Mechanical Engineering Publications

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Generalized Damped Outrigger Systems for Suppressing Multimode Vibrations of Tall Buildings
(World Scientific, 2024) Wen, Yongkui; Chen, Lin; Nagarajaiah, Satish
Damped outrigger is a viable means for reducing dynamic responses of tall buildings. This study focuses on generalized damped outrigger (GDO) systems. A GDO is composed of a damper for energy dissipation, a negative stiffness device and an inerter for damping enhancement. The GDO system incorporates GDOs at different floors of the tall building optimized to varied structural modes. Frequency equation of a tall building simplified as a cantilever beam with multiple GDOs is first derived by complex modal analysis. A finite different model of such a system is used for verification. Parametric analyses are then performed to compare damping effects of different GDO systems. It is found that a negative stiffness damped outrigger (NSDO) or inerter damped outrigger (IDO) needs to be optimized for maximizing damping of a specific mode. GDOs, respectively, tuned to different modes can largely improve the multimode damping effects. The optimal parameters of the GDOs are slightly different from those in the case when they are installed separately. With both negative stiffness and nonzero inertance, a GDO still needs to be tuned to a specific mode because multimode damping is sensitive to the damper coefficient. The combination of an NSDO optimized to the first mode and an IDO tuned to a higher mode seems the best solution. The IDO additionally improves the first mode damping provided by the NSDO and the two-mode damping is not sensitive to the damper coefficient of the NSDO. The findings are confirmed through seismic response analyses of a tall building with different GDO systems.
Tribological Properties of h-BN, Ag and MgO Nanostructures as Lubricant Additives in Vegetable Oils
(MDPI, 2024) Granja, Victoria; Jogesh, Kollol; Taha-Tijerina, Jaime; Higgs, C. Fred; Particle Flow and Tribology Laboratory
There exists an ever-growing need for sustainable engineering solutions to improve emission control and the energy efficiency of tribosystems. This study examines the tribological properties of two environmentally friendly vegetable fluids, soybean and sunflower oil, with the addition of three non-toxic nanostructures (h-BN, silver and MgO) at different concentrations. It was found that nanostructures added to vegetable oils at specific concentrations can exhibit good friction reduction and wear preventive properties. The addition of h-BN nanosheets in sunflower oil decreased the coefficient of friction and the wear damage, as measured by the wear scar diameter. Silver and magnesium oxide nanoparticles further reduced the friction and wear, respectively. In addition to the tribological testing of the samples, investigations were performed using an optical microscope, SEM and EDX to elucidate the mechanisms that may have led to the observed friction reduction and wear-preventive properties of different nanostructure additives. The thermophysical properties of the samples were also measured. It was found that the thermal conductivity of both base oils could be enhanced by 24% when using h-BN at 0.25 wt% concentration.
Space–time flow computation with boundary layer and contact representation: a 10-year history
(Springer Nature, 2024) Takizawa, Kenji; Tezduyar, Tayfun E.
In computation of flow problems with moving solid surfaces, moving-mesh methods such as the space–time (ST) variational multiscale method enable mesh-resolution control near the solid surfaces and thus high-resolution boundary-layer representation. There was, however, a perception that in computations where the solid surfaces come into contact, high-resolution boundary-layer representation and actual-contact representation without leaving a mesh protection opening between the solid surfaces were mutually exclusive objectives in a practical sense. The introduction of the ST topology change (ST-TC) method in 2013 changed the perception. The two objectives were no longer mutually exclusive. The ST-TC makes moving-mesh computation possible even without leaving a mesh protection opening. The contact is represented as an actual contact and the boundary layer is represented with high resolution. Elements collapse or are reborn as needed, and that is attainable in the ST framework while retaining the computational efficiency at a practical level. The ST-TC now has a 10-year history of achieving the two objectives that were long seen as mutually exclusive. With the ST-TC and other ST computational methods introduced before and after, it has been possible to address many of the challenges encountered in conducting flow analysis with boundary layer and contact representation, in the presence of additional intricacies such as geometric complexity, isogeometric discretization, and rotation or deformation of the solid surfaces. The flow analyses conducted with these ST methods include car and tire aerodynamics with road contact and tire deformation and ventricle-valve-aorta flow. To help widen awareness of these methods and what they can do, we provide an overview of the methods, including those formulated in the context of isogeometric analysis, and the computations performed over the 10-year history of the ST-TC.
