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Special Topics in Structural Dynamics, Volume 6: Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015, the sixth volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on:


Active Control

Analytical Methods

System Identification

Sensors and Instrumentation



Chapter 1. Development of Reduced Order Models to Non-modeled Regions

Model reduction and model expansion techniques have been used in many structural dynamic modeling applications to map detailed FEM at the full set of DOF (NDOF) to an abbreviated set of active DOF (ADOF) while preserving the dynamic characteristics of interest. In order to perform model reduction and model expansion, the ADOF model must be a subset of the NDOF model. For complex structures with hollow spaces (i.e. wind turbine blades, airframes, hollow fuselage sections, etc.), model reduction to a “beam-like” neutral axis is not possible.
An approach for model reduction to a “line element style model with a neutral axis” is developed in this work. Several analytical models using hollow cantilever beams as academic structures are presented to illustrate the technique. This technique can be extremely useful for development of simplistic beam models from full 3D FEM that possess hollow regions where a neutral axis would exist. These simplistic beam models can be desirable for analyses such as flutter where computation is intensive for structures such as fuselage, aircraft wings, wind turbine blades, etc.
Kevin Truong, Peter Avitabile

Chapter 2. Prediction of Forced Response Using Expansion of Perturbed Reduced Order Models with Inexact Representation of System Modes

Variability in measured data is a common problem in the engineering practice. Changes in the mass and stiffness of the same structural component can occur due to minor variability in the tolerances used during the production/manufacturing process. Differences can exist between the real physical structure and its mathematical model representation (FEM) as well as the predicted response and the actual dynamic behavior of the system. For models in which limited data exists or is collected, the quality of the equivalent reduced order model is dependent on the retained modal parameters as well as the level of correlation of the mode shapes. Prediction of system level forced response from the expansion of these reduced order models can be affected by the use of inexact representations of the system modes such as those from Guyan reduced models. Furthermore, the reduction methodology used, the degrees of freedom selected, as well as the number of retained modes can play an important role in the accuracy of the predicted dynamics of the system.
In this work, a truth model (real answer) is created from the perfect analytical representation of a cantilevered beam. A perturbed variation of the analytical representation of the cantilever beam model is also created to correspond to the simulated imperfections of a FEM of the system. The analytical models will be created to investigate the prediction of the full field dynamic response obtained from the expansion of reduced model information (or data at limited number of DOF) and using the inexact mode shapes of the perturbed model (FEM). The perturbed system representation will have the same geometry and properties as the original unmodified beam (perfect analytical model) but imperfections will be introduced by the addition of mass. The models will be created first at full space as a reference and then reduction techniques will be used to determine the necessary information in order to accurately predict the response at all DOF. Aspects involved in model reduction/expansion, DOF selection, and number of retained modes for the analytical cantilever models are investigated for common reduction techniques such as Guyan condensation and SEREP. The use of a perturbed model (not perfectly correlated to the model) for the expansion of measured real time response data will be shown to produce very accurate full field response even though the model does not perfectly correlate to the real truth model.
Sergio E. Obando, Peter Avitabile, Jason Foley

Chapter 3. Estimation of Rotational Frequency Response Functions

As it is widely known, in structural dynamic applications, ranging from structural coupling to model updating, the incompatibility between measured and simulated data is inevitable, due to the problem of coordinate incompleteness. Usually, the experimental data from conventional vibration testing is collected at a few translational degrees of freedom (DOF) due to applied forces, using hammer or shaker exciters, over a limited frequency range. Hence, one can only measure a portion of the receptance matrix, few columns, related to the forced DOFs, and rows, related to the measured DOFs. In contrast, by finite element modeling, one can obtain a full data set, both in terms of DOFs and identified modes. Over the years, several model reduction techniques have been proposed, as well as data expansion ones. However, the latter are significantly fewer and the demand for efficient techniques is still an issue. In this work, one proposes a technique for expanding measured frequency response functions (FRF) over the entire set of DOFs. This technique is based upon a modified Kidder’s method and the principle of reciprocity, and it avoids the need for modal identification, as it uses the measured FRFs directly. In order to illustrate the performance of the proposed technique, a set of simulated experimental translational FRFs is taken as reference to estimate rotational FRFs, including those that are due to applied moments.
T. A. N. Silva, N. M. M. Maia

Chapter 4. Estimation of Spatial Distribution of Disturbances

The information of spatial distribution of unmeasured disturbances is utilized in controller and observer design. In reality, due to the complexity in the systems, this information is seldom known a priori. Our focus in this study is to estimate the spatial distribution of disturbances from available measurements using a correlations approach that is developed in Kalman filter theory. In this approach one begins by “guessing” a filter gain and then the approach calculates the disturbance covariance matrices from analysis of the resulting innovations. This paper reviews the innovations correlations approach and examines its merit to localize the disturbances.
Yalcin Bulut, Omer F. Usluogullari, Ahmet Temugan

