Andreas Linderholt

Damping elastomers for wooden constructions : Dynamic properties

Abstract Elastomers are commonly used to decrease the sound transmission between apartments in timber framed houses. In previous studies, different types of connections have been evaluated. However, the frequency dependent dynamic properties in different directions of a connection including elastomers are not fully investigated yet. Previous studies have actually shown that elastomers cause the vibrations to increase in the direction perpendicular to the applied load within the low frequency span. The properties of the elastomers are needed in order to model the dynamic behaviour and thereby be able to predict sound and vibration transmissions in wooden houses in the future. With known properties, the elastomer connections can be modelled using springs and dashpots. In this study, dynamic experiments have been made on elastomer strips half embedded. The test setup has been subjected to various loads using an electromagnetic shaker. The responses have been measured and evaluated using modal analysis. With different loads, non-linear characteristics of the elastomers’ behaviour have been obtained. The elastomers have also been tested quasi-statically, to obtain a load-deflection curve. Finally, the estimated properties of the elastomers have been included in an FE model using springs and the analytical results are compared with the experimental results.

Finding Local Non-Linearities Using Error Localization from Model Updating Theory : Proceedings of the 30th IMAC, A Conference on Structural Dynamics, 2012

Within the aerospace industry, linear finite element models are traditionally used to describe the global structural dynamics of an aircraft. Ground vibration test data serve to facilitate the vali ...

Model calibration of a locally non-linear structure utilizing multi harmonic response data

Model correlation and model calibration using test data are natural ingredients in the process of validating computational models. Here, model calibration for the important sub-class of non-linear systems consisting of structures dominated by linear behavior having presence of local non-linear effects is studied. The focus is on the selection of uncertain model parameters together with the forming of the objective function to be used for calibration. To give precise estimation of parameters in the presence of measurement noise, the objective function data have to be informative with respect to the parameters chosen. Also, to get useful data the excitation force is here designed to be multi-harmonic since steady-state responses at the side frequencies are shown to contain valuable information for the calibration process. In this paper, test data from a replica of the Ecole Centrale de Lyon (ECL) nonlinear benchmark together with steady-state solutions stemming from calculations using the Multi-Harmonic Balancing method are used for illustration of the proposed model calibration procedure.

Model Calibration and Uncertainty of A600 Wind Turbine Blades

Recently, a lot of work has been done on modeling, testing and calibrating Ampair 600 W wind turbine blades, owing to the use of that turbine as a test bed structure for the Dynamic Substructuring Focus Group within the Society of Experimental Mechanics. In Sweden alone, more than 20 blades have been tested for dynamical properties, geometrical differences and material properties as was presented in several papers at IMAC XXXI. The quantity of blades, originating from different manufacturing batches, makes them ideal for investigations of component variability.

Locally Non-linear Model Calibration Using Multi Harmonic Responses: Applied on Ecole de Lyon Non-linear Benchmark Structure

In industry, linear FE-models commonly serve to represent global structural behavior. However, when test data are available they may show evidence of nonlinear dynamic characteristics. In such a case, an initial linear model may be judged being insufficient in representing the dynamics of the structure. The causes of the non-linear characteristics may be local in nature whereas the major part of the structure is satisfactorily represented by linear descriptions. Although the initial model then can serve as a good foundation, the parameters needed to substantially increase the model’s capability of representing the real structure are most likely not included in the initial model. Therefore, a set of candidate parameters controlling nonlinear effects, opposite to what is used within the vast majority of model calibration exercises, have to be added. The selection of the candidates is a delicate task which must be based on engineering insight into the structure at hand.The focus here is on the selection of the model parameters and the data forming the objective function for calibration. An over parameterized model for calibration render in indefinite parameter value estimates. This is coupled to the test data that should be chosen such that the expected estimate variancesof the chosen parameters are made small. Since the amount of information depends on the raw data available and the usage of them, one possibility to increase the estimate precision is to process the test data differently before calibration. A tempting solution may be to simply add more test data but, as shown in this paper, the opposite could be an alternative; disregarding low excessive data may make the remaining data better to discriminate between different parameter settings.Since pure mono-harmonic excitation during test is an abnormality, the excitation force is here designed to contain sub and super harmonics besides the fundamental one. Further, the steady-state responses at the side frequencies are here shown to contain most valuable information for the calibration process of models of locally nonlinear structures.Here, synthetic test data stemming from a model representing the Ecole Centrale de Lyon (ECL) nonlinear benchmark are used for illustration. The nonlinear steady state solutions are found using iterative linear reverse path state space calculations. The model calibration is here based on nonlinear programming utilizing several parametric starting points. Candidates for starting points are found by the Latin Hypercube sampling method. The best candidates are selected as starting points for optimization.

