Calculation Methodology of the Natural Frequencies and Modes of Mechanical Systems of an Arbitrary Structure with a Plurality of Possible States

Abstract

Methodical approaches to determination of the natural frequencies and modes of transmissions of mobile machines and similar to them badly conditioned systems with a wide natural frequencies spectrum and a plurality of states are considered. The problem is solved in a general formulation taking into account the characteristic features of the transmission in its schematization. The calculation is reduced to the computation of eigenvalues and eigenvectors of a matrix of a special form. An approach based on the preliminary matrix symmetrization and the application of the iterative numerical method of Jacobi rotations is used. This allows to evaluate all natural frequencies and modes of badly conditioned systems with a very high precision. The process of the system stiffness matrix forming is automated by means of replacing the absolutely rigid links (if any) with links with finite stiffness. To form the equations of natural oscillations of systems with a plurality of possible states, the use of the state indicators of devices with variable structure is suggested. That approach allows to obtain universal equations describing the system motion for its any possible state. Based on the developed methodology, a computer program was created and registered, an example with its application is given.

Keywords

• transmission
• natural frequencies and modes
• methodology
• mechanical system with a plurality of possible states
• state indicator