Dynamic stability of Timoshenko beams on Pasternak viscoelastic foundation

Abstract

The dynamic stability problem of a Timoshenko beam supported by a generalized Pasternak-type viscoelastic foundation subjected to compressive axial loading, where rotary inertia is neglected, is investigated. Each axial force consists of a constant part and a time-dependent stochastic function. By using the direct Liapunov method, bounds of the almost sure asymptotic stability of a beam as a function of viscous damping coefficient, variance of the stochastic force, shear correction factor, parameters of Pasternak foundation, and intensity of the deterministic component of axial loading are obtained. With the aim of justifying the use of the direct Liapunov method analytical results are firstly compared with numerically obtained results using Monte Carlo simulation method. Numerical calculations are further performed for the Gaussian process with a zero mean as well as a harmonic process with random phase. The main purpose of the paper is to point at significance damping parameter of foundation on dynamic stability of the structure.2010 Mathematics Subject Classification: 74H55.

Implementation and analysis of viscoelastic damping in a 2D + 1D model of railway track vibrations

“…In [27,28], the response of an infinite Timoshenko beam on a viscoelastic foundation to a harmonic moving load is studied by means of the dynamic stiffness matrix, as a function of the velocity and frequency of the load. In [29], the dynamic stability of a Timoshenko beam supported by a Pasternak viscoelastic foundation subjected to compressive axial loading is investigated. Nevertheless, all these studies suffer from the same shortcomings listed above for models based on beam theory.…”

Timoshenko Beam Theory: Exact Solution for First-Order Analysis, Second-Order Analysis, and Stability

“…Onyia and Rowland-Lato (2018) presented a finite element formulation for the determination of the critical buckling load of unified beam element that is free from shear locking using the energy method; the proposed technique provides a unified approach for the stability analysis of beams with any end conditions. Pavlovic and Pavlović (2018) investigated the dynamic stability problem of a Timoshenko beam supported by a generalized Pasternak-type viscoelastic foundation subjected to compressive axial loading, where rotary inertia is neglected; the direct Liapunov method was used. In stability analysis Timoshenko and Gere (1961) proposed formulas to account for shear stiffness by means of calculation of buckling loads of the associated Euler-Bernoulli beams.…”