A thermal regulator using passive all-magnetic actuation
(Elsevier, 2023) Castelli, Lorenzo; Garg, Ajay; Zhu, Qing; Sashital, Pooja; Shimokusu, Trevor J.; Wehmeyer, Geoff
Thermal regulators are two-terminal devices used for passive temperature control of electronics, batteries, or buildings. Existing thermal expansion regulators suffer from large thicknesses and substantial hysteresis. Here we report an all-magnetic thermal regulator in which the temperature of the control terminal (Tcontrol) leads to passive steady-state surface mating/demating that enables/blocks heat conduction. The mechanism relies on Tcontrol-dependent magnetic forces between gadolinium and neodymium iron boron magnets when Tcontrol is near gadolinium’s Curie temperature of 21oC. Our centimeter-scale prototype has a thermal switch ratio of 34−13+30 in vacuum and 2.1−0.2+0.2 in air, a vacuum OFF state thermal conductance of 3.5 mW/K, an average switching temperature of 20oC, a small thermal deadband of 5oC, and a relatively compact thickness <2 cm. We quantify the regulator performance over >2,000 cycles and construct the regulator using commercially available materials, showing that this thermomagnetic device can be used for effective thermal regulation near room temperature.
Hybrid method for full-field response estimation using sparse measurement data based on inverse analysis and static condensation
(Elsevier, 2022) Pal, Ashish; Meng, Wei; Nagarajaiah, Satish; Smalley-Curly Institute
In structural health monitoring, measuring the accurate and spatially dense response near critical locations of the structure can be advantageous to estimate damage to the structure. Due to several physical restrictions or limitations of the sensing method, it may not always be possible to generate reliable data at critical locations. In this study, a hybrid method is presented that makes use of the measured displacement data and finite element (FE) model of the structure to predict dense full-field response. The presented method can incorporate unknown boundary conditions and unknown body forces by applying correction/fictitious forces to match predicted and measured responses. Using static condensation followed by inverse analysis, these additional forces are found by setting up a least square problem. Due to the problem being ill-posed, L2-penalty is used to control the prediction error. Numerical simulation of a plate subjected to body force showed an accurate prediction of full-field response except for a few boundary locations. To handle this, the proposed method is used in conjunction with linear interpolation near boundary locations. The method is validated in a laboratory experiment for a plate with a notch having displacement measured using Digital Image Correlation (DIC). On comparing strains calculated using predicted displacements, FEM, and DIC, the predicted strains show better agreement with the FEM than DIC. This affirms that the proposed hybrid technique can be used at critical locations where DIC fails to provide reliable strain data.
Hybrid FES-exoskeleton control: Using MPC to distribute actuation for elbow and wrist movements
(Frontiers Media S.A., 2023) Dunkelberger, Nathan; Berning, Jeffrey; Schearer, Eric M.; O'Malley, Marcia K.; Mechatronics and Haptics Interfaces Laboratory
IntroductionIndividuals who have suffered a cervical spinal cord injury prioritize the recovery of upper limb function for completing activities of daily living. Hybrid FES-exoskeleton systems have the potential to assist this population by providing a portable, powered, and wearable device; however, realization of this combination of technologies has been challenging. In particular, it has been difficult to show generalizability across motions, and to define optimal distribution of actuation, given the complex nature of the combined dynamic system.MethodsIn this paper, we present a hybrid controller using a model predictive control (MPC) formulation that combines the actuation of both an exoskeleton and an FES system. The MPC cost function is designed to distribute actuation on a single degree of freedom to favor FES control effort, reducing exoskeleton power consumption, while ensuring smooth movements along different trajectories. Our controller was tested with nine able-bodied participants using FES surface stimulation paired with an upper limb powered exoskeleton. The hybrid controller was compared to an exoskeleton alone controller, and we measured trajectory error and torque while moving the participant through two elbow flexion/extension trajectories, and separately through two wrist flexion/extension trajectories.ResultsThe MPC-based hybrid controller showed a reduction in sum of squared torques by an average of 48.7 and 57.9% on the elbow flexion/extension and wrist flexion/extension joints respectively, with only small differences in tracking accuracy compared to the exoskeleton alone.DiscussionTo realize practical implementation of hybrid FES-exoskeleton systems, the control strategy requires translation to multi-DOF movements, achieving more consistent improvement across participants, and balancing control to more fully leverage the muscles' capabilities.