Chapter 5. Body Wise Time Integration of Multi Body Dynamic Systems

Several papers have been published in the past on the issue of decomposing a nonlinear system into subsystems for more efficient time integration. In this paper each body of a multi body system is considered as one subsystem. The subsystems (the bodies) are interacting via connection forces. The sources of such connection forces are constraints or directly applied forces. This contribution is restricted to constraint forces only. During a step which is named “body iteration”, those forces are considered as constant and the state of the system is computed for each body separately. This can be massively parallelized which can be an efficiency advantage in case of computational costly problems like the ones occurring in parameter estimation. During an “constraint update step” the constraints are evaluated based on the body’s current state. If the error is not small enough the interface forces are updated and the inner loop is executed once again until the error of the constraints is negligible. It turns out, that the constraints can be updated separately as well, which can be used again for parallel computing. In the paper, the theory will be outlined and implemented using an N body pendulum. Finally, the advantages and disadvantages of this approach are critically discussed.
Wolfgang Witteveen

Chapter 6. Structural Dynamic Modeling: Tales of Sin and Redemption

The great twentieth century mathematician, John von Neumann, once said, “At a great distance from its empirical source, or after much abstract inbreeding, a mathematical subject is in danger of degeneration. Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less empirical ideas.” This wisdom is especially applicable to the field of structural dynamics. The present paper takes a look at the historical and empirical bases of key aspects of structural dynamic phenomena including damping of materials and built-up assemblies, behavior of viscoelastic materials, interaction of structures and fluids, and general parametric uncertainties. Migration of misconceptions in engineering practice and, in particular, commercial software products are cited. Illustrative examples of the benefits of recollection of fundamentals in aerospace, marine and civil applications are described.
Robert N. Coppolino

Chapter 7. Muscle Property Identification During Joint Motion Using the NL-LTP Method

This work develops a simple low order model of the lower leg that incorporates the effects of a nonlinear biceps femoris muscle actuator and explores the feasibility of identifying a nonparametric model for the knee joint’s rotational behavior as well as the joint activation function that drives the motion. The NL-LTP algorithm is applied to this system and some promising results are obtained. In particular, the nonlinear equations of motion and the joint activation moment are estimated from the “measured responses”. The accuracy of these nonlinear parameter estimates and the implications for future experimental studies of biomechanical systems are discussed.
Michael W. Sracic

Chapter 8. On the Detectability of Femoral Neck Fractures with Vibration Measurements

A suspicion of a femoral neck fracture is a frequently recurring situation, especially in nursing homes. For the clarification of such a suspicion normally imaging techniques are used. Such equipment is expensive and therefore is located in hospitals. In addition to the costs, a transport causes stress for the patient. This pilot study is devoted to the question whether the detection of a femoral neck fracture with vibration measurements is possible in principal. For this purpose vibration measurements on a dead body with intact, with partially fractured and with complete cut femoral neck have been performed. The frequency response function has been determined for all combinations on both sides of the body. It turned out that there is a difference in the frequency response functions of the fractured bone with respect to the intact bone when shaker testing is used.
Wolfgang Witteveen, Carina Wagner, Patrick Jachs, Stefan Froschauer, Harald Schöffl

Chapter 9. Static Calibration of Microelectromechanical Systems (MEMS) Accelerometers for In-Situ Wind Turbine Blade Condition Monitoring

As wind turbines get larger, operation and maintenance costs can be expected to rise unless reliability is improved. One important strategy for achieving this is through condition monitoring. Condition monitoring is a preventive type of maintenance based on the actual health of the wind turbine under observation. Its use allows an operational strategy to be employed based on information measured and provided by a condition monitoring system. This paper outlines the procedure for least square static calibration of inexpensive Microelectromechanical Systems accelerometers identified and instrumented for detecting and measuring changes in natural frequency (key information useful for condition monitoring) of a 4.5 m long wind turbine blade. The calibration procedure converts the local accelerometer coordinates to the global coordinate system of the blade and eliminates the accelerometer offsets from results. The objective is to enable easier comparison of results obtained from multiple accelerometers positioned arbitrarily along the blade, independent of the accelerometer orientation on the usually curved wind turbine blade surface.
O. O. Esu, J. A. Flint, S. J. Watson

Chapter 10. Predicting Full-Field Strain on a Wind Turbine for Arbitrary Excitation Using Displacements of Optical Targets Measured with Photogrammetry

