L. Gaul

Nonlinear dynamics of structures assembled by bolted joints

SummaryThe nonlinear transfer behaviour of an assembled structure such as a large lightweight space structure is caused by the nonlinear influence of structural connections. Bolted or riveted joints are the primary source of damping compared to material damping, if no special damping treatment is added to the structure. Simulation of this damping amount is very important in the design phase of a structure. Several well known lumped parameter joint models used in the past to describe the dynamic transfer behaviour of isolated joints by Coulomb friction elements are capable of describing global states of slip and stick only.The present paper investigates the influence of joints by a mixed experimental and numerical strategy. A detailed Finite Element model is established to provide understanding of different slip-stick mechanisms in the contact area. An advanced lumped parameter model is developed and identified by experimental investigations for an isolated bolted joint. This model is implemented in a Finite Element program for calculating the dynamic response of assembled structures incorporating the influence of micro- and macroslip of several bolted joints.

Smart layer for damage diagnostics

In this research damage diagnostics is carried out by a novel design of a smart layer that consists of piezoelectric films. This thin layer is attached to the structure being monitored. First, some fundamental investigations are carried out in order to examine the influence of the thickness of the film, the influence of different adhesives, and the influence of the couplant. The wave field generated by the smart layer propagates into a solid. The directional dependency is investigated. Moreover, an improved type of polyvinylidene fluoride (PVDF) copolymer is presented and investigated for the potential application in the field of structural health monitoring. The use of this PVDF copolymer makes the manufacturing process of a self-sensing actuating layer in ultrasonics much easier than conventional PVDF films since the piezoelectric film is directly sputtered onto the surface of a metallic specimen or onto a metallic layer. This smart layer technique is a valuable tool for identifying the location and size of cracks and delaminations in composites as well as for determining local material thicknesses which might occur due to corrosion. It can be applied in order to monitor the so-called ‘hot spots’ on new structures as well as on already existing structures. The application of the smart layer is demonstrated on a plate-like structure containing a damage. The identified damage corresponds well with the actual damage.

A new uncertainty analysis for the transformation method

In this paper, a new uncertainty analysis for the transformation method (TM) is proposed. As a practical implementation of fuzzy arithmetic, the TM is a convenient tool for the simulation and analysis of systems with uncertain parameters that are expressed by fuzzy numbers. The proposed uncertainty analysis and the sensitivity analysis of the TM complete each other in providing some quantification of the relationship between the uncertainties of the system input and the system output. The computation of gain factors is proposed, which allows the estimation of the absolute and relative measures of uncertainty. These measures allow the quantification of the influence of the uncertainty of the input on the uncertainty of the output.

Semi-Active Friction Damping of Large Space Truss Structures

The present approach for vibration suppression of flexible structures is based on friction damping in semi-active joints. At optimal locations conventional rigid connections of a large truss structure are replaced by semi-active friction joints. Two different concepts for the control of the normal forces in the friction interfaces are implemented. In the first approach each semi-active joint has its own local feedback controller, whereas the second concept uses a global, clipped-optimal controller. Simulation results of a 10-bay truss structure show the potential of the proposed semi-active concept.

Modal Vibration Control for PVDF Coated Plates

Since advanced technical systems, such as aircrafts, space structures and automobiles, have to combine high performance with low weight, passive vibration absorbers reach their limits. This is why active control has become more important in structural dynamics with successful applications. Vibration control requires sensors, actuators and a controller. In this paper Polyvinylidene fluoride (PVDF) is used as actuator and sensor material. The PVDF elements are segmented in arrays on the plate. The sensors act as point sensors and the sensor signals are filtered by a modal sensor matrix. The modal displacements and modal velocities are used as input data for the controller and for a so-called Actuator Management System (AMS) as well. A modal actuator matrix transforms the controller output into driving actuator voltages. The AMS switches elements of the modal actuator matrix which results in quasi modal actuator groups. A rectangular aluminum plate has been equipped with PVDF actuators and sensors and experimental tests have been carried out in order to validate the proposed concept.

