Initial forms of analytical models created to simulate real engineering structures may generally yield dynamic response predictions different than those obtained from experimental tests. Since testing a real structure under every possible excitation is not practical, it is essential to transform the initial mathematical model to a model which reflects the characteristics of the actual structure in a better way. By using structural model updating techniques, the initial mathematical model is adjusted so that it simulates the experimental measurements more closely. In this study, a sensitivity-based finite element (FE) model updating method using experimental frequency response (FRF) data is presented. This study bases on a technique developed in an earlier study on the computation of the so-called Mis-correlation Index (MCI) used for identifying the system matrices which require updating. MCI values are calculated for each required coordinate, and non-zero numerical values indicate coordinates carrying error. In this work a new model updating procedure based on the minimization of this index is developed. The method uses sensitivity approach. FE models are iteratively updated by minimizing MCI values using sensitivities. The validation of the method is realized through some case studies. In order to demonstrate the application of the method for real systems, a real test data obtained from the modal test of a scaled aircraft model (GARTEUR SM-AG19) is used. In the application, the FE model of the scaled aircraft is updated. In the case studies the generic software developed in this study is used along with some commercial programs.

In this study, the efficiency of linear and rotational tuned mass dampers (TMD) and lever type vibration isolators (LVI) in improving ride comfort is investigated based on a vehicle quarter-car model. TMDs reduce vibration levels by absorbing the energy of the system, especially at their natural frequencies. Both types of TMDs are investigated in the first part of this study. Although linear TMDs can be implemented more easily on suspension systems, rotational TMDs show better performance in reducing vibration levels / since, the inertia effect of rotational TMDs is higher than the linear TMDs. In order to obtain better results with TMDs, configurations with chain of linear TMDs are obtained in the second part of the study without changing the original suspension stiffness and damping coefficient. In addition to these, the effect of increasing the number of TMDs used in the chain configuration is investigated. Results show that performance deterioration at lower frequencies than wheel hop is reduced by using chain of TMDs. In the third part of this study, various configurations of LVIs with different masses are considered and significant attenuation of vibration amplitudes at both body bounce and wheel hop frequencies is achieved. Results show that TMDs improve ride comfort around wheel hop frequency while LVIs are quite efficient around body bounce frequency. Finally, parameter uncertainty due to aging of components and manufacturing defects are investigated.

Remotely Operated Vehicles (ROVs) provide access to underwater environments too deep and dangerous for commercial divers. A tether connects the ROV to a vessel on the surface, providing power and communication channels. During extended manoeuvres, hydrodynamic forces on the tether produce large tensions which hinder ROV manoeuvrability. The research presented in this thesis focuses on the design of new tether management strategies that alleviate the tether disturbance problem, and the implementation of a navigation suite for tracking the ROV position and velocity which are needed to close the loop on the tether management method. To improve the estimation of the ROV state, an Extended Kalman Filter (EKF) is developed.

