In particular, the investigation of the reduction of escape load for several varying system parameters highlights the remarkable loss of safety and dynamic integrity of the structure due to penetration of eroding fractal tongues into the safe basin. This paper makes a first step in this direction, focusing on the mechanics of machines, solids and structures, with applications in both classical and novel technological areas. Also, in the literature, methodology to study bifurcations are presented for most of the cases. The method proves to succeed in delaying the drop down of the erosion profile, thus increasing the overall robustness of the system during operating conditions. In this paper the global dynamics and topological integrity of the basins of attraction of a parametrically excited cylindrical shell are investigated through a two-degree-of-freedom reduced order model. It was found that the horizontal component of excitation has a larger effect on the shift in position of the saddle node bifur-cations for the elliptically excited case than for the pendulum excited along a tilted axis.
In this paper we apply the so called act-and-wait control concept, a specific periodic controller, to the digital position control of a single DoF system. The numerical results show that the test is able to unambiguously distinguish periodic from chaotic trajectories. Poznan - about 210 km from Lodz,. Local bifurcation analyses are carried out to identify the overall stability boundary in the excitation parameter space as the envelope of system local escapes, to be compared with the one obtained via numerical simulations. The analysis is based on the computation of the control parameter K that approaches asymptotically 0 or 1 for regular and chaotic motions, respectively. For this reason, the constitutive models that are typically used to study the nonlinear dynamics are often of a rather simplified nature that neglects one or more aspects.
The simplified model has only 2 unknowns which can be easily reduced to a single unknown , versus the 8 of the original problem, and has only 2 dimensionless parameters, versus the 14 of the original problem, and thus can be handled more easily. The elastic von Mises truss model is a prototype for bi-stable structures. They decrease the static buckling load and distort the topology of the safe potential well. I hope I shall not shock the experimental physicists too much if I add that it is also a good rule not to put overmuch confidence in the observational results that are put forward until they have been confirmed by theory. The analytical procedure, based on Melnikov method, is applied to the homoclinic bifurcation involving the system hilltop saddle, and its practical effects as regards possibly increasing the system overall robustness are numerically investigated by means of a dynamical integrity analysis.
Then, as an example of a continuous system exhibiting strong modal coupling and interaction, a two-degree-of-freedom model of the thin-walled cylindrical shell is investigated in terms of global behavior and dynamic integrity. Recent results are presented, and the possibility to implement effective dedicated control procedures based on global safety concepts is explored. To this aim, attention is systematically devoted to the strongly nonlinear dynamics of the system under beam vertical or scan horizontal excitation, which realize conditions of external or parametric resonance, respectively, by considering the relevant primary fundamental and subharmonic principal resonances of the dominant beam mode. The analytical bifurcation threshold is determined through the asymptotic Melnikov method, for the reference system and for the controlled system. In contrast, for the pendulum excited along the tilted axis, the direction of the rotation has a minor effect for low frequency values and the addition of the horizontal component always results in a larger region of the solution existence.
We do not have specific contract with any hotel, but we are glad to recommend several hotels nearby close to the University and Conference place that have appropriate standard. However, the interaction of two different Neimark—Sacker bifurcations steers the system to much more complicated behavior. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Three mechanical engineering problems are presented: i a vibro-impact system in the form of a moling device, ii the influence of the opening and closing of a fatigue crack on the host system dynamics, and iii nonlinear interactions between a rotor and snubber ring system. It integrates mechanical and thermal aspects, by addressing them in parallel via the introduction of generalized 2D variables and equations also for the latter. The ensuing compact reduced order model with different coupling features allows to account for nonlinear mechanical and thermal phenomena, along with their interactions, under a variety of thermomechanical assumptions, boundary conditions and excitations. In these applications, many primary and secondary structural elements can be idealized as beams.
Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. However, the modal interaction leads to unstable post-buckling paths that entail a complex dynamic behavior and imperfection sensitivity, with a marked influence on the dynamic integrity and safety. The asymptotic development method is used to study the effects of axial and rotational inertia, of shear deformations and of interface normal compliance in the vibrations of a two-layer beam. The performed investigation shows the appearance of quasiperiodic motions and the existence of regions with coexisting periodic stable attractors, in the space of the control gains. Non-smooth dynamics of a cantilever beam subjected to a transverse harmonic force and impacting onto a soft obstacle is studied. Five multi-author monographs on nonlinear material and dynamic mechanical phenomena are presented. Nonlinear mechanics has to be used to explain undesired response in slender footbridges, such as that occurred in the famous event of the London Millenium Bridge.
The effects of the dynamic excitation on the load carrying capacity of mechanical systems are investigated with reference to the archetypal model addressed in Part I, which permits to highlight the main ideas without spurious mechanical complexities. Z˙ ak and Olga A. The stability charts are presented in the parameter space of the sampling time and the control gains. When the pendulum and the pivot rotate in opposite directions, the boundary is shifted upwards significantly limiting the region of the solution existence. Systematic numerical analyses in the case of thermal dynamics passively entrained by the solely active mechanical excitations allow to unveil the main features of the nonlinear response, while highlighting fundamental aspects associated with the thermomechanical coupling. Variable attractive-repulsive effects are highlighted, along with the possible presence of a coexisting multi-periodic orbit when the system is excited at second resonance. The dynamical integrity of periodic bounded solutions is studied, and basin erosion is evaluated by means of two different integrity measures.
Nonlinear mechanics has to be used to explain undesired response in slender footbridges, such as that occurred in the famous event of the London Millenium Bridge. Nandakumar, Marian Wiercigroch and Chris Pearson. A variety of features of nonlinear multimodal interaction in different resonance conditions are comparatively addressed. Settimi: Bifurcation, response scenarios and dynamic integrity in a single-mode model of noncontact atomic force microscopy. The results show that even small variations in cross section and material gradation have profound influence on the bifurcation diagrams and the dynamic behavior of the structure. The existence of coupled and uncoupled motion is discussed. Transient escape is a significant issue in many structural systems since it may lead to unwanted stresses and strains or exceed some safe design requirements in terms of maximum displacements and velocities.
In addition, the Galerkin method is applied to obtain a set of discretized equations of motion, which are in turn solved by numerical integration using the Runge—Kutta method. Results are discussed also in the background of theoretical and experimental outcomes available in the literature. The system is generally losing stability through Neimark—Sacker bifurcations, with relatively simple dynamics. The three-dimensional motion of a slender clamped-free beam with a cruciform cross-section of low torsional stiffness, subject to lateral harmonic excitation, is investigated. The observed phenomena can be explained by an analytical nonlinear discrete-time model.