Wind turbine blades and other structures are often subjected to dynamic loading that may not be predicted or measurable at critical locations of interest. Therefore, a non-contacting measurement technique that can provide information throughout an entire structure with the absence of instrumented sensors is desirable. Such an approach is particularly beneficial and relevant to operating rotor or wind turbine blades. In this paper, a three-bladed wind turbine placed in a semi-built-in boundary condition was subjected to a variety of different loadings. The turbine was excited using a sinusoidal excitation, a pluck test, arbitrary impacts on three blades, and random force excitations with a mechanical shaker. The response of the structure to these excitations at optical targets mounted to the blades was measured using three-dimensional point tracking. The limited set of measured displacement at the optical targets was expanded using a modal expansion algorithm. The expanded displacement was used in conjunction with a finite element model of the turbine to extract dynamic strain throughout the entire structure. The results from the technique were compared to instrumented strain gages and are shown be in close agreement. The predicted strain using the proposed approach is not limited to the locations of the optical targets or where the cameras have line of sight. This new technique may enable a new structural health-monitoring approach that has the ability to interrogate an entire structure, inside and outer surface.
Javad Baqersad, Peyman Poozesh, Christopher Niezrecki, Peter Avitabile

Chapter 11. Predicting the Vibration Response in Subcomponent Testing of Wind Turbine Blades

Currently new wind turbine blade materials are certified by starting with coupon testing for initial strength and fatigue analysis, followed by full-scale blade testing as a final quality control to assess material characteristics. Subcomponent testing has been proposed as a supplement to the structural analysis and material characterization, bridging the gap between coupon and full-scale tests. In this study, similitude theory is applied to a simply-supported rectangular plate that is representative of a wind turbine blade spar cap with the goal of designing a validated scaled-down subcomponent. The vibration of a specially orthotropic rectangular laminated plate is analyzed to extract the scaling laws based on direct use of the field equations. The accuracy of the derived scaling laws is analyzed as a model validation criteria by mapping the first natural frequency of the variant subcomponents to the full-scale plate. The effect of the ply stack up scheme and size of the subcomponents in predicting accuracy of the scaling laws are then investigated by applying partial and complete similarity conditions. According to the results, subcomponents with modified ply stack up could be found that have a good accuracy in predicting the first natural frequency of the full-scale plate. However, picking an appropriate aspect ratio is critical to the success of the prediction of full scale plate response as shown in the cases studied.
Mohamad Eydani Asl, Christopher Niezrecki, James Sherwood, Peter Avitabile

Chapter 12. Linear Modal Analysis of a Horizontal-Axis Wind Turbine Blade

In this work, mode shapes and modal frequencies of a horizontal axis wind turbine blade are found. The blade is modeled as a pre-twisted beam under bend-bend-twist deformations, and the strain, gravitational potential and kinetic energy expressions are found. These expressions are then simplified for linear theory, and further by using the assumed modes method in which assumed modes are chosen independently for flapwise, edgewise, and twist deflections from a cantilevered uniform beam. Lagrange’s equations of motion are applied to the assumed modal coordinates, and coupled linear equations are thus found. Modal analysis is applied to the assumed modal equations to find the resonance frequencies, and the resulting mode shapes are recombined to express the mode shapes in the bend-bend-twist coordinates. The approach was applied to a uniform twisted rectangular beam, and the first three mode shapes are found to be combinations of the in-plane and out-of-plane bending. The results of the modal analysis are compared with results from a finite element analysis, and the mode shapes and frequencies are consistent. The method is also applied to NREL’s 5 MW wind turbine blade to find its bend-bend-twist mode shapes and natural frequencies.
Gizem Acar, Brian F. Feeny

Chapter 13. Reduced-Order Modeling of Turbine Bladed Discs by 1D Elements

The dynamic behavior of turbine bladed discs is deeply influenced by blades geometry, which is determined as a compromise between fluid-dynamic and mechanical needs. One of the most important issue from the mechanical side is the tailoring of the dynamic characteristics to allow a sufficient separation between the natural frequencies and the harmonics of the rotational speed. The most common approach to predict the natural frequencies of bladed discs involves the realization of 3D FE models using solid elements. This approach is highly demanding in terms of time for the realization of the models as well as for the computation, even when only one blade if explicitly modeled and a cyclic symmetry constraint is employed.
In this work, we propose a reduced order model based on mono-dimensional finite elements. The proposed element is based on the Timoshenko beam formulated for non-symmetrical cross sections. The shape functions are based on the exact solution of the beam equation to avoid shear-locking. Torsional stiffness includes the effect of warping. The proposed model is compared with accurate 3D FE models in terms of modal properties. Blades of different shape and slenderness taken from turbine and compressor of a large gas turbine are considered.
Luigi Carassale, Mirko Maurici, Laura Traversone

Chapter 14. Damping Estimation for Turbine Blades Under Non-stationary Rotation Speed

