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Non-linear Dynamics

Xiao-Jun Yang

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Articles 31 - 38 of 38

Full-Text Articles in Other Mathematics

Local Fractional Fourier’S Transform Based On The Local Fractional Calculus, Yang Xiao-Jun Jan 2010

Local Fractional Fourier’S Transform Based On The Local Fractional Calculus, Yang Xiao-Jun

Xiao-Jun Yang

A new modeling for the local fractional Fourier’s transform containing the local fractional calculus is investigated in fractional space. The properties of the local fractional Fourier’s transform are obtained and two examples for the local fractional systems are investigated in detail.


Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun Jun 2009

Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun

Xiao-Jun Yang

Since Mandelbrot proposed the concept of fractal in 1970s’, fractal has been applied in various areas such as science, economics, cultures and arts because of the universality of fractal phenomena. It provides a new analytical tool to reveal the complexity of the real world. Nowadays the calculus in a fractal space becomes a hot topic in the world. Based on the established definitions of fractal derivative and fractal integral, the fundamental theorems of fractal derivatives and fractal integrals are investigated in detail. The fractal double integral and fractal triple integral are discussed and the variational principle in fractal space has …


The Fundamentals Of Local Fractional Derivative Of The One-Variable Non-Differentiable Functions, Yang Xiaojun Jan 2009

The Fundamentals Of Local Fractional Derivative Of The One-Variable Non-Differentiable Functions, Yang Xiaojun

Xiao-Jun Yang

Based on the theory of Jumarie’s fractional calculus, local fractional derivative is modified in detail and its fundamentals of local fractional derivative are proposed in this paper. The uniqueness of local fractional derivative is obtained and the Rolle’s theorem, the mean value theorem, the Cauchy’s generalized mean value theorem and the L’Hospital’s rules are proved.


Local Fractional Newton’S Method Derived From Modified Local Fractional Calculus, Yang Xiao-Jun Jan 2009

Local Fractional Newton’S Method Derived From Modified Local Fractional Calculus, Yang Xiao-Jun

Xiao-Jun Yang

A local fractional Newton’s method, which is derived from the modified local fractional calculus , is proposed in the present paper. Its iterative function is obtained and the convergence of the iterative function is discussed. The comparison between the classical Newton iteration and the local fractional Newton iteration has been carried out. It is shown that the iterative value of the local fractional Newton method better approximates the real-value than that of the classical one.


Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun Dec 2008

Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun

Xiao-Jun Yang

It is proposed that local fractional calculas introduced by Kolwankar and Gangal is extended by the concept of Jumarie’s fractional calculus and local fractional definite integral is redefined. The properties and the theorems of local fractional calculus are discussed in this paper.


The Adaptability Principle Of Mechanical Law And The Scale-Invariant Principle Of Mechanical Law In Fractal Space, Yang Xiaojun Jan 2008

The Adaptability Principle Of Mechanical Law And The Scale-Invariant Principle Of Mechanical Law In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

The adaptability principle of mechanical law and the scale-invariant principle of mechanical law in fractal space are proved by using parameter-space and scale-space transforms in renormalization groups.From the space-transform angle,the transform of mechanical law from fractal space to European space is the scale-invariant transform while the transform of mechanical law from European space to fractal space is the adaptability transform.Their deductions are that law of conservation of energy and vectorial resultant of force and displacement in fractal space hold the line in form and Carpinteri's dimensional formula of fractal space is also proved. Namely,the spilling dimension of volume in fractal …


Fractional Definite Integral, Yang Xiaojun Jan 2008

Fractional Definite Integral, Yang Xiaojun

Xiao-Jun Yang

Fractional definite integral is that a value of the integral calculus over given interva1.Under the circumstance of fractional dimension,fractional definite integral is important to compute some value in given interva1.It is complied with starting introducing definition,the properties,leads into fractional integral function of definition and the properties,and then induces to basic theorems for fractional integral calculus


Application Of Ansys In Seismic Response Analysis Of Constructing Of High Buildings, Yang Xiaojun Jan 2007

Application Of Ansys In Seismic Response Analysis Of Constructing Of High Buildings, Yang Xiaojun

Xiao-Jun Yang

The dynamic feature of high buildings is discussed in the present study with the application of ANSYS,the large finite element analysis software,aimed at the analysis of dynamic response of high buildings.Based on the case of a 15一story-building,a model of beam and shell 3-D finite element structure is built and the frequency of structure and the mode of vibration are computed in the study;furthermore,the structural dynamic response is discussed under different seismic waves with the use of the history analysis method.The results show that the more intense the seismic wave is,the bigger is the dynamic response of the buildings.The information can …