Abstract
The second-order ordinary differential spectral problem governing eigenvibrations of a bar with attached harmonic oscillator is investigated. We study existence and properties of eigensolutions of formulated bar-oscillator spectral problem. The original second-order ordinary differential spectral problem is approximated by the finite difference mesh scheme. Theoretical error estimates for approximate eigenvalues and eigenfunctions of this mesh scheme are established. Obtained theoretical results are illustrated by computations for a model problem with constant coefficients. Theoretical and experimental results of this paper can be developed and generalized for the problems on eigenvibrations of complex mechanical constructions with systems of harmonic oscillators.
Highlights
We investigate the longitudinal eigenvibrations of a bar of length l
This paper develops and generalizes results of the papers [1,2,3,4,5,6]
∫ m = 1, 2,! and corresponding eigenfunctions um = um (x), r(x)um (x)um (x)dx = 1, m = 1, 2,!. The proof of this theorem uses the statements of problem (7), (8), parameter spectral problems (9), (10), and (11), (12)
Summary
We investigate the longitudinal eigenvibrations of a bar of length l. By w(x,t) we denote the deflection of the bar cross-section with coordinate x ∈ Ω at time t > 0 and by η(t) the longitudinal deflection of the load of mass M from the equilibrium position at time t > 0. These functions satisfy the following system of equations. The rational bar-oscillator differential spectral problem (5), (6), is approximated by the finite difference scheme. Preconditioned iterative methods for solving linear spectral problems are proposed and investigated in the papers [7,8,9,10,11,12,13,14]. This paper develops and generalizes results of the papers [1,2,3,4,5,6]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
