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 expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and fo...In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.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.
This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functio...This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functions of them by operator calculus built from the derivative and the positional operators.展开更多
The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational...The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.展开更多
本文提出一种新的非平稳非线性信号特征提取方法。首先,利用Chebyshev插值法建立非平稳信号的最佳一致逼近函数;然后,通过对该函数进行偏正交分解获取对应的特征值及特征向量。特征值及特征向量作为信号特征,具有较高的稳定性。该方法...本文提出一种新的非平稳非线性信号特征提取方法。首先,利用Chebyshev插值法建立非平稳信号的最佳一致逼近函数;然后,通过对该函数进行偏正交分解获取对应的特征值及特征向量。特征值及特征向量作为信号特征,具有较高的稳定性。该方法计算量少,具有较高的模式稳定性。运用该方法通过对CWRU(Case Western Reserve University Bearing Data Center)轴承数据分析计算,得到正常滚动轴承与各类故障滚动轴承的特征值向量。实验表明:特征值向量与正常滚动轴承,故障滚动轴承有明显的差异,取得了良好的分类效果。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.
文摘In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.
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.
文摘This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functions of them by operator calculus built from the derivative and the positional operators.
文摘The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.
文摘本文提出一种新的非平稳非线性信号特征提取方法。首先,利用Chebyshev插值法建立非平稳信号的最佳一致逼近函数;然后,通过对该函数进行偏正交分解获取对应的特征值及特征向量。特征值及特征向量作为信号特征,具有较高的稳定性。该方法计算量少,具有较高的模式稳定性。运用该方法通过对CWRU(Case Western Reserve University Bearing Data Center)轴承数据分析计算,得到正常滚动轴承与各类故障滚动轴承的特征值向量。实验表明:特征值向量与正常滚动轴承,故障滚动轴承有明显的差异,取得了良好的分类效果。
