Matlab Application to Calculate Natural Oscillations of Beam Systems

This paper presents Matlab application in course project in discipline Dynamics of Machines for students learning Applied Mechanics in NRU MPEI, Institute of Power Engineering and Mechanics. Determining of natural frequencies and shapes is shown by example a hinge-supported beam with a concentrated mass supported by springs. It is considered three methods for finding natural frequencies and shapes of the system: 1) direct method from non-triviality condition of solution of governing equation, 2) method of initial parameters and 3) finite element method. Matlab functions and procedures, including graphical representation of the results, is illustrated. Numerical investigation and comparative analysis of accuracy by three methods are given.