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Halfrange orthogonality relations basic to the solution of timedependent boundary value problems in the kinetic theory of gase


Characterizations of real inner product spaces among normed linear spaces have been obtained by exploring properties of and relationships between various orthogonality relations which can be defined in such spaces.


We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relations which admit a dual system of orthogonal polynomials.


In particular, we deduce some structure and orthogonality relations for the successive partial derivatives of the polynomials.


It is based on the orthogonality relations for uniform Bsplines in weighted Sobolev spaces, as introduced in (Reif, 1997).

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 Introducing the definitions of two kinds of inner product and utilizing the principle of mechanical energy conservation of a conservative system, this paper presents the general form of orthogonality relations and unifiedproof for the system to be considered. At the end of this paper, some applications to various structures are presented.  本文引进两种内积的定义,给出了无阻尼混合参数系统的固有振型的正交关系的一般形式,且利用机械能守恒原理普遍地、简明地证明了固有振型的正交性关系。最后给出了若干应用。  In this paper, according to the characteristics of linear vibrating defective systems, a complete set of linearly independent generalized eigenvectors is found for the defective system. Such eigenvectors many be called as generalized modes. The partially biorthogonality relation between the generalized modes of the original and the adjoint systems i's also found and demonstrated. By use of the biorthogonality relation, the most general expressions of the transfer function and the pulse response... In this paper, according to the characteristics of linear vibrating defective systems, a complete set of linearly independent generalized eigenvectors is found for the defective system. Such eigenvectors many be called as generalized modes. The partially biorthogonality relation between the generalized modes of the original and the adjoint systems i's also found and demonstrated. By use of the biorthogonality relation, the most general expressions of the transfer function and the pulse response function of linear vibrating system are derived.A sample example is given to show the correctness and effectiveness of the suggested theory and method.  本文求出了线性振动亏损系统的一个完备的广义特征向量系,称之为广义模态;找出并证明了系统与其伴随系统的广义模态之间的部分双正交关系,并据此导出线性振动系统最一般的传递函数和脉冲响应函数表达式,示例表明了本文理论和方法的正确性和有效性。  What is presented in this paper is a method of finite element model updating via design parameters using test modal data. Based on orthogonality relation ships, the method adjusts the design parameters instead of the elements of mass and stiffness matrices. The Taylor's series of the system matrices expanded with respect to design parameters is adopted. The conducted set of linear equations is solved by a singular value decomposition technique. Because of the linear relation of system matrices with... What is presented in this paper is a method of finite element model updating via design parameters using test modal data. Based on orthogonality relation ships, the method adjusts the design parameters instead of the elements of mass and stiffness matrices. The Taylor's series of the system matrices expanded with respect to design parameters is adopted. The conducted set of linear equations is solved by a singular value decomposition technique. Because of the linear relation of system matrices with the most design parameters, the method is suitable to the cases of the severe change of the parameters, and the parameters converge to the “true value” by only several iterations. The problems, such as the effect of errors on the test modal parameters, the expansion of the degree of freedoms of test mode shapes, etc, are handled. The weighted global fit procedure is used to preprocess the test mode shapes to smooth the shapes and expand the degree of freedoms of the shapes simultaneously. The method can not be only applied to the finite element model updating, but also to the structural dynamics redesign. Numerical and practical examples show the efficiency and accuracy of the method.  本文提出了一种设计参数型的有限元模型修正方法。依据正交条件,采用系统矩阵对设计参数的台劳展开式,建立参数修改量的线性方程式,用奇异值分解方法求解。在本方法中充分考虑了试验模态参数误差的影响,及试验振型自由度扩充等问题。计算机仿真及实际算例的结果表明,本方法计算量小、精确度较好。   << 更多相关文摘 
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