Use of Matrix Displacement Method for Vibrational Analysis of Structures

摘要

A study of the matrix displacement method for modeling the vibrations of structures is presented in this report. The model can analyze both the free and forced vibrations of a structure. Static loading on a structure is treated as a special case of the forced vibration analysis. A brief review of the Finite Element Method and its present use is first given. This is followed by a discussion of the methodology of the matrix displacement approach and a description of the specific model used. Examples of the use of the model to analyze the frequencies and mode shapes of the free and forced response of a beam structure and the static deflections of a beam structure are shown and compared with the closed form solutions. Finally, ways of extending the model to a more complicated structure, a turbine blade, are discussed. Conclusions are then drawn.