Computerized Symbolic Manipulation in ViBration Analysis

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Computerized manipulation procedure is seldom found in the vibration analysis, and hence there are a number of unclarified points regarding fundamental algorithms, programming, and limitations in applications. The present report therefore aims at developing symbolic manipulation algorithms for solution of vibration problems and unifying numerical methods and symbolic methods in order to simplifying analysis process.The potential of using computerized symbolic manipulation procedure in vibration analysis is discussed at first in the present report. Tasks which can be efficiently performed using computerized symbolic manipulation are as follows : (1) solving governing equations in linear vibration systems, (2) natural frequencies and modes in multiple degrees of freedom, (3) approximation methods in nonlinear systems, such as perturbation method and asymptotic method. By applying a special algorithm decomposing into simultaneous first order differential equations, an important improvement is obtained in the solution of governing equations. The gradient function is implemented for simplifying the derivation of the mass and stiffness matrices of multiple degrees of freedom.In the present report, it is also pointed out that both programming efficiency and flexibility are greatly improved by applying the symbolic manipulation procedure to the experimental modal analysis. Effects of radius of curvature on the dynamic characteristics of piping systems in refrigerator can be analyzed successfully by the experimental modal analysis using the symbolic mathematical system.