Frequency Response Calculations of a Nonlinear Structure a Comparison of Numerical Methods

Mechanical systems having presence of nonlinearities are often represented by nonlinear ordinary differential equations. For most of such equations, exact analytic solutions are not found; thus numerical techniques have to be used. In many applications, among which model calibration can be one, steady-state frequency response functions are the desired quantities to calculate.

Transmission Simulator Mass Loading Effects in Experimental Substructuring – A Study of the Ampair 600 Benchmark System

During the last years, a lot of research focusing on appropriate interfaces between substructures has been made; the transmission simulator method has become a tool in that strive. In this paper, the end effects on assembled structures consisting of finite element substructure models representing experimental setups with different levels of transmission simulator mass loadings at their interfaces are studied. Here, components of the Society of Experimental Mechanics, SEM, substructuring focus group’s benchmark; the Ampair A600 wind turbine, constitute the structure studied. Models of an A600 blade and bracket system attached to dummy masses of different sizes are coupled to models representing an A600 hub together with two blades attached to dummy masses of different sizes after numerical subtraction of the dummy masses on each of the substructures. The results are compared to data stemming from a model of the assembled system.

Experimental Validation of a Nonlinear Model Calibration Method Based on Multiharmonic Frequency Responses

Correlation and calibration using test data are natural ingredients in the process of validating computational models. Model calibration for the important subclass of nonlinear systems which consists of structures dominated by linear behavior with the presence of local nonlinear effects is studied in this work. The experimental validation of a nonlinear model calibration method is conducted using a replica of the Ecole Centrale de Lyon (ECL) nonlinear benchmark test setup. The calibration method is based on the selection of uncertain model parameters and the data that form the calibration metric together with an efficient optimization routine. The parameterization is chosen so that the expected covariances of the parameter estimates are made small. To obtain informative data, the excitation force is designed to be multisinusoidal and the resulting steady-state multiharmonic frequency response data are measured. To shorten the optimization time, plausible starting seed candidates are selected using the Latin hypercube sampling method. The candidate parameter set giving the smallest deviation to the test data is used as a starting point for an iterative search for a calibration solution. The model calibration is conducted by minimizing the deviations between the measured steady-state multiharmonic frequency response data and the analytical counterparts that are calculated using the multiharmonic balance method. The resulting calibrated models output corresponds well with the measured responses. Copyright

Bias Errors of Different Simulation Methods for Linear and Nonlinear Systems

Responses of mechanical systems are often studied using numerical time-domain methods. Discrete excitation forces require a transformation of the dynamic system from continuous time into discrete time. Such a transformation introduces an aliasing error. To reduce the aliasing error, different discretization techniques are used. The bias errors introduced by some discretization techniques are studied in this paper.

A Pretest Planning Method for Model Calibration for Nonlinear Systems

With increasing demands on more flexible and lighter engineering structures, it has been more common to take nonlinearity into account. Model calibration is an important procedure for nonlinear analysis in structural dynamics with many industrial applications. Pretest planning plays a key role in the previously proposed calibration method for nonlinear systems, which is based on multi-harmonic excitation and an effective optimization routine. This paper aims to improve the pretest planning strategy for the proposed calibration method. In this study, the Fisher information matrix (FIM), which is calculated from the gradients with respect to the chosen parameters with unknown values, is used for determining the locations, frequency range, and the amplitudes of the excitations as well as the sensor placements. This pretest planning based model calibration method is validated by a structure with clearance nonlinearity. Synthetic test data is used to simulate the test procedure. Model calibration and K-fold cross validation are conducted for the optimum configurations selected from the pretest planning as well as three other configurations. The calibration and cross validation results show that a more accurate estimation of parameters can be obtained by using test data from the optimum configuration.