Oscillation properties of delaminated structures are governed by dissipative impact-like contacts in the debonded region. The contribution focuses on the numerical simulation of this special type of contact. A robust and efficient contact strategy is presented mainly based on the theory of sudden impacts embedded in Finite Element methods.

Stationary resonant oscillations of delaminated structures lead to non-smooth dynamic systems arising from unilateral constraints and impact-like contacts along the interface of the debonded zone. The objective of this contribution is to establish nonlinear dynamic approach as framework in the field of non-destructive damage prognosis. First, the emphasis lies on the phenomenology of the vibrational behaviour of damaged structures exemplified by numerical treatment of a beam structure. In particular, the description of the special type of contact as it occurs on delaminated structures is discussed. Second, the practical applicability of the proposed procedure is demonstrated by experimental investigations on a delaminated rotor blade.

Zwangserregte Schwingungen kontinuierlicher Systeme mit flächenhaftem, dissipativem Stoßkontakt zeigen eine große Vielfalt möglicher Bewegungstypen. Neben nahezu harmonischen Systemantworten existieren weite Frequenzbereiche mit einperiodischen Antworten sowie verzweigten Bewegungsformen. Für die Kontaktbeschreibung bei der numerische Simulation erweist sich ein Projektionsverfahren als effiziente Alternative zur üblicherweise verwendeten Penalty‐Regularisierung. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Impacts in forced dynamic systems lead to non-smooth vibrations, showing a scenario of bifurcations. Mechanical and numerical modelling is known for rigid body systems with distinct points of contact. In contrast. continuous systems can have a line of possible contact. As an example a vibrating beam with a delaminated layer will be considered. The objective is to establish a finite element formulation for stationary nonlinear oscillation arising from the evolution of impacts along the contact line between the delaminated layer and the remaining beam. The objectives are focussed on the choice of the unknown values of a set of parameters that mainly describe energy dissipation. A calibration of these parameters can be achieved by experimental results and by investigation of a minimal mechanical model. (C) 2004 Elsevier Ltd. All rights reserved.

Forced oscillations of delaminated sandwich structures are dominated by impacts. During motion the gap between the two adjacent parts of the structure opens and closes periodically. Each contact gives rise to an impact, which leads to energy loss. A 4 DOF beam model with concentrated masses allows discussion of principle on the influence of internal dissipation due to the impacts on the non‐linear system's response and the evolution of impacts near resonance points. Experimental investigations confirm the numerical results.

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 mass–spring 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.

An experimental study was conducted to investigate the transmission of shear forces in sheet pile interlocks. This transmission strongly determines the safety of retaining walls made up of U-sheet piles. The limits are given by no and full transfer of the shear at the interlock between the piles. The bending stiffness in the first case is only about one-third compared to that of the second case. Operating values for real systems given in literature and code vary in a broad range within those limits. By estimating the characteristic of the shear force F versus the relative displacement x of small elements at different positions y along the interlocks, it was possible to explain the different results. It was found that F(x,y) depends not only on the coordinates but also on several uncertain, unknown factors. The uncertainty results mainly from the unknown penetration process. The process is determined by the velocity of the penetration, which itself is influenced by the state of the soil inside the clutches, the parameters of the vibrator, and a noncentered penetration of one clutch against the other. Furthermore, the behavior of the wall during excavation at one side and in service is not predictable.

Forced oscillations of delaminated sandwich structures are dominated by impacts. A rigid body-spring model allows a discussion of the influence of internal dissipation on the system's response and the evolution of the number of impacts.

The properties of a passive vibration absorber with dry friction significantly differ from those of the classical linear absorber. The exceptional phenomenon is the possibility of suppressing all excited modes. This effect is influenced to a small extent by a special shape of the friction characteristic, but mainly by an appropriately adjusted threshold of the static friction. The theoretical predictions are confirmed by experimental investigations.

Considering different friction laws the stability of decelerative sliding motions of a driven mechanical system is investigated. Both sudden and permanent disturbances are applied. The resulting stick–slip phenomena mainly depend on the properties of the mechanical system, especially on the drive, and less on different characteristics of the friction laws.

The influence of a time-variant normal force on the motion of a pendulum with dry friction is investigated. The main interest is focused on the characteristic of the friction force.

Investigated are sliding motions of a rigid body on a harmonically driven inclined plane. Coulomb's law with a random coefficient of friction is assumed. The mean sliding velocity in a steady state of deterministic motions is taken as a measure to compare deterministic with stochastic behavior. Not only do the random parameters influence the deviation in the results but strongly influence the typical features of the different motions themselves. [S0021-8936(00)01701-3].

A pretwisted beam shows a rotation of the principal axes of the cross-sections along its straight center line. All kinematic and static quantities for bending in two orthogonal planes are coupled. This leads to spatial vibrations even for plane excitation. The influence of a small pretwist depends on the ratio of both bending stiffnesses. Deep-webbed beams are mostly affected.

Investigated was the influence of different friction models onto periodicity and uniqueness of stationary motions of a mechanical system.

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 79, Issue S1 p. 105-108 Article Orbitale Stabilität nichtglatter Bewegungen bei permanenten numerischen Störungen P. Vielsack, Inst. für Mechanik, 76128 Universität KarlsruheSearch for more papers by this author P. Vielsack, Inst. für Mechanik, 76128 Universität KarlsruheSearch for more papers by this author First published: 18 March 2011 https://doi.org/10.1002/zamm.19990791328Citations: 2AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Citing Literature Volume79, IssueS1Supplement: Minisymposia University of Bremen, Germany April 6‐9, 19981999Pages 105-108 RelatedInformation

Developing a mathematical model of a mechanical system with friction and impact leads to problems regarding the integration of systems with variable structure. The main point of interest is the influence of permanent disturbances (both Of physical and numerical nature) on the orbital stability of the non-disturbed solution. It is shown that both types of disturbances have similar effects and that, depending on, the type of solution. different stability limits exist. MSC (1991): 73T05, 65L07, 34D10.

Calculated are forced oscillations of a clamped elastic beam with a friction device at its free end. Considering partial states, namely sticking and sliding, and applying FEM leads to a discrete non-smooth dynamic problem. Stationary oscillations are of interest, depending on the number of finite elements and on different types of friction laws. Due to the linearity of partial states of motion, the numerical integration is reduced to the calculation of switching times which separate the sequence of partial states. Appropriate chosen internal damping diminishes the numerical effort considerably.