Frequency independent damped outrigger systems for multi-mode seismic control of super tall buildings with frequency independent negative stiffness enhancement
(Wiley, 2023) Wang, Meng; Sun, Fei-Fei; Koetaka, Yuji; Chen, Lin; Nagarajaiah, Satish; Du, Xiu-Li
Damped outrigger system is effective for improving energy dissipation for tall buildings. However, conventional damped outrigger (CDO) system with viscous damping has two limitations: (i) its maximum damping ratio cannot be improved when outrigger/column stiffness is inadequate; (ii) different modes achieve their maximum damping ratios at different outrigger damping values, and thus the dampers cannot be optimized to simultaneously reduce vibrations of multiple modes of concern to their minimum. In this paper, a purely frequency-independent negative stiffness damped outrigger (FI-NSDO) system is proposed by combining frequency-independent damper (FID) and negative stiffness device (NSD). The damped outrigger with FID can achieve the maximum damping ratio for all modes as compared to frequency-dependent damper like viscous damper. As the NSD has the features of assisting and enhancing motion and frequency-independence, the utilization of NSD will considerably improve the maximum damping ratios when outrigger/column stiffness is inadequate and maintain the frequency-independent feature of the whole system. Therefore, the FI-NSDO has the capability of simultaneously increasing the damping ratios of all target modes to their maximum values. Analysis in frequency domain and time domain, demonstrate that the proposed FI-NSDO performs better in controlling the multi-mode vibration of seismic responses.
Practical negative stiffness device with viscoelastic damper in parallel or series configuration for cable damping improvement
(Elsevier, 2023) Chen, Lin; Liu, Zhanhang; Zou, Yiqing; Wang, Meng; Nagarajaiah, Satish; Sun, Feifei; Sun, Limin
Negative stiffness mechanism has been found able to improve damping performance of dampers on a stay cable which otherwise is limited by the damper installation distance from a cable end. This study provides a practical negative stiffness device (NSD) with adjustable negative stiffness and experiments are performed to validate the negative stiffness effect. The NSD is then combined with a viscoelastic damper in parallel or series for cable damping improvement. Explicit design formulas are derived for optimal design with a target enhancement effect in damping considering the damper described respectively using the Kelvin model and the linear hysteretic damping model. The formulas are verified by analytical and numerical solutions. Parametric analyses show damping enhancement effects of the NSD and it is found more efficient when combined with a damper in series because both deformation amplitudes of the damper and the NSD are further increased in this configuration. Subsequently, case studies are carried out based on two cables of the Sutong Bridge respectively with a shear-type viscous damper and a high damping rubber damper. The results show that the designed NSD can fulfill practical requirements. Particularly, a 100% increase in damping can be achieved by the presented NSD when combined with the damper installed on a cable of 546.9 m long.
Towards a predictive, physics-based friction model for the dynamics of jointed structures
(Elsevier, 2023) Porter, Justin H.; Brake, Matthew R.W.
Bolted connections are ubiquitous in mechanical designs and pose a significant challenge to understanding and predicting the vibration response of assembled structures. The present paper develops a physics-based rough contact model of the frictional interactions within a joint. This model sums over the probable interactions of asperities – defined as locally maximum surface features – to determine the contact forces. Here, the tangential contact forces vary smoothly between sticking and slipping and allow the model to better capture the qualitative trends of experimental amplitude dependent frequency and damping than previous studies. Furthermore, the novel model is generalized to allow for arbitrarily varying normal pressure including potential separation to better represent the interfacial dynamics. This includes developing a new, computationally tractable approximation to the analytical Mindlin partial slip solution for tangential loading of contacting spheres. The results highlight the importance of accurately characterizing the as-built topology of the interface, the plastic behavior of the contacting asperities, the relevant length scale of asperities, and the eccentricity of asperities. A predictive friction coefficient based on plasticity provides a poor match to experiments, so fitting the friction coefficient is also considered. Numerical results are compared to experiments on the Brake-Reuß Beam to assess the predictive potential of the models. While blind predictions over-predict the slip limit, the current model presents a significant improvement in physics-based modeling and highlights areas for ongoing research.
