solutions are found on the coarse grid points and refined towards higher accuracy by increasing the level of the Haar wavelets. A distinctive feature of the proposed method is its simplicity and applicability for a variety of boundary conditions. Numerical tests are performed to check the applicability and efficiency. C++ program is developed to find the wavelet solution.
基金support by the NSFC(11371012,11401359,11471200)the FRF for the Central Universities(GK201301007)the NSRP of Shaanxi Province(2014JQ1010)
文摘In this work, by choosing an orthonormal basis for the Hilbert space L^2[0, 1], an approximation method for finding approximate solutions of the equation （I ＋ K）x = y is proposed, called Haar wavelet approximation method （HWAM）. To prove the applicabifity of the HWAM, a more general applicability theorem on an approximation method （AM） for an operator equation Ax = y is proved first. As an application, applicability of the HWAM is obtained. Fhrthermore, four steps to use the HWAM are listed and three numerical examples are given in order to illustrate the effectiveness of the method.
文摘Investigation on vibration of laminated composite beam(LCB)is an important issue owing to its wide use as fundamental component.In the present work,we study the free vibration of arbitrarily LCB with generalized elastic boundary condition(BC)by using Haar wavelet discretization method(HWDM).Timoshenko beam theory is utilized to model the free vibration of LCB.The LCB is first split into several segments,and then the displacement for each segment is obtained from the Haar wavelet series and their integral.Hamilton’s principle is applied to construct governing equations and the artificial spring boundary technique is adopted to obtain the general elastic boundary and continuity conditions at two ends of LCB.The vibration characteristics of beam with different fiber orientations and lamina numbers is investigated and its displacements are compared with those in previous works.Numerical results are shown graphically and demonstrate the validation of our method.
