This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and tw...This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.展开更多
In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin...In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green＇s function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.展开更多
In this paper, the nonlinear Hunter–Saxton equation, which is a famous partial differential equation,is solved by using a hybrid numerical method based on the quasilinearization method and the bivariate generalized f...In this paper, the nonlinear Hunter–Saxton equation, which is a famous partial differential equation,is solved by using a hybrid numerical method based on the quasilinearization method and the bivariate generalized fractional order of the Chebyshev functions(B-GFCF) collocation method. First, using the quasilinearization method,the equation is converted into a sequence of linear partial differential equations(LPD), and then these LPDs are solved using the B-GFCF collocation method. A very good approximation of solutions is obtained, and comparisons show that the obtained results are more accurate than the results of other researchers.展开更多
The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generali...The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .展开更多
In this paper, we study the generalized Chebyshev function related to automorphic L-functions of GLm（AQ）, and estimate its asymptotic behavior with respect to the parameters of the original automorphic objects.
In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic l...In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived.展开更多
文摘This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.
基金The project supported by the State Key Project of Fundamental Research of China under Grant No. G2000067101
文摘In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green＇s function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.
文摘In this paper, the nonlinear Hunter–Saxton equation, which is a famous partial differential equation,is solved by using a hybrid numerical method based on the quasilinearization method and the bivariate generalized fractional order of the Chebyshev functions(B-GFCF) collocation method. First, using the quasilinearization method,the equation is converted into a sequence of linear partial differential equations(LPD), and then these LPDs are solved using the B-GFCF collocation method. A very good approximation of solutions is obtained, and comparisons show that the obtained results are more accurate than the results of other researchers.
文摘The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .
文摘In this paper, we study the generalized Chebyshev function related to automorphic L-functions of GLm（AQ）, and estimate its asymptotic behavior with respect to the parameters of the original automorphic objects.
基金supported by the National Natural Science Foundation of China(No.11271261)the Natural Science Foundation of Anhui Province(No.1308085MA08)the Doctoral Program Foundation(2012)of Anhui Normal University
文摘In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived.