Turbine blades are critical components in thermal power plants and their design process usually includes experimental tests in order to tune or confirm numerical analyses. These tests are generally carried out on full-scale rotors having some blades instrumented with strain gauges and usually involve a run-up and/or a run-down phase. The quantification of damping in these conditions is rather complicated, since the finite sweep velocity produces a distortion of the vibration amplitude with respect to the Frequency-Response Function that would be expected for an infinitely slow crossing of the resonance. In this work, we demonstrate through a numerical simulation that the usual identification procedures procedure lead to a systematic overestimation of damping due both to the finite sweep velocity, as well as to the variation of the blade natural frequency with the rotation speed. An identification procedure based on the time-frequency analysis is proposed and validated through numerical simulations.
Luigi Carassale, Michela Marrè-Brunenghi, Stefano Patrone

Chapter 15. Finite Element Modeling of a 40m Space Frame Wind Turbine Tower

The “20 % Wind Energy by 2030” initiative by the U.S. Department of Energy initiated the investigation of taller wind turbines. The highway infrastructure in the U.S. is causing the wind energy industry to investigate alternative designs; the lattice tower design is one such solution. One company designed a lattice tower that utilizes interference between the bolt and the clamped components. To study the dynamics of this tower an intensive model was created using beam, shell, and solid finite elements. Due to experimental results the model was originally modeled using a fixed boundary; however, the resulting frequencies for the first two modes were high. To investigate if the boundary was the cause of this error, the soil surrounding the tower was modeled using a relatively large linear solid continuum. The addition of the solid continuum greatly improved the results; resulting in a maximum difference of − 7 % and mode shapes for the experiment and model follow the same trend.
S. A. Smith, W. D. Zhu, Y. F. Xu

Chapter 16. Experimental Validation of Modal Parameters in Rotating Machinery

In this paper, instability of rotating machinery systems due to rotating damping is investigated through experimental modal analysis. Generally, advanced methods are needed for these kind of systems because of the asymmetry of the matrices. However, it is shown by means of cyclic energy dissipation that the rotating damping can be handled as damping which changes due to the rotating speed. The use of damping matrix estimation techniques is discussed and a method is proposed to estimate and model the influence of the rotating damping matrix. A dedicated experimental setup, with negligible gyroscopic effect, is presented for validation purposes. It is shown experimentally that the estimation of the rotating damping matrix is able to predict the decay rate of the first forward mode.
Bram Vervisch, Kurt Stockman, Mia Loccufier

Chapter 17. Estimation of Modal Damping for Structures with Localized Dissipation

Damping plays an important role in bolted joints of assembled structures due to their significant capacity to dissipate energy. The underlying mechanisms of these dissipative phenomena are generally poorly understood and result from contact and friction effects within the joint interfaces. In order to provide useful virtual prototyping tools for reducing response levels, accurate model-based estimation of modal damping is required. The present study employs an energetic method to calculate the loss factor associated with the localized dissipative interfaces of a global linear structure. This method is based on the concept of the dissipated energy in the interfaces for which the closed-form expression of the loss factor is the ratio between dissipated energy and maximal potential energy, over a cycle of periodic vibration. The aim of this work is to investigate the advantages and drawbacks of this approach for particular conditions such as: modal projection, localized damping level and model density. Simulated academic examples, where accurate estimations of the exact solutions are available, will be used to illustrate the methodology and to explore the potential difficulties that may arise in more complex industrial applications.
M. Krifa, N. Bouhaddi, S. Cogan

Chapter 18. Design of UAV for Surveillance Purposes

Two main algorithms are presented to use an UAV for surveillance purposes. A very fast algorithm for the scan of an unknown area has been implemented and tested: it permits to scan a domain for the definition of layout, boundaries, obstacles… Once that the area has been acquired, a second algorithm is used to monitor the regions of interest in an efficient way. A neural network has been built in order to choose the shortest path to reach a determined point, giving the drone the possibility to avoid unexpected obstacles. Finally these two algorithms has been tested to verify their accuracy and speed.
F. Cheli, F. Ripamonti, D. Vendramelli

Chapter 19. An Innovative Solution for Carving Ski Based on Retractile Blades

This paper presents the design of a new ski to improve the performances focusing especially on steering conditions. In the proposed solution an additional retractile edge has been added modifying the lower surface of the ski. It consists of a thin stainless steel plate suitably reinforced with two longitudinal ribs welded along the plate borders to create the blades. Then this element is constrained to the ski along the longitudinal symmetry axis. In unload and straight conditions the gap between the ski and the edge is null while in curves the retractile blade is deformed and pushed out by the force applied by the skier, penetrating the snow. The mechanism for the force transmission is based on two revolution joints, allowing small rotations of the boot with respect to the ski and compensating the ski deformation, and several pistons, pushing on the edge. Two ski prototypes have been manufactured, instrumented and tested on a snow track. In particular, in order to show the differences in terms of performance, the modified skis have been compared to the classic version. Additional considerations about the variations on stiffness and friction behavior introduced by the new solution have been drawn too.
F. Cheli, L. Colombo, F. Ripamonti
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