Rattling models from deterministic to stochastic processes

Pfeiffer, Friedrich; Kunert, A.

doi:10.1007/bf01857585

Cited by 80 publications

(26 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A detailed description of a transition from a deterministic to a stochastic process for rattling vibrations is outlined in [5]. The abstract model used in the following is shown in Figure 10.…”

Section: Example: Rattling Vibrationsmentioning

confidence: 99%

See 1 more Smart Citation

Description of chaotic motion by an invariant probability density

Kunert

Pfeiffer

1991

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

An observation of single trajectories exhibiting chaotic motion turns out to be disadvantageous because even smallest variations of the initial conditions grow exponentially in time and result in an unpredictable long-time behaviour, The paper gives a different approach based on a probability distribution of the state space variables which is invariant on the area of attraction and results in a global description of chaotic motion.

show abstract

Section: Example: Rattling Vibrationsmentioning

confidence: 99%

“…The solution technique is similar to equations (5, 6), for more detail see [5]. Figure 11 shows a typical strange attractor for chaotic rattling vibrations.…”

Section: Example: Rattling Vibrationsmentioning

confidence: 99%

Description of chaotic motion by an invariant probability density

Kunert

Pfeiffer

1991

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

show abstract

“…This method is based on singular value decomposition and is called singular spectrum analysis (SSA) [20]. 4. EXPERIMENTAL INVESTIGATION 4.1.…”

Section: Noise Reductionmentioning

confidence: 99%

The Application of Correlation Dimension in Gearbox Condition Monitoring

Jiang

Chen

1999

Journal of Sound and Vibration

View full text Add to dashboard Cite

“…the vibro-impact systems, which are driven in some way and which also undergo intermittent or a continuous sequence of contacts with motion limiting constraints [1,2]. There are many references on this topic [3][4][5][6][7][8][9][10][11][12][13][14][15] . However, it is very difficult to investigate those systems.…”

mentioning

confidence: 99%

Discrete Models of a Class of Isolation Systems

Feng

2006

Arch Appl Mech

View full text Add to dashboard Cite

In this paper, a class of isolation systems with rigid limiters has been considered. For this class of systems, some general discrete-time models described by means of some impact Poincaré maps have been established. Two examples: a simple isolation system of one-stage and a real isolation system of two-stages have been investigated. The calculated results show that those models can reveal complex nonlinear behaviors. And even a small random perturbation may change the dynamical character of the system. KeywordsIsolation systems with rigid limiters · Impact Poincaré map · Vibro-impact systems IntroductionIsolation systems with stops, (Fig. 1) are usually used in real engineering in order to safeguard equipment and to restrict the vibrating amplitudes of systems. The limiters can be divided into rigid, elastic and plastic ones. When the isolation systems are constructed with rigid limiters, in mechanics, they belong to a class of non-smooth systems, i.e. the vibro-impact systems, which are driven in some way and which also undergo intermittent or a continuous sequence of contacts with motion limiting constraints [1,2]. There are many references on this topic [3][4][5][6][7][8][9][10][11][12][13][14][15] . However, it is very difficult to investigate those systems. The main difficulty is that the dynamics of such systems are not continuous, but rather of intermittent type. A general way to characterize the behavior of impacting systems is to study the discrete-time system associated to the overall dynamics.More precisely, if between the impacts the systems hold smoothness properties, by integrating the smooth vector field and incorporating the impact conditions, a so-called impact Poincaré map for this system may be theoretically derived [16]. If the system is subject to an in-finiteness of impacts and if the derived map is explicitly calculable, one can obtain a discrete-time system, which is easily simulated by iterations. Unfortunately, to obtain the closed solution of equation at free-flight phase is difficult, even for very simple systems, so it may be impossible to obtain the impact Poincaré map.In this paper, a class of vibro-impact systems, i.e. isolation systems with rigid limiters for marine engine, is considered. Due to small angular velocity, this class of systems can be restricted using the following assumptions: (1) during the free-flight time, the equation of motion for those systems is smooth, and there are only some small nonlinear terms in the equation. Because of the weak nonlinearity of the equation, one can use the perturbation method to obtain an approximated solution in closed form, so that some approximated impact Poincaré maps can be derived; (2) the motion of those systems can be divided into two periods: during shock and after shock. Due to large shock action, during shock the external excitations can be neglected. The external excitations after shock are here assumed as deterministic and random cases.

show abstract

Rattling models from deterministic to stochastic processes

Cited by 80 publications

References 7 publications

Description of chaotic motion by an invariant probability density

Description of chaotic motion by an invariant probability density

The Application of Correlation Dimension in Gearbox Condition Monitoring

Discrete Models of a Class of Isolation Systems

Contact Info

Product

Resources

About