Evidence suggests that the basic neural elements controlling and coupling the arms and the legs in humans during coordinated rhythmic movements are similar to that observed in quadrupedal animals. Further, it is possible that these interlimb connections may be exploited to assist in locomotor rehabilitation after neurotrauma. Specifically, the effect of arm activity on leg neural circuitry has great implications for walking retraining. However, our understanding of the neuromechanics of rhythmic arm movement as well as the neuronal connections between arms and legs active during rhythmic movement is lacking. Greater knowledge on details of interlimb coupling and combined neural and mechanical measurement of rhythmic arm movement are necessary to optimize parameters of interlimb coupling for use in walking rehabilitation. The primary goals of this thesis were to further our understanding of neural interlimb connections during combined arm and leg rhythmic movement and conduct neuromechanical investigations of rhythmic arm movement. First, this thesis developed a method for multiple parameter analysis of the Hoffmanreflex recruitment curve. A sigmoid function was found to be a reliable analysis technique that mimics the physiologically based prediction of the input/output relation of the ascending limb of the recruitment curve. This technique provided a baseline for evaluation of neural interactions between the arms and the legs during rhythmic movement and was utilized during following experiments. Second, the effect of rhythmic leg cycling on reflexes within, and corticospinal projections to, stationary arm muscles was examined. Rhythmic leg cycling significantly suppressed H-reflexes in forearm muscles. Additionally, sub-threshold transcranial magnetic stimulation (TMS) facilitation of H-reflexes was similar during leg cycling as during static contraction suggesting a considerable sub-cortical component. These results supports the hypothesis of a loose, but significant, neural coupling between the arms and the legs during rhythmic movement. Third, we used a reduced walking model of combined arm and leg cycling to examine the separate and combined effects of rhythmic arm and leg movement on the modulation of lower limb H-reflexes with and without stimulating a nerve innervating the hand. The suppressive effect of arm movement was less than that for leg movement and combined arm and leg rhythmic movement, which were generally equivalent. For H-reflexes conditioned by cutaneous input to the hand, amplitudes during combined arm and leg movement instead were in between those for modulation produced by arm movement and leg movement alone. Further a significant contribution for arm movement was revealed only in trials when hand stimulation was used to condition H-reflex amplitudes. Therefore a measurable interaction between neural activity regulating arm and leg movement during locomotion is specifically enhanced when cutaneous input from the hand is present. Fourth, we explored interlimb interactions during a locomotor-like, 3 limb stepping paradigm involving movement of both arms and one leg while eliciting an H-reflex in the stationary test limb. The conditioning effect of contralateral leg movement, bilateral arm movement, and combined bilateral arm and contralateral leg movement on H-reflex amplitude was evaluated at different phases across all tasks. Significant interactions between arm and leg activity could be revealed using the 3-limb paradigm. Further, across phases we observed differential suppressive effects of separate and combined arm and leg movement suggesting phase dependent contributions of arm and leg activity to overall 3-limb suppression. These results support the role of the arms in modulating activity in the legs during human locomotor tasks. Fifth, the mechanical effects of stimulating a cutaneous nerve innervating the dorsum of the hand during arm cycling were quantified. The results show that mechanical responses to cutaneous stimulation of the hand during arm cycling are related to the task and phase and consistent with the anatomical location of the stimulus (local sign). Therefore, these responses are comparable to functionally relevant responses in the legs during lower limb rhythmic movement. However, unlike the responses in the lower limbs, the mechanical responses cannot be easily described in the neuromechanical context of arm cycling. Therefore we suggest that the superimposed task constraints and control variable of arm cycling limit the kinematic reflex expression and make it difficult to decipher the true functional role of the reflexes. Overall, these results provide evidence for mechanical correlates to neural responses during arm cycling and further support parallels between the neural regulation of arm and leg rhythmic movement. Sixth, a combined neural and mechanical measurement approach was used to compare three rhythmic arm movement tasks: arm cycling; arm swing while standing; and arm swing while treadmill walking. The results highlight important neural and mechanical features that distinguish differences between tasks. Overall, differences in neural control between tasks (i.e., pattern of muscle activity) reflected changes in the mechanical constraints unique to each task while the results are consistent with conserved common central motor control mechanisms operational for arm cycling, arm swing while walking, and arm swing alone yet appropriately sculpted to demands unique to each task. Taken together the data in this thesis suggest that, in addition to understanding details of neural interlimb coupling, mechanical considerations may play an important role in the coordination of locomotor movements. Additionally, the use of rhythmic arm movement as a locomotor adjunct in rehabilitation is revealed through combined neural and mechanical measurement.

ABSTRACT NON-LINEAR MATHEMATICAL MODELING OF GEAR-ROTOR-BEARING SYSTEMS INCLUDING BEARING CLEARANCE G&Uuml / RKAN, Niyazi Ersan M.S. Department of Mechanical Engineering Supervisor: Prof. Dr. H. Nevzat &Ouml / ZG&Uuml / VEN November 2005, 130 pages In this study, a non-linear mathematical model of gear-rotor systems which consists of elastic shafts on elastic bearings with clearance and coupled by a non-linear gear mesh interface is developed. The mathematical model and the software (NLGRD 2.0) developed in a previous study is extended to include the non-linear effects due to bearing clearances by using non-linear bearing models. The model developed combines the versatility of using finite element method and the rigorous treatment of non-linear effect of backlash and bearing clearances on the dynamics of the system. The software uses the output of Load Distribution Program (LDP), which computes loaded static transmission error and mesh compliance for the contact points of a typical mesh cycle, as input. Although non-varying mesh compliance is assumed in the model, the excitation effect of time varying mesh stiffness is indirectly included through the loaded static transmission error, which is taken as a displacement input into the system. Previous computer program which was written in Fortran 77 is rewritten by using MatLAB 7.0 and named as NLGRD (Non-Linear Geared Rotor Dynamics) Version 3.0. The program is highly flexible and open to further developments. The program calculates dynamic to static load ratio, dynamic transmission error, forces and displacements at bearings. The mathematical model suggested and the code (NLGRD version 3.0) are validated by comparing the numerical results obtained from the model suggested with experimental data available in literature. The results are also compared with those of previously developed non-linear models. The effects of different system parameters such as bearing stiffness, bearing clearance and backlash on the gears are investigated. The emphasis is placed on the interaction of clearances in bearings with other system parameters.