T-splines computational membrane–cable structural mechanics with continuity and smoothness: II. Spacecraft parachutes
(Springer Nature, 2023) Terahara, Takuya; Takizawa, Kenji; Avsar, Reha; Tezduyar, Tayfun E.
In this second part of a two-part article, we present spacecraft parachute structural mechanics computations with the T-splines computational method introduced in the first part. The method and its implementation, which was also given in the first part, are for computations where structures with different parametric dimensions are connected with continuity and smoothness. The basis functions of the method were derived in the context of connecting structures with 2D and 1D parametric dimensions. In the first part, the 2D structure was referred to as “membrane” and the 1D structure as “cable.” The method and its implementation, however, are certainly applicable also to other 2D–1D cases, and the test computations presented in the first part included shell–cable structures. Similarly, the spacecraft parachute computations presented here are with both the membrane and shell models of the parachute canopy fabric. The computer model used in the computations is for a subscale, wind-tunnel version of the Disk–Gap–Band parachute. The computations demonstrate the effectiveness of the method in 2D–1D structural mechanics computation of spacecraft parachutes.
T-splines computational membrane–cable structural mechanics with continuity and smoothness: I. Method and implementation
(Springer Nature, 2023) Terahara, Takuya; Takizawa, Kenji; Tezduyar, Tayfun E.
We present a T-splines computational method and its implementation where structures with different parametric dimensions are connected with continuity and smoothness. We derive the basis functions in the context of connecting structures with 2D and 1D parametric dimensions. Derivation of the basis functions with a desired smoothness involves proper selection of a scale factor for the knot vector of the 1D structure and results in new control-point locations. While the method description focuses on $$C^0$$and $$C^1$$continuity, paths to higher-order continuity are marked where needed. In presenting the method and its implementation, we refer to the 2D structure as “membrane” and the 1D structure as “cable.” It goes without saying that the method and its implementation are applicable also to other 2D–1D cases, such as shell–cable and shell–beam structures. We present test computations not only for membrane–cable structures but also for shell–cable structures. The computations demonstrate how the method performs.
A three-terminal magnetic thermal transistor
(Springer Nature, 2023) Castelli, Lorenzo; Zhu, Qing; Shimokusu, Trevor J.; Wehmeyer, Geoff
Three-terminal thermal analogies to electrical transistors have been proposed for use in thermal amplification, thermal switching, or thermal logic, but have not yet been demonstrated experimentally. Here, we design and fabricate a three-terminal magnetic thermal transistor in which the gate temperature controls the source-drain heat flow by toggling the source-drain thermal conductance from ON to OFF. The centimeter-scale thermal transistor uses gate-temperature dependent magnetic forces to actuate motion of a thermally conducting shuttle, providing thermal contact between source and drain in the ON state while breaking contact in the OFF state. We measure source-drain thermal switch ratios of 109 ± 44 in high vacuum with gate switching temperatures near 25 °C. Thermal measurements show that small heat flows into the gate can be used to drive larger heat flows from source to drain, and that the switching is reversible over >150 cycles. Proof-of-concept thermal circuit demonstrations show that magnetic thermal transistors can enable passive or active heat flow routing or can be combined to create Boolean thermal logic gates. This work will allow thermal researchers to explore the behavior of nonlinear thermal circuits using three-terminal transistors and will motivate further research developing thermal transistors for advanced thermal control.
