Study On The Accurate Method Of The Dynamic Problem Of The Member Structures Including Infinite Stiffness Truss Based On The Matrix Displacement Method

Along with the development of computer technology, structure dynamic calculation has been updated. Before the computer revolution, dynamic calculation is still stuck in the elastic analysis method and can only solve typical problems of some simple structures. After the emergence of computer, the electronic computing develops rapidly. Due to the unified and regular format, matrix computing can solve the dynamic mechanics problem of large and complex structures that could not be done with analytic method in the past. Therefore, structure matrix analysis has become more and more popular.It is a difficult problem in the teaching and practice to calculate the dynamic calculation of the member structures including infinite stiffness truss(rod with infinite bending rigidity or tensile rigidity). In this paper, a new measure based on the matrix analysis of matrix displacement method is presented to solve the problem. It mainly embodies three aspects:(1) This paper solves accurately the free vibration problem of member structures including infinite stiffness truss. Because of the existence of infinitely rigid rod, its two-terminal displacements have restraint relations that are the non-independent displacement and independent displacement established by the constraint equation. The natural frequencies and main vibration modes of the structure can be obtained according to the characteristic equation which is composed of the stiffness matrix and mass matrix integrated by the element location vector matrix. Due to the existence of non- independent displacement, traditional structural mechanics method can not directly analyze the vibration problem of infinite rigid rod.(2) The theory of this article based on the matrix analysis theory uses the advanced language Fortran90 to compile the relevant procedures to calculate, which makes the operation more convenient and meets the practical needs.(3) This paper addresses accurately the forced vibration problem of member structures including infinite stiffness truss under harmonic load. It puts forward two methods that are linear equation method and modal analysis method to analyze the forced vibration problem of infinite rigid frame structure. To solve the linear equation method based on differential equation of structure vibration deduces the linear equation about displacement, and the amplitude of dynamic displacement and moment of the structure are obtained according to the static method. The modal analysis method based on the characteristics of the principal mode orthogonality transforms the coupled multi- freedom degree system into a plurality of independent single degree of freedom, which makes the complex problem into simple problems.