The presented contribution maps the possibilities of exploitation of the massive parallel computational hardware (namely GPU) for solution of the initial value problems of ordinary differential equations. Two cases are discussed: parallel solution of a single ODE and parallel execution of scalar ODE solvers. Whereas the advantages of the special architecture in the case of a single ODE are problematic, repeated solution of a single ODE for different data can profit from the parallel...
The response of an arbitrary discretized system to the random movement has been solved in probabilistic terms. The excitation has been defined as a combination of the time modulated band
limited stationary random processes approximating the evolutionary power spectra of a true seismic record. The solution is based either on the modified version of the stochastic Newmark method or on the spectral differential decomposition of the excitation. Special attention has been paid to the applicability of...
The Lyapunov exponents (LE) provide a simple numerical measure of the sensitive dependence of the dynamical system on initial conditions. The positive LE in dissipative systems is often regarded as an indicator of the occurrence of deterministic chaos. However, the values of LE can also help to assess stability of particular solution branches of dynamical systems. The contribution brings a short review of two methods for estimation of the largest LE from discrete data series. Two methods are analysed...
Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes an implementation...
The pendulum damper modelled as a two degree of freedom strongly non-linear
auto-parametric system is investigated using two approximate differential systems. Uni-directional harmonic external excitation at the suspension point is considered. Semi-trivial solutions and their stability are
analyzed. The thorough analysis of the non-linear system using less simplification than it is used in the paper [2] is performed. Both approaches are compared and conclusions are drawn.
In nonlinear dynamical systems, strong quasiperiodic beating effects appear due to combination of self-excited and forced vibration. The presence of symmetric or asymmetric beatings indicates an exchange of energy between individual degrees of freedom of the model or by multiple close dominant frequencies. This effect is illustrated by the case of the van der Pol equation in the vicinity of resonance. The approximate analysis of these nonlinear effects uses the harmonic balance method and the multiple...
The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplification, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can...
A simple beam subjected to a row of regularly distributed moving forces and simultaneous vertical motions of its supports is described using a simplified theoretical model and a finite differences approach. Several levels of simplification of the structure and input data are supposed. Numerical results confirm legitimacy of the assumptions.
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