Non-smooth mechanical systems — an overview

Popp, Karl

doi:10.1007/pl00010860

Cited by 13 publications

(3 citation statements)

References 66 publications

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“…It can either stick to a given position, represented by x τ in each slip-stick cycle, or it can start slipping/moving if the force in tangential direction is larger than the maximum friction force. Drawing on similar systems presented and discussed by Den Hartog [6], Popp [7] and Hong et al [5], a slip-stick system with a position and velocity dependent Coulomb friction force is introduced. In the following, the equations of The Coulomb friction force can be calculated as: This friction force shows that motion of the slipjoint will be piecewise and dependent on the tangential velocity.…”

Section: Slip-stick Equations Of Motionmentioning

confidence: 99%

Investigation of a slip joint connection between the monopile and the tower of an offshore wind turbine

Segeren

Lourens

Tsouvalas

et al. 2014

IET Renewable Power Generation

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Section: Slip-stick Equations Of Motionmentioning

confidence: 99%

Investigation of a slip joint connection between the monopile and the tower of an offshore wind turbine

Segeren

Lourens

Tsouvalas

et al. 2014

IET Renewable Power Generation

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“…Accurately prediction of vibration responses of the structure is closely related to the friction model in the system. A general rule concerning modeling holds for friction force is that the models must be as simple as possible and as accurate as necessary [3] . Three popular friction models were discussed below.…”

Section: Friction Modelmentioning

confidence: 99%

Influence of Friction on the Vibratory Response of Structure

Miao

Huang

2011

AMR

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Friction is a phenomenon caused by relative motion, which can be used to absorb vibrational energy. The influence of friction on vibration responses of structures is complex due to the complicacy and nonlinear of the friction itself. In this paper, a 3-DOF spring-damper model with/without friction force was studied to expose how the friction governed the vibratory responses. Several popular friction models were reviewed and LuGre Model was used in this paper. The vibration properties under sine excitation and random were simulated by the Matlab Simulink Software. The results showed that friction absorbed vibration well and vibration damping was rapid. The characteristics of friction influence resulted from comprehensive functions of all factors, such as types of excitation, excitation amplitude and frequency and the location of friction.

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“…The analytical procedure for the integration of such non-smooth motions is to compute the history dependent separation times and to patch together a sequence of solutions for successive smooth problems, Popp (1998). However, this very accurate procedure has limits even for a relatively low number of generalized coordinates because of the required computational effort.…”

mentioning

confidence: 99%

FE-regularization of non-smooth vibrations due to friction and impacts

Engleder¹,

Vielsack²,

Schweizerhof³

2002

Computational Mechanics

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Friction and impacts during oscillations lead to discontinuities of the velocity and of the internal forces in the time-domain and to changes in the number of degrees of freedom, Ibrahim (1994). The analytical procedure for the integration of such non-smooth motions is to compute the history dependent separation times and to patch together a sequence of solutions for successive smooth problems, Popp (1998). However, this very accurate procedure has limits even for a relatively low number of generalized coordinates because of the required computational effort. Regularization techniques as usually used with FE allow to avoid the exact computation of all discontinuities by smoothing. But there is a big uncertainty in the choice of the regularization parameters needed for a sufficiently correct description of the oscillations under investigation. Stationary solutions of two forced massspring oscillators are used to calibrate the regularization parameters by comparing analytical results with regularized ones. This allows to compute the self-excitation of a continuous system and to prove the phenomena with known experimental data.A non-smooth discrete system changes its mechanical properties during the course of time. Examples are the possibility of sliding or sticking at contact points or the change from a motion in contact to a free motion or vice versa. Generally there exists a set of possible states which can differ in their degrees of freedom. At the beginning of a motion it is neither known how many possible states will become active in the future, nor the sequence of the active states is predetermined. However, we have to note, that each state represents itself a smooth problem. If X denotes the vector of generalized coordinates, the total solution in the time domain is given in general by a sequence of smooth solutionsLet us assume, the solution X i corresponding to a distinct element of the set of possible states is known by integration up to a certain time t > t i . Then a condition must be given, to determine the end of this state at t iþ1 . This condition is found by checking switching conditions for each t ! t i . Knowing t iþ1 a switching decision allows to choose the new state X iþ1 out of the set of all possible states. The complete information about the mechanical quantities at the end of the state X i is used as initial conditions for X iþ1 . By sequential application the total solution is patched together at the points of discontinuities t i .The spatial discretization of a continuum by the FEmethod leads to equations of motions with a finite number of degrees of freedom. Therefore all dynamic contact problems lead to non-smooth mechanical systems. In principle, analytical solutions can be computed as described above. In practice such an exact solution can only be obtained if the number of all possible states is relatively low, which leads essentially to the restriction to a small number of coordinates and contact points, Vielsack and Kammerer (1999). FE discretizations, however, lead to large number...

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Non-smooth mechanical systems — an overview

Cited by 13 publications

References 66 publications

Investigation of a slip joint connection between the monopile and the tower of an offshore wind turbine

Investigation of a slip joint connection between the monopile and the tower of an offshore wind turbine

Influence of Friction on the Vibratory Response of Structure

FE-regularization of non-smooth vibrations due to friction and impacts

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