APPLICATION OF THE FAST MULTIPOLE BEM FOR STRUCTURAL–ACOUSTIC SIMULATIONS

The fast multipole method is employed to accelerate the Galerkin boundary element method for acoustics. Important parameters as the nearfield size and the expansion length are discussed and numerical examples are provided. An approximate inverse preconditioner and a preconditioner based on spectral properties of the boundary integral operators are presented. For the example of sound radiation from a brake disk, both approaches prove suitable to reduce the iteration count and to improve the efficiency of the method.

Non-conservative beating in sliding friction affected systems: transient amplification of vibrational energy and a technique to determine optimal initial conditions

Systems with friction are non-conservative as a consequence of the fundamental character of friction as a physical phenomenon: usually friction is associated with dissipative effects, but sometimes also with self-excitation. The present paper deals with the effect that sliding friction has on beating phenomena, which are very common in multidimensional systems with imperfect symmetries. It turns out that sliding friction has a significant influence on the energy budget of beating states, it may even lead to substantial transient amplification of the total vibrational energy. After describing the phenomenon a technique is provided to determine the initial conditions leading to optimal transient amplification of vibrational energy in sliding friction affected beating oscillations. Also intuitive as well as formal explanations for the effects mechanism are given.

Damping prediction of structures with bolted joints

Friction in joints significantly contributes to the observed overall damping of mechanical structures. Especially if the material damping is low, the frictional effects in joints and clamping boundary conditions dominate the structural damping. The damping and the stiffness of the structure are nonlinear functions of the system states and consequently of the excitation signal and amplitude. If these nonlinear effects should be incorporated in the design process, transient simulations must be employed in order to predict and analyze the damping for a given excitation, though they need excessive computation power due to the nonlinear constitutive laws and the high contact stiffnesses. As one approach to alleviate transient simulations, the application of component mode synthesis (CMS) methods to structures with friction is investigated exploiting the linearity of the jointed substructures. The friction and the nonlinear normal contact is modeled by constitutive laws that are implemented in node-to-node finite elements. The necessary considerations for accurate damping prediction by the reduced models, the accuracy and the computational times for transient simulations are discussed. The developed model reduction techniques allow a strong reduction of the computation time which in turn makes it a promising tool for model updating and predictive parameter studies. As an application example, a beam-like structure with attached friction damper is investigated in simulations and the obtained numerical results after model updating are compared to experiments.

Towards Finite Element Model Updating Based on Nonlinear Normal Modes

Local nonlinearities typically occur due to large deformation in certain parts of a structure or due to the presence of nonlinear coupling elements. Often the dynamic behavior of such elements is a priori unknown and has to be investigated experimentally before they can be included in numerical calculations. In this contribution an integrated method for estimation of linear as well as nonlinear system parameters based on the nonlinear normal modes (NNMs) of the structure is proposed. The characteristics of the nonlinear and linear parts of an assembly both contribute to its NNMs. Assuming that the functional form of the nonlinearity is known or can be estimated through non-parametric identification techniques, this feature can be exploited for the purpose of model updating. For the updating process the measured and calculated NNMs of a system are compared and their difference is minimized. In this context the numerical calculation of NNMs is performed using the Harmonic Balance Method (HBM). The properties of the proposed method are demonstrated on the numerical example of a 4DOF oscillator with a cubic nonlinearity. Furthermore, the effectiveness of the method is shown by updating the FE-model of a beam with cubic nonlinearity based on experimental data.

Non-singular symmetric boundary element formulation for elastodynamics

In this paper, a non-singular boundary element formulation for 3D-elastostatics and 3D-elastodynamics is presented. The proposed method is based on a generalized variational principle. A weighted superposition of static fundamental solutions is used for the field approximation in the domain, whereas the displacement and stress field on the boundary are interpolated by well-known polynomial shape functions. By separating time- and space-dependence a symmetric equation of motion is derived with time-independent mass and stiffness matrix. The domain integral over inertia terms, leading to the mass matrix, is analytically transformed to the boundary. Thus, a boundary only formulation is derived. Comparing numerical results with analytical solutions clearly shows that the obtained system of equations is well-suited for dynamic problems.