应用数学和力学

1992 Vol. 13, No. 9

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General Analytic Solution of Dynamic Response of Beams with Nonhomogeneity and Variable Cross Section

Yeh Kai-yuan, Tong Xiao-hua, Ji Zhen-yi

1992, 13(9): 753-764.

Abstract(2007) PDF(647)

Abstract:
In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new m...

Theory of Nonlocal Asymmetric Elastic Solids

Gao Jian, Chen Zhi-da

1992, 13(9): 765-774.

Abstract(2318) PDF(527)

Abstract:
In this paper, a nonlinear theory of nonlocal asymmetric, elastic solids is developed on the basis of basic theories of nonlocal continuum field theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic field theory developed by Eringen and others. The linear theory of n...

Unsteady Transonic Aerodynamic Loadings on the Airfoil Caused by Heaving, Pitching Oscillations and Control Surface

Gao Zheng-hong

1992, 13(9): 775-783.

Abstract(2523) PDF(430)

Abstract:
An implicit upwind finite volume solver for the Euler equations using the improved flux-splitting method is established and used to calculate the transonic flow past the airfoils with heaving, pitching oscillations and the control surface. Results are given for the NACA64A-10 airfoil which is in har...

Perturbation Formulation of Continuation Method Including Limit and Bifurcation Points

Wu Yi, Ren Wen-min, Zhang Wei

1992, 13(9): 785-794.

Abstract(2011) PDF(466)

Abstract:
This paper gives the perturbation formulation of continuation method for nonlinear equations. Emphasis is laid on the discussion of searching for the singular points on the equilibrium path and of tracing the paths over the limit or bifurcation points. The method is applied to buckling analysis of t...

Some General Theorems and Generalized and Piecewise Generalized Variational Principles for Linear Elastodynamics

Xing Jing-tang, Zheng Zhao-chang

1992, 13(9): 795-810.

Abstract(2716) PDF(515)

Abstract:
From the concept of four-dimensional space and under the four kinds of time limit conditions, some general theorems for elastodynamics are developed, such as the principle of possible work action, the virtual displacement principle, the virtual stress-momentum principle, the reciprocal theorems and ...

The Holder Continuity for the Gradient of Solutions to One-Sided Obstacle Problems

Wang Xiang-dong, Liang Xi-ting

1992, 13(9): 811-820.

Abstract(2640) PDF(476)

Abstract:
There is a gap in case 1<p<2 to the C^1+a regularity for solutions of variational inequalities with degenerate ellipticity.In this paper, basad on the fundamental of the C^0+a. reglarity of solutions,the Holder continuity for the gradient of solutions is proved in case 1<p<2 to a one-sided...

The Principles of Least Action of Vairable Mass Nonholonomic Nonconservative Systems in Noninertial Reference Frames

Luo Shao-kai, Mei Feng-xiang

1992, 13(9): 821-828.

Abstract(2471) PDF(664)

Abstract:
This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Holder form and Suslov form, and then obtains differential equations of motion of variable mass nonholonomic nonconservat...

Extension and Application of Newton’s Method in Nonlinear Oscillation Theory

Huo Lin-chun

1992, 13(9): 829-842.

Abstract(2574) PDF(578)

Abstract:
In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our ...

A Kind of General Influence Measure on the Linear Weighted Regression

Yang Hu

1992, 13(9): 843-847.

Abstract(1829) PDF(463)

Abstract:
The linear weighted regression model is one of the models studied in many articles in recent years. Some further problems, such as disturbation, influence measure and estimate efficiency, have been discussed in this paper on the basis of the regression diagnosties. The partial conclusions of this pa...

Topological Structure of the Singular Points of the Third Order Phase Locked Loop Equations with the Character of Detected Phase Being g(φ)=(1+k)sinφ/(1+kcosφ)

Jin Jun

1992, 13(9): 849-854.

Abstract(1879) PDF(461)

Abstract:
In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(φ)=(1+k)sinφ/1+kcosφ.