Spline-Method for Numerical Calculation of Natural-Vibration Frequency of Beam with Variable Cross-Section

摘要

This paper presents the results of research into the possibilities of a new spline-method of degree 5 defect 1 for the numerical calculations of natural frequencies for transverse vibrations of straight beams with variable cross-section. The significantly improved values of beam natural frequencies with exponentially varying width of rectangular cross-section were obtained to accuracy evaluation of the developed spline-method. This method is the second order of convergence and gives the calculation accuracy with almost six significant figures to the first ten natural mode shapes that was checked on the base of all standard problems. Thus, high precision of calculation allows us to declare that the proposed spline-method is very effective in transverse vibrations analysis of beam with variable cross-section.