Modelisation du comportement vibratoire transverse des plaques sous differentes configurations

Abstract

By this work, we intend our self, to develop à methodology about dynamic investigation of rectangular plate, to have information on the risk coming from the phenomenon of resonance. We hope to contribute in this area of vibration this insufficiency which is based on the background and investigation in this area using energy method. The dynamic analysis of strategic elements of thin rectangular isotropic and orthotropic plates with various conditions limits was considered. This study was reinforced by addition a load uniformly distributed and a hole on the isotropic thin plates. In this work we develop a good program using mathematical software “MAPLE” , to investigate dynamic behavior of rectangular plate with various conditions limits. The development and solutions of free dynamic behavior are use as responses factors and obtained based on Rayleigh-Ritz. To enhance the possibility of the developed program in performing dynamic analysis, we use many type of shapes functions consistent with the usual boundaries conditions, and based on trigonometry or polynomial parameter, or with combination of both one. To test the good performance of those selected shape functions, we compare the frequencies solutions calculated from the program with those obtained from literature. Using the same steps as indicated from the literature and then performing the dynamic analysis based on those combinations and lead to response within good tolerances. Others investigations are performed to certify the performance of the program from one hand, and then open new perspectives about the capability to handle the dynamic behavior analysis, concerning rectangular plates subjected to some assumptions, that is: 1. A study on parametric frequency for dynamic analysis of rectangular isotopic thin plate with different combinations of boundaries conditions (SSSS, SCSS, SCSC, CCSS, CCCS, CCCC, CSSF, CSCF,CCSF, SCSF,CSFF, SSSF). 2. A study on parametric frequency for dynamic analysis of rectangular orthotropic thin plate with different combinations of boundaries conditions (CCCC,SSSS,SSCC,SCSC,CFCC,SFSS). 3. Effect of distributed load on the free dynamic behavior of rectangular thin plate (SSSS ,SSCC,SCSC,SSCS,CSCC,CCCC). 4. Analysis of free vibration response of rectangular thin plate with the presence of rectangular hole (SSSS , SSCC,CCCC,CSSF,CCSF,SCSF,SSSF,CSFF).