Physics-Guided Real-Time Full-Field Vibration Response Estimation from Sparse Measurements Using Compressive Sensing
(MDPI, 2023) Jana, Debasish; Nagarajaiah, Satish
In civil, mechanical, and aerospace structures, full-field measurement has become necessary to estimate the precise location of precise damage and controlling purposes. Conventional full-field sensing requires dense installation of contact-based sensors, which is uneconomical and mostly impractical in a real-life scenario. Recent developments in computer vision-based measurement instruments have the ability to measure full-field responses, but implementation for long-term sensing could be impractical and sometimes uneconomical. To circumvent this issue, in this paper, we propose a technique to accurately estimate the full-field responses of the structural system from a few contact/non-contact sensors randomly placed on the system. We adopt the Compressive Sensing technique in the spatial domain to estimate the full-field spatial vibration profile from the few actual sensors placed on the structure for a particular time instant, and executing this procedure repeatedly for all the temporal instances will result in real-time estimation of full-field response. The basis function in the Compressive Sensing framework is obtained from the closed-form solution of the generalized partial differential equation of the system; hence, partial knowledge of the system/model dynamics is needed, which makes this framework physics-guided. The accuracy of reconstruction in the proposed full-field sensing method demonstrates significant potential in the domain of health monitoring and control of civil, mechanical, and aerospace engineering systems.
Carrier-Domain Method for high-resolution computation of time-periodic long-wake flows
(Springer Nature, 2023) Liu, Yang; Takizawa, Kenji; Tezduyar, Tayfun E.; Kuraishi, Takashi; Zhang, Yufei
We are introducing the Carrier-Domain Method (CDM) for high-resolution computation of time-periodic long-wake flows, with cost-effectives that makes the computations practical. The CDM is closely related to the Multidomain Method, which was introduced 24 years ago, originally intended also for cost-effective computation of long-wake flows and later extended in scope to cover additional classes of flow problems. In the CDM, the computational domain moves in the free-stream direction, with a velocity that preserves the outflow nature of the downstream computational boundary. As the computational domain is moving, the velocity at the inflow plane is extracted from the velocity computed earlier when the plane’s current position was covered by the moving domain. The inflow data needed at an instant is extracted from one or more instants going back in time as many periods. Computing the long-wake flow with a high-resolution moving mesh that has a reasonable length would certainly be far more cost-effective than computing it with a fixed mesh that covers the entire length of the wake. We are also introducing a CDM version where the computational domain moves in a discrete fashion rather than a continuous fashion. To demonstrate how the CDM works, we compute, with the version where the computational domain moves in a continuous fashion, the 2D flow past a circular cylinder at Reynolds number 100. At this Reynolds number, the flow has an easily discernible vortex shedding frequency and widely published lift and drag coefficients and Strouhal number. The wake flow is computed up to 350 diameters downstream of the cylinder, far enough to see the secondary vortex street. The computations are performed with the Space–Time Variational Multiscale method and isogeometric discretization; the basis functions are quadratic NURBS in space and linear in time. The results show the power of the CDM in high-resolution computation of time-periodic long-wake flows.
A computational method for estimating trunk muscle activations during gait using lower extremity muscle synergies
(Frontiers Media S.A., 2022) Li, Geng; Ao, Di; Vega, Marleny M.; Shourijeh, Mohammad S.; Zandiyeh, Payam; Chang, Shuo-Hsiu; Lewis, Valerae O.; Dunbar, Nicholas J.; Babazadeh-Naseri, Ata; Baines, Andrew J.; Fregly, Benjamin J.; Rice Computational Neuromechanics Laboratory
One of the surgical treatments for pelvic sarcoma is the restoration of hip function with a custom pelvic prosthesis after cancerous tumor removal. The orthopedic oncologist and orthopedic implant company must make numerous often subjective decisions regarding the design of the pelvic surgery and custom pelvic prosthesis. Using personalized musculoskeletal computer models to predict post-surgery walking function and custom pelvic prosthesis loading is an emerging method for making surgical and custom prosthesis design decisions in a more objective manner. Such predictions would necessitate the estimation of forces generated by muscles spanning the lower trunk and all joints of the lower extremities. However, estimating trunk and leg muscle forces simultaneously during walking based on electromyography (EMG) data remains challenging due to the limited number of EMG channels typically used for measurement of leg muscle activity. This study developed a computational method for estimating unmeasured trunk muscle activations during walking using lower extremity muscle synergies. To facilitate the calibration of an EMG-driven model and the estimation of leg muscle activations, EMG data were collected from each leg. Using non-negative matrix factorization, muscle synergies were extracted from activations of leg muscles. On the basis of previous studies, it was hypothesized that the time-varying synergy activations were shared between the trunk and leg muscles. The synergy weights required to reconstruct the trunk muscle activations were determined through optimization. The accuracy of the synergy-based method was dependent on the number of synergies and optimization formulation. With seven synergies and an increased level of activation minimization, the estimated activations of the erector spinae were strongly correlated with their measured activity. This study created a custom full-body model by combining two existing musculoskeletal models. The model was further modified and heavily personalized to represent various aspects of the pelvic sarcoma patient, all of which contributed to the estimation of trunk muscle activations. This proposed method can facilitate the prediction of post-surgery walking function and pelvic prosthesis loading, as well as provide objective evaluations for surgical and prosthesis design decisions.
