Mathematical Modeling and Algorithms for Studying Vibrations of a Beam with Built in Ends at Different Properties of the Material

EasyChair Preprint 15844

Abstract

The paper deals with mathematical modeling and algorithms for studying vibrations of a beam with built-in ends, with regard to rheological properties of the beam material. By the method of Laplace integral transform the solution of the integro-differential equation of a beam is constructed in the form of a series, whose first term coincides with the solution of this equation obtained by the averaging method. For a specific Abel kernel, algorithm and software for the numerical analysis of the stated problem was developed. It was obtained that the amplitudes of vibrations decrease exponentially over time and taking into account of the subsequent terms of the series of solutions enable to determine a more exact solution to the problem.

Keyphrases: Exponential law, amplitude, beam, image, integro-differential, kernel, original

@booklet{EasyChair:15844,
  author    = {Ulviyya Aliyeva},
  title     = {Mathematical Modeling and Algorithms for Studying Vibrations of a Beam with Built in Ends at Different Properties of the Material},
  howpublished = {EasyChair Preprint 15844},
  year      = {EasyChair, 2025}}