4-Vibration Analysis Procedure 振动的分析过程.ppt

Vibration Analysis Procedure 振动的分析过程 Contents Mathematical Modeling,数学建模 Governing Equations （控制方程，基本方程）Derivation, 系统微分方程推导 Equations Solution,微分方程求解 Results Interpretation. 结果分析 Vibratory System A vibratory system is a dynamic system for which the variables such as the excitations (inputs) and responses (output) are time-dependent. (振动系统是一个动态系统，其中的变量例如激励（输入）、响应（输出）都是随时间变化的) The response of a vibration system generally depends on the initial conditions as well as the external excitations. (响应通常依赖于初始条件和外界激励) Step 1: Mathematical Modeling (数学建模) The purpose of mathematical modeling is to represent all the important features of the system for the purpose of deriving the mathematical (or analytical) equations governing the system’s behavior. The mathematical model is gradually improved to obtain more accurate results Step 2: Derivation of Governing Equation.( 推导系统微分方程) Using the principles of dynamics and derive the equations that describe the vibration of the system Newton’s second law of motion (牛顿第二定律), D’Alembert’s principle (达朗贝尔原理), and the principle of conservation of energy (能量守恒定律). Step3: Governing Equation Solution (微分方程求解) Laplace Transform Methods, (拉普拉斯变换) Matrix Methods (矩阵法), Numerical Methods (数值法). Step 4: Results Interpretation (结果分析) The solution of the governing equations gives the displacements, velocities and accelerations of the various masses of the system. These results must be interpreted with a clear view of the purpose of the analysis and the possible design implications of the results. Example