Jiří Náprstek et al., Pořadatelé: Ústav teoretické a aplikované mechaniky AV ČR, v. v. i., Ústav termomechaniky AV ČR, v. v. i, Ústav mechaniky těles, mechatroniky a biomechaniky FSI VUT, ŽĎAS, a.s., Česká společnost pro mechaniku, International Federation for the Promotion of Mechanism and Machine Science., and Věnováno památce Prof. Ing. Aleše Tondla, DrSc. a Ing. Ladislava Půsta, DrSc.
Double degree of freedom (DDOF) linear systems are frequently used to model the aero-elastic response of slender prismatic systems until the first critical state is reached. Relevant mathematical models appearing in literature differ in principle by way of composition of aero-elastic forces. This criterion enables to sort them roughly in three groups: (i) neutral models - aero-elastic forces are introduced as suitable constants independent from excitation frequency and time; (ii) flutter derivatives - they respect the frequency dependence of aero-elastic forces; (iii) indicial functions - they are defined as kernels of convolution integrals formulating aero-elastic forces as functions of time. The paper tries to put all three groups together on one common basis to demonstrate their linkage and to eliminate gaps in mathematical formulations between them. This approach allows formulate more sophisticated models combining main aspects of all groups in question keeping the DDOF basis. These models correspond by far better to results of wind tunnel and full scale measurements. and Obsahuje seznam literatury
The paper makes a sketch of an SDOF system response analysis subjected to a random excitation having a form of the additive Poisson driven independent random impulses. A special generalised Fokker-Planck equation having a form of an integro-differential equation is presented together with boundary and initial conditions. Later the Galerkin-Petrov process as a method of a numerical solution of the respective evolutionary integro-differential equation for the probability density function (PDF) is presented in general. Various analytic and semi-analytic solution methods have been developed for various systems to obtain results requested. However numerical approaches offer a powerful altemative. In particular the Finite Element Method (FEM) seems to be very effective. Shape and weighting functions for purposes of a numerical solution procedure are carred out and corresponding ordinary differential system for PDF values in nodes is deduced. As a demonstration particular SDOF systems are investigated. Resulting PDFs are analysed and mutually compared. and Obsahuje seznam literatury
Many theoretical models of slender prismatic beams in a cross-wind have been developed during last decades. They mostly follow various types of the linear approach. Therefore their applicability is very limited especially for prediction of the system post-critical behavior. The subject considered in this paper represents a part of a complex theoretical background of the general nonlinear model which would enable fo predict any system reaction in the pre- and post-critical domain. In particular, the aeroelastic self-induced oscillaton of a mechanical system with generalized single degree of freedom (SDOF) is discussed. The motion is described by an ordinary differential equation of Duffing type with special generalized aero-elastic damping of Van der Pol type. A new semi-analytical approach is introduced to identify the limit cycles both stable and unstable. The latter are not possible to be identified by means of experiments nor by the numerical integration. and Obsahuje seznam literatury
The Fokker-Planck (FP) equation is frequently used when the response of the dynamic system subjected to additive and/or multiplicative ramdom noises is investiagted. It provides the probability density function (PDF) representing the key information for further study of the dynamic system. Various analytic and semi-analytic solution methods have been developed for various systems to obtain results requested. However numerical approaches offer a powerful alternative. In particular the Finite Element Method (FEM) seems to be very effective. A couple of single dynamic linear/non-linear systems under additive and multiplicative random excitations are discussed using FEM as a solution tool of the FP equation. and Obsahuje seznam literatury