Regenerative chatter is a well-known machining problem that results in unstable cutting process, poor surface quality, reduced material removal rate and damage on the machine tool itself. Stability lobe diagrams supply stable depth of cut &amp / #8211 / spindle speed combinations and they can be used to avoid chatter. The main requirement for generating the stability lobe diagrams is the system dynamics information at the tool tip in the form of point frequency response function (FRF). In this work, an analytical model that uses structural coupling and modification methods for modeling the dynamics of spindle-holder-tool assemblies in order to obtain the tool point FRF is presented. The resulting FRF obtained by the model can be used in the existing analytical and numerical models for constructing the stability lobe diagrams. Timoshenko beam theory is used in the model for improved accuracy and the results are compared with those of Euler-Bernoulli beam theory. The importance of using Timoshenko beam theory in the model is pointed out, and the circumstances, under which the theory being used in the model becomes more important, are explained. The model is verified by comparing the results obtained by the model with those of a reliable finite element software for a case study. The computational superiority in using the model developed against the finite element software is also demonstrated. Then, the model is used for studying the effects of bearing and contact dynamics at the spindle-holder and holder-tool interfaces on the tool point FRF. Based on the results of the effect analysis, a new approach is suggested for the identification of bearing and interface parameters from experimental measurements, which is demonstrated on a spindle-holder-tool assembly. The model is also employed for studying the effects of design and operational parameters on the tool point FRF, from the results of which, suggestions are made regarding the design of spindles and selection of operational parameters. Finally, it is experimentally demonstrated that the stability lobe diagram of an assembly can be predicted pretty accurately by using the model proposed, and furthermore the stability lobe diagram can be modified in a predictable manner for improving chatter stability.

Indiana University-Purdue University Indianapolis (IUPUI) / This thesis presents a comprehensive study of the effects of material, geometric and operational parameters on flat belt-drives steady-state belt stresses, belt slip, and belt-drive efficiency. The belt stresses include: belt rubber shear, normal, axial and lateral stresses; reinforcements tension force; and tangential and normal belt-pulley contact stresses. Belt slip is measured using the driven over driver pulleys’ angular velocity ratio. Each parameter was varied over a range to understand its impact on the steady-state belt-drive response. The material parameters studied are belt axial stiffness and damping, belt bending stiffness and damping, and belt-pulley friction coefficient. The geometric parameters studied are pulley center distance, pulleys diameter ratio, and belt thickness. The operational parameters studied are the driver pulley angular velocity and the driven pulley opposing torque (load). A high-fidelity flexible multibody dynamics parametric model of a two-pulley belt-drive system was created using a commercial multibody dynamics code. In the model the belt’s rubber matrix is represented using three-dimensional brick elements and the belt’s reinforcements are represented using one dimensional beam elements at the top surface of the belt. An asperity-based Coulomb friction model is used for the friction forces between the pulley and belt. The pulleys are modeled as rigid bodies with a cylindrical contact surface. The equations of motion are integrated using an explicit solution procedure. Unlike prior models which use one-dimensional truss or beam elements for the belt, the present model uses a three-dimensional belt model which introduces the effect of the thickness of the belt rubber matrix (modeled using brick elements). This enables a more accurate prediction of the belt stresses and slip than prior models. This thesis resolves in more details the complex stick-slip friction behavior of an axially flexible belt coupled with the shear effects of a flexible rubber cushion and at the same time shows the effect of the main system parameters on this stick-slip behavior. Some of the important conclusions of the thesis include: (1) the driver pulley has two distinct contact zones - a negative traction zone and a positive traction zone - while only one traction zone is present over the driven pulley; (2) the width of the negative traction zone on the driver pulley increases with the belt-pulley coefficient of friction and decreases with the belt axial stiffness; (3) the maximum belt tension and normal contact stress occur on the driver pulley and increase with the belt thickness, belt axial stiffness, and coefficient of friction; (4) belt-drive energy efficiency increases with the belt axial stiffness, and decreases with belt thickness, belt bending damping, belt operating speed, and operating torque load. The belt-drive modeling methodology presented in this thesis which enables accurate prediction of the belt stresses and slip can in turn be used to more accurately predict the fatigue life, wear life, and energy efficiency of belt-drives.

