Murat Aykan

Parametric Identification of Nonlinearity from Incomplete FRF Data Using Describing Function Inversion

Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisticated structures such as satellites require even the smallest nonlinear behavior to be considered for better performance. Therefore, it is very important to successfully detect, localize and parametrically identify nonlinearity in such cases. In engineering applications, the location of nonlinearity and its type may not be always known in advance. Furthermore, in most of the cases, test data will be incomplete. These handicaps make most of the methods given in the literature difficult to apply to engineering structures. The aim of this study is to improve a previously developed method considering these practical limitations. The approach proposed can be used for detection, localization, characterization and parametric identification of nonlinear elements by using incomplete FRF data. In order to reduce the effort and avoid the limitations in using footprint graphs for identification of nonlinearity, describing function inversion is used. Thus, it is made possible to identify the restoring force of more than one type of nonlinearity which may co-exist at the same location. The verification of the method is demonstrated with case studies.

Identification of Restoring Force Surfaces in Nonlinear MDOF Systems from FRF Data Using Nonlinearity Matrix

The sensitivity of the response characteristics of a nonlinear structure to load level may prevent us to predict the linear behavior of a nonlinear system. The nonlinear identification method recently proposed by the authors is based on the measured linear and nonlinear Frequency Response Functions (FRFs). The method is easy to implement and requires standard testing methods. The data required is limited with measured linear and nonlinear FRFs. In order to obtain the linear FRFs in a nonlinear system, it is the general practice to use low level forcing, unless the nonlinearity is due to dry friction. However, depending on the level of nonlinearity it may not be possible to lower the harmonic forcing amplitude beyond a practical limit, and this may not be sufficient to obtain linear FRFs. The approach presented in this study aims to perform the nonlinear identification directly from a series of measured nonlinear FRFs. It is shown that Restoring Force Surfaces (RFS) can be identified more accurately by employing this approach. The verification of the method is demonstrated with simulated and experimental case studies.

Parametric Nonlinearity Identification of a Gearbox from Measured Frequency Response Data

Structural nonlinearity is commonly encountered at mechanical connections such as bearings and gears under dynamic loading. Usually, linear approximations of the nonlinearity will yield acceptable results. However, when the nonlinearity is dominant, the nonlinear analysis becomes unavoidable. Most of the time, in engineering assemblies the whole design is too complex to include the nonlinearity in the model. Then it becomes necessary to simplify the structure in order to analyze the nonlinear element separately. In this study, a method developed in an earlier work is implemented on a test rig containing gearbox. The method is capable of parametrically identifying nonlinearities from measured frequency response functions. In this paper, it is aimed to present the validity of the method by applying it to a real test structure and thus parametrically identifying the nonlinear element in the system to obtain a mathematical model, and then employing the model in harmonic response analysis of the system in order to compare predicted responses with measured ones.

Parameter Identification of Riveted Joints Using Vibration Methods

Rivets are widely used in several industries including aerospace, shipbuilding and construction. Aircraft components such as wings and fuselages are some examples of riveted structures. Accurate parameter identification of these joints is critical since excessive number of rivets is present in such structures. Furthermore, modeling structures with fasteners has always been a challenge since these members might show nonlinear behavior. In this study, the FEM of a continuous plate is constructed and modal tests are performed in order to have a valid modeling strategy. After a good correlation between finite element analyses (FEA) and tests is obtained, a finite element model with riveted joints is constructed and parameters of these fasteners are identified by means of vibration measurements and optimization.

Energy Harvesting from Piezoelectric Stacks Using Impacting Beam

Piezoelectric materials can be used for energy harvesting from ambient vibration due to their high power density and ease of application. Two basic methods, namely, tuning the natural frequency to the operational frequency and increasing the operation bandwidth of the harvester are commonly employed to maximize the energy harvested from piezoelectric materials. Majority of the studies performed in recent years focus mostly on tuning the natural frequency of the harvester. However, small deviations in operating frequency from the natural frequency can cause excessive loss in the power output. It is then advantageous to design a harvester which is capable operating in a wide frequency band. This goal could be achieved both by expanding effective bands of natural frequencies and introducing a frequency-rich external input to the system. The main idea is to supply constant excitation energy into the harvester system to obtain high energy levels by changing system characteristics. In this study, in order to investigate the effects of impacts on energy harvested, an analytical model of an impacting beam with piezoelectric stack at its tip is developed. Experimental validation of analytical results is also performed.

Flexible Dynamic Modeling of Turret Systems by Means of Craig-Bampton Method and Experimental Validation

Today’s mechanical systems are designed and manufactured with increasing functionality due to the increase in the design requirements. This leads to use of higher numbers of degrees of freedom, causing system modeling process become more complicated, including structural and dynamic aspects. The sources of complexity arise mainly from the connection mechanisms like gears, bearings and gear boxes and dynamic behavior of the structural parts in motion. Usually, each of these subsystems is analyzed individually by analytical and/or numerical methods. However, the whole system performance should be modeled and analyzed in the assembly configuration in order to observe the interaction of subsystems. Furthermore, critical structural parts should be modeled flexible and connection mechanisms’ dynamic properties need to be identified accurately. Modeling parts elastically also result in additional degrees of freedom which makes the model difficult to solve for kinematic analysis. Therefore, Craig-Bampton reduction method is used to reduce the size of elastically modeled parts. In this study, dynamic modeling process and analysis results of a turret will be presented. Furthermore, comparisons between the analysis results and the assembled prototype turret tests are presented.

Detection of Structural Damage Through Nonlinear Identification by Using Modal Testing

Structural damages usually introduce nonlinearity to the system. A previously developed nonlinear identification method is employed to detect crack type structural damage. The method requires the measurement of FRFs at various points in order to locate the damage. The method makes it also possible to determine the extent of damage by identifying the level of nonlinearity. The verification of the method is demonstrated with experimental case studies using beams with different levels of cracks. The approach proposed in this study is very promising to be used in practical systems, but still open to further improvements.

Material Characterization of Gyroscope Isolator Using Modal Test Data

Gyroscopes are widely used in stabilization of turret systems where high shocks are encountered. Use of isolation material with them is essential to obtain reliable rotation data considering the intensity of shocks. Usually, each gyroscope comes with an isolator panel specific to itself. In certain situations, however, a proper isolator configuration is unavailable for the gyroscope. In this study, analyses required to use a sandwich panel isolator with a gyroscope other than its original one are presented. Isolation material is modeled as orthotropic and its characteristic properties are obtained from the comparison between the modal tests and the finite element model by using optimization. Effects of full realization of the boundary conditions on the modal data are also shown.