1,253 research outputs found
Memory in random bouncing ball dynamics
The bouncing of an inelastic ball on a vibrating plate is a popular model
used in various fields, from granular gases to nanometer-sized mechanical
contacts. For random plate motion, so far, the model has been studied using
Poincar{\'e} maps in which the excitation by the plate at successive bounces is
assumed to be a discrete Markovian (memoryless) process. Here, we investigate
numerically the behaviour of the model for continuous random excitations with
tunable correlation time. We show that the system dynamics are controlled by
the ratio of the Markovian mean flight time of the ball and the mean time
between successive peaks in the motion of the exciting plate. When this ratio,
which depends on the bandwidth of the excitation signal, exceeds a certain
value, the Markovian approach is appropriate; below, memory of preceding
excitations arises, leading to a significant decrease of the jump duration; at
the smallest values of the ratio, chattering occurs. Overall, our results open
the way for uses of the model in the low excitation regime, which is still
poorly understood.Comment: Final published version, 5 pages, 4 figure
Direct numerical simulation of the dynamics of sliding rough surfaces
The noise generated by the friction of two rough surfaces under weak contact
pressure is usually called roughness noise. The underlying vibration which
produces the noise stems from numerous instantaneous shocks (in the microsecond
range) between surface micro-asperities. The numerical simulation of this
problem using classical mechanics requires a fine discretization in both space
and time. This is why the finite element method takes much CPU time. In this
study, we propose an alternative numerical approach which is based on a
truncated modal decomposition of the vibration, a central difference
integration scheme and two algorithms for contact: The penalty algorithm and
the Lagrange multiplier algorithm. Not only does it reproduce the empirical
laws of vibration level versus roughness and sliding speed found experimentally
but it also provides the statistical properties of local events which are not
accessible by experiment. The CPU time reduction is typically a factor of 10.Comment: 16 pages, 16 figures, accepted versio
Statistics of the separation between sliding rigid rough surfaces: Simulations and extreme value theory approach
When a rigid rough solid slides on a rigid rough surface, it experiences a
random motion in the direction normal to the average contact plane. Here,
through simulations of the separation at single-point contact between
self-affine topographies, we characterize the statistical and spectral
properties of this normal motion. In particular, its rms amplitude is much
smaller than that of the equivalent roughness of the two topographies, and
depends on the ratio of the slider's lateral size over a characteristic
wavelength of the topography. In addition, due to the non-linearity of the
sliding contact process, the normal motion's spectrum contains wavelengths
smaller than the smallest wavelength present in the underlying topographies. We
show that the statistical properties of the normal motion's amplitude are well
captured by a simple analytic model based on the extreme value theory
framework, extending its applicability to sliding-contact-related topics
Experiments and numerical results on nonlinear vibrations of an impacting hertzian contact. Part 1: harmonic excitation
The purpose of this paper is to investigate experimental and numerical
dynamic responses of a preloaded vibro-impacting Hertzian contact under
sinusoidal excitation. Dynamic response under random excitation is analysed in
the second part of this paper. A test rig is built corresponding to a double
sphere-plane contact preloaded by the weight of a moving cylinder. Typical
response curves are obtained for several input levels. Time traces and spectral
contents are explored. Both amplitude and phase of harmonics of the dynamic
response are investigated. Linearised resonance frequency and damping ratio are
identified from the almost linear behaviour under very small input amplitude.
Increasing the external input amplitude, the softening behaviour induced by
Hertzian nonlinear stiffness is clearly demonstrated. Resonance peak is
confined in a narrow frequency range. Jump discontinuities are identified for
both amplitude and phase responses. Forced response spectrum exhibits several
harmonics because of nonlinear Hertzian restoring force. Numerical simulations
show a very good agreement with experimental results. For higher input
amplitude, system exhibits vibro-impacts. Loss of contact non-linearity clearly
dominates the dynamic behaviour of the vibroimpacting contact and leads to a
wide frequency range softening resonance. Spectral content of the response is
dominated by both the first and the second harmonics. Evolution of the
experimental downward jump frequency versus input amplitude allows the
identification of the nonlinear damping law during intermittent contact.
Simulations of the vibroimpacting Hertzian contact are performed using a
shooting method and show a very good agreement with experimental results
Response of an impacting hertzian contact to an order-2 subharmonic excitation : theory and experiments
Response of a normally excited preloaded Hertzian contact is investigated in
order to analyze the subharmonic resonance of order 2. The nonlinearity
associated with contact losses is included. The method of multiple scales is
used to obtain the non-trivial steady state solutions, their stability, and the
frequency-response curves. To this end, a third order Taylor series of the
elastic Hertzian contact force is introduced over the displacement interval
where the system remains in contact. A classical time integration method is
also used in conjunction with a shooting method to take into account losses of
contact. The theoretical results show that the subharmonic resonance
constitutes a precursor of dynamic responses characterised by loss of contact,
and consequently, the resonance establishes over a wide frequency range.
Finally, experimental validations are also presented in this paper. To this
end, a specific test rig is used. It corresponds to a double sphere-plane
contact preloaded by the weight of a moving mass. Experimental results show
good agreements with theoretical ones
Experiments and numerical results on nonlinear vibrations of an impacting hertzian contact. Part 2: random excitation
Non linear dynamic behaviour of a normally excited preloaded Hertzian contact
(including possible contact losses) is investigated using an experimental test
rig. It consists on a double sphere plane contact loaded by the weight of a
rigid moving mass. Contact vibrations are generated by a external Gaussian
white noise and exhibit vibroimpact responses when the input level is
sufficiently high. Spectral contents and statistics of the stationary
transmitted normal force are analysed. A single-degree-of-freedom non linear
oscillator including loss of contact and Hertzian non linearities is built for
modelling the experimental system. Theoretical responses are obtained by using
the stationary Fokker-Planck equation and also Monte Carlo simulations. When
contact loss occurrence is very occasional, numerical results shown a very good
agreement with experimental ones. When vibroimpacts occur, results remain in
reasonable agreement with experimental ones, that justify the modelling and the
numerical methods described in this paper. The contact loss non linearity
appears to be rather strong compared to the Hertzian non linearity. It actually
induces a large broadening of the spectral contents of the response. This
result is of great importance in noise generation for a lot of systems such as
mechanisms using contacts to transform motions and forces (gears,
ball-bearings, cam systems, to name a few). It is also of great importance for
tribologists preoccupied to prevent surface dammage
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