Forced response analysis of bladed disk assemblies plays a vital role in rotor blade design and has been drawing a great deal of attention both from research community and engine industry for more than half a century. However because of the phenomenon called &lsquo / mistuning&rsquo / , which destroys the cyclic symmetry of a rotor, there have been several difficulties related to forced response analysis ever since, two of which are addressed in this thesis: efficient non-linear forced response analysis of mistuned bladed disks and mistuning identification. On the nonlinear analysis side, a new solution approach is proposed studying the combined effect of non-linearity and mistuning, which is relatively recent in this research area and generally conducted with methods whose convergence and accuracy depend highly on the number of degrees of freedom where non-linear elements are attached. The proposed approach predicts nonlinear forced response of mistuned bladed disk assemblies considering any type of nonlinearity. In this thesis, special attention is given to the friction contact modeling of bladed disks which is the most common type of nonlinearity found in bladed disk assemblies. In the modeling of frictional contact a friction element which enables normal load variation and separation of the contact interface in three-dimensional space is utilized. Moreover, the analysis is carried out in modal domain where the differential equations of motions are converted to a set of non-linear algebraic equations using harmonic balance method and modal superposition technique. Thus, the number of non-linear equations to be solved is independent of the number of non-linear elements used. On the mistuning identification side, a new method is enclosed herein which makes use of neural networks to assess unknown mistuning parameters of a given bladed disk assembly from its assembly modes, thus being suitable for integrally bladed disks. The method assumes that a tuned mathematical model of the rotor under consideration is readily available, which is always the case for today&rsquo / s realistic bladed disk assemblies. A data set of selected mode shapes and natural frequencies is created by a number of simulations performed by mistuning the tuned mathematical model randomly. A neural network created by considering the number of modes, is then trained with this data set for being used to identify mistuning of the rotor from measured data. On top of these, a new adaptive algorithm is developed for harmonic balance method, several intentional mistuning patterns are investigated via excessive Monte-Carlo simulations and a new approach to locate, classify and parametrically identify structural non-linearities is introduced.

Indiana University-Purdue University Indianapolis (IUPUI) / We numerically investigate the underlying physics of two peculiar phenomena, which are axis-switching and saddle-back velocity profile, in both laminar and turbulent rectangular jets using lattice Boltzmann method (LBM). Previously developed computation protocols based on single-relaxation-time (SRT) and multiple-relaxation-time (MRT) lattice Boltzmann equations are utilized to perform direct numerical simulation (DNS) and large eddy simulation (LES) respectively. In the first study, we systematically study the axis-switching behavior in low aspect-ratio (AR), defined as the ratio of width over height, laminar rectangular jets with <italic>AR=1</italic> (square jet), 1.5, 2, 2.5, and 3. Focuses are on various flow properties on transverse planes downstream to investigate the correlation between the streamwise velocity and secondary flow. Three distinct regions of jet development are identified in all the five jets. The <italic>45&deg</italic> and <italic>90&deg</italic> axis-switching occur in characteristic decay (CD) region consecutively at the early and late stage. The half-width contour (HWC) reveals that <italic>45&deg</italic> axis-switching is mainly contributed by the corner effect, whereas the aspect-ratio (elliptic) feature affects the shape of the jet when <italic>45&deg</italic> axis-switching occurs. The close examinations of flow pattern and vorticity contour, as well as the correlation between streamwise velocity and vorticity, indicate that <italic>90&deg</italic> axis-switching results from boundary effect. Specific flow patterns for <italic>45&deg</italic> and <italic>90&deg</italic> axis-switching reveal the mechanism of the two types of axis-switching respectively. In the second study we develop an algorithm to generate a turbulent velocity field for the boundary condition at jet inlet. The turbulent velocity field satisfies incompressible continuity equation with prescribed energy spectrum in wave space. Application study of the turbulent velocity profile is on two turbulent jets with <italic>Re=25900</italic>. In the jets with <italic>AR=1.5</italic>, axis-switching phenomenon driven by the turbulent inlet velocity is more profound and in better agreement with experimental examination over the laminar counterpart. Characteristic jet development driven by both laminar and turbulent inlet velocity profile in square jet (<italic>AR=1</italic>) is also examined. Overall agreement of selected jet features is good, while quantitative match for the turbulence intensity profiles is yet to be obtained in future study. In the third study, we analyze the saddle-back velocity profile phenomenon in turbulent rectangular jets with AR ranging from 2 to 6 driven by the developed turbulent inlet velocity profiles with different turbulence intensity (<italic>I</italic>). Saddle-back velocity profile is observed in all jets. It has been noted that the saddle-back's peak velocities are resulted from the local minimum mixing intensity. Peak-center difference <italic>&Delta_pc</italic> and profound saddle-back (PSB) range are defined to quantify the saddle-back level and the effects of AR and <italic>I</italic> on saddle-back profile. It is found that saddle-back is more profound with larger AR or slimmer rectangular jets, while its relation with <italic>I</italic> is to be further determined.