Finite element analysis of screw fixation durability under multiple boundary and loading conditions for a custom pelvic implant
(Elsevier, 2023) Zhu, Yuhui; Babazadeh-Naseri, Ata; Dunbar, Nicholas J.; Brake, Matthew R.W.; Zandiyeh, Payam; Li, Geng; Leardini, Alberto; Spazzoli, Benedetta; Fregly, Benjamin J.
Despite showing promising functional outcomes for pelvic reconstruction after sarcoma resection, custom-made pelvic implants continue to exhibit high complication rates due to fixation failures. Patient-specific finite element models have been utilized by researchers to evaluate implant durability. However, the effect of assumed boundary and loading conditions on failure analysis results of fixation screws remains unknown. In this study, the postoperative stress distributions in the fixation screws of a state-of-the-art custom-made pelvic implant were simulated, and the risk of failure was estimated under various combinations of two bone-implant interaction models (tied vs. frictional contact) and four load cases from level-ground walking and stair activities. The study found that the average weighted peak von Mises stress could increase by 22-fold when the bone-implant interactions were modeled with a frictional contact model instead of a tied model, and the likelihood of fatigue and pullout failure for each screw could change dramatically when different combinations of boundary and loading conditions were used. The inclusion of additional boundary and loading conditions led to a more reliable analysis of fixation durability. These findings demonstrated the importance of simulating multiple boundary conditions and load cases for comprehensive implant design evaluation using finite element analysis.
Kolmogorov n–width and Lagrangian physics-informed neural networks: A causality-conforming manifold for convection-dominated PDEs
(Elsevier, 2023) Mojgani, Rambod; Balajewicz, Maciej; Hassanzadeh, Pedram
We make connections between complexity of training of physics-informed neural networks (PINNs) and Kolmogorov n-width of the solution. Leveraging this connection, we then propose Lagrangian PINNs (LPINNs) as a partial differential equation (PDE)-informed solution for convection-dominated problems. PINNs employ neural-networks to find the solutions of PDE-constrained optimization problems with initial conditions and boundary conditions as soft or hard constraints. These soft constraints are often blamed to be the sources of the complexity in the training phase of PINNs. Here, we demonstrate that the complexity of training (i) is closely related to the Kolmogorov n-width associated with problems demonstrating transport, convection, traveling waves, or moving fronts, and therefore becomes apparent in convection-dominated flows, and (ii) persists even when the boundary conditions are strictly enforced. Given this realization, we describe the mechanism underlying the training schemes such as those used in eXtended PINNs (XPINN), curriculum learning, and sequence-to-sequence learning. For an important category of PDEs, i.e., governed by non-linear convection–diffusion equation, we propose reformulating PINNs on a Lagrangian frame of reference, i.e., LPINNs, as a PDE-informed solution. A parallel architecture with two branches is proposed. One branch solves for the state variables on the characteristics, and the second branch solves for the low-dimensional characteristics curves. The proposed architecture conforms to the causality innate to the convection, and leverages the direction of travel of the information in the domain, i.e., on the characteristics. This approach is unique as it reduces the complexity of convection-dominated PINNs at the PDE level, instead of optimization strategies and/or schedulers. Finally, we demonstrate that the loss landscapes of LPINNs are less sensitive to the so-called “complexity” of the problems, i.e., convection, compared to those in the traditional PINNs in the Eulerian framework.
Wave-based analysis of jointed elastic bars: nonlinear periodic response
(Springer Nature, 2022) Balaji, Nidish Narayanaa; Brake, Matthew R.W.; Leamy, Michael J.
In this paper, we develop two wave-based approaches for predicting the nonlinear periodic response of jointed elastic bars. First, we present a nonlinear wave-based vibration approach (WBVA) for studying jointed systems informed by re-usable, perturbation-derived scattering functions. This analytical approach can be used to predict the steady-state, forced response of jointed elastic bar structures incorporating any number and variety of nonlinear joints. As a second method, we present a nonlinear Plane-Wave Expansion (PWE) approach for analyzing periodic response in the same jointed bar structures. Both wave-based approaches have advantages and disadvantages when compared side-by-side. The WBVA results in a minimal set of equations and is re-usable following determination of the reflection and transmission functions, while the PWE formulation can be easily applied to new joint models and maintains solution accuracy to higher levels of nonlinearity. For example cases of two and three bars connected by linearly damped joints with linear and cubic stiffness, the two wave-based approaches accurately predict the expected Duffing-like behavior in which multiple periodic responses occur in the near-resonant regime, in close agreement with reference finite element simulations. Lastly, we discuss extensions of the work to jointed structures composed of beam-like members, and propose follow-on studies addressing opportunities identified in the application of the methods presented.
Wave-based analysis of jointed elastic bars: stability of nonlinear solutions
(Springer Nature, 2022) Balaji, Nidish Narayanaa; Brake, Matthew R.W.; Leamy, Michael J.
In this paper we develop two new approaches for directly assessing stability of nonlinear wave-based solutions, with application to jointed elastic bars. In the first stability approach, we strain a stiffness parameter and construct analytical stability boundaries using a wave-based method. Not only does this accurately determine stability of the periodic solutions found in the example case of two bars connected by a nonlinear joint, but it directly governs the response and stability of parametrically forced continuous systems without resorting to discretization, a new development in of itself. In the second stability approach, we pose a perturbation eigenproblem residue (PER) and show that changes in the sign of the PER locate critical points where stability changes from stable to unstable, and vice-versa. Lastly, we discuss follow-on research using the developed stability approaches. In particular, we identify an opportunity to study stability around internal resonance, and then identify a need to further develop and interpret the PER approach to directly predict stability.
Computational modeling and simulation of closed chain arm-robot multibody dynamic systems in OpenSim
(Springer Nature, 2022) Green, Matthew; Hong, Yoon No Gregory; Roh, Jinsook; Fregly, Benjamin J.
Rehabilitation robot efficacy for restoring upper extremity function post-stroke could potentially be improved if robot control algorithms accounted for patient-specific neural control deficiencies. As a first step toward the development of such control algorithms using model-based methods, this study provides general guidelines for creating and simulating closed chain arm-robot models in the OpenSim environment, along with a specific example involving a three-dimensional arm moving within a two degree-of-freedom upper extremity rehabilitation robot. The closed chain arm-robot model developed in OpenSim was evaluated using experimental robot motion and torque data collected from a single healthy subject under four conditions: 1) active robot alone, 2) active robot with passive arm, 3) passive robot with active arm, and 4) active robot with active arm. Computational verification of the combined model was performed for all four conditions, whereas experimental validation was performed for only the first two conditions since torque measurements were not available for the arm. For the four verification problems, forward dynamic simulations reproduced experimentally measured robot joint angles with average root-mean-square (RMS) errors of less than 0.3 degrees and correlation coefficients of 1.00. For the two validation problems, inverse dynamic simulations reproduced experimentally measured robot motor torques with average RMS errors less than or equal to 0.5 Nm and correlation coefficients between 0.92 and 0.99. If patient-specific muscle–tendon and neural control models can be successfully added in the future, the coupled arm-robot OpenSim model may provide a useful testbed for designing patient-specific robot control algorithms that facilitate recovery of upper extremity function post-stroke.

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