Higher-Order Plate Elements for Large Deformation Analysis in Multibody Applications

This study introduces higher-order three-dimensional plate elements based on the absolute nodal coordinate formulation (ANCF) for large deformation multibody applications. The introduced elements employ four to eight nodes and the St. Venant-Kirchhoff material law. A newly proposed eight-node element is carefully verified using various numerical experiments intended to discover possible locking phenomena. In the introduced plate elements, the usage of polynomial approximations of second order in all three directions is found to be advantageous in terms of numerical performance. A comparison of the proposed eight-node element to the introduced four-node higher-order plate elements reveals that the usage of in-plane slopes as nodal degrees of freedom has a negative effect on numerical convergence properties in thin-plate use-cases.

Characterizing the Effective Bandwidth of Tri-Stable Energy Harvesters

This paper aims to investigate the response and characterize the effective frequency bandwidth of tri-stable vibratory energy harvesters. To achieve this goal, the method of multiple scales is utilized to construct analytical solutions describing the amplitude and stability of the intra- and inter-well dynamics of the harvester. Using these solutions, critical bifurcations in the parameter’s space are identified and used to define an effective frequency bandwidth of the harvester. A piezoelectric tri-stable energy harvester consisting of a uni-morph cantilever beam is considered. Stiffness nonlinearities are introduced into the harvesters design by applying a static magnetic field near the tip of the beam. Experimental studies performed on the harvester are presented to validate some of the theoretical findings.

Tracking and Disturbance Rejection for Uncertain Periodic Load Disturbed Power System by Adaptive Output Feedback Control

This paper studies energy storage based output tracking and disturbance rejection problems for a simple interconnected power system suffered from a periodic load disturbance with unknown amplitude and frequency. By constructing a new exosystem, the problem is converted into output regulation problem of a composite system. Internal model theorem is introduced for the composite system, and output regulation problem is changed into stabilization problem of a new augmented system by imposing an appropriate transformation. An adaptive dynamical energy storage based controller can solve stabilization problem of the augmented system as well as output tracking and disturbance rejection problem for the original system. Finally, simulation results show the effectiveness of the proposed controller.

Bifurcation Tree of Period-1 Motion to Chaos in a Pendulum With Periodic Excitation

In this paper, the bifurcation trees of period-1 motions to chaos are presented in a periodically driven pendulum. Discrete implicit maps are obtained through a mid-time scheme. Using these discrete maps, mapping structures are developed to describe different types of motions. Analytical bifurcation trees of periodic motions to chaos are obtained through the nonlinear algebraic equations of such implicit maps. Eigenvalue analysis is carried out for stability and bifurcation analysis of the periodic motions. Finally, numerical simulation results of various periodic motions are illustrated in verification to the analytical prediction. Harmonic amplitude characteristics are also be presented.

Improvement of a Forward Dynamic MPC Based Human Gait Model

This paper develops an improvement to an existing forward dynamic human gait model. A human gait model was developed previously to assist virtual testing prostheses and orthoses. The model consists of a plant model and a controller model. The central tenet to the model is the model predictive control (MPC) algorithm, which is a highly robust controller. In the previous model, however, there are several drawbacks. First, the anthropometric and mechanical parameters in the parts of the model are specific to one person. Second, the simulation result of ground reaction force (GRF) is not realistic. In this paper, the anthropometric parameters are calculated based on commonly used models that approximate an average person’s size. As for the mechanical parameters, the spring and damper coefficients in the human joints and ground reaction force (GRF) system are estimated by using the parameter estimation module in MATLAB based on the experimental subject data. The paper concludes with a simulation results between the new improved model and the previous developed model.

Dynamics Study and Sensitivity Analysis of Flexible Multibody Systems With Interval Parameters

The dynamics of flexible multibody systems with interval parameters is studied based on a non-intrusive computation methodology. The Absolute Nodal Coordinate Formulation (ANCF) is used to model the rigid-flexible multibody system, including the finite elements of the ANCF and the ANCF Reference Nodes (ANCF-RNs). The Chebyshev sampling methods including Chebyshev tensor product (CTP) sampling method and Chebyshev collocation method (CCM), are utilized to generate the Chebyshev surrogate model for Interval Differential Algebraic Equations (IDAEs). For purpose of preventing the interval explosion problem and maintaining computation efficiency, the interval bounds of the IDAEs are determined by scanning the deduced Chebyshev surrogate model. To further improve the computation efficiency, OpenMP directives are also used to parallelize the solving process of the Differential Algebraic Equations (DAEs) by fixing the uncertain interval parameter at the given sampling points. The sensitivity analysis of flexible multibody systems with interval parameters is initially performed by using the direct differentiation method. The direct differentiation method differentiates the dynamic equations with respect to the design variable, which yields the system sensitivity equations governed by DAEs. The generalized alpha method is introduced to integrate the sensitivity DAEs. The sensitivity equations of flexible multibody systems with interval parameters are also described by the IDAEs. Based on the continuum mechanics, the computational efficient analytical formulations for the derivative items of the system sensitivity equations are deduced. Three examples are studied to validate the proposed methodology, including the complicated spatial rigid-flexible multibody systems with a large number of uncertain interval parameters, the flexible system with uncertain interval clearance size joint, and the first order sensitivity analysis of flexible multibody systems with interval parameters. Firstly, the dynamics analysis of a six-arm space robot with six interval parameters is performed. For this case study, the interval dynamics cannot be obtained by directly scanning the IDAEs because extremely huge sets of DAEs with deterministic samples have to be solved. The estimated total computational time for solving the scanned IDAEs will be 1850 days! However, the computational time for solving the scanned Chebyshev surrogate model is 9796.97 seconds. It shows the effectiveness of the proposed computation methodology. Then, the nonlinear dynamics of a planar slider-crank mechanism with uncertain interval clearance size joint is studied in this work. The kinetics model of the revolute clearance joints is formulated under the ANCF-RN framework. Moreover, the influence of the LuGre and the modified Coulomb’s friction force models on the system’s dynamic response is investigated. By analyzing the bounds of dynamic response, the bifurcation diagrams are observed. It must be highlighted that with increasing the size of clearance, it does not automatically lead to unstable behaviors. Finally, the first order sensitivity analysis of flexible multibody systems with interval parameters is also studied in this work. The third one of a flexible mechanism with interval parameters is used to perform the sensitivity analysis.

Dynamics of Upright Posture on an Active Balance Board With Tunable Time-Delay and Stiffness

Neurological disorders, a concussion, or aging can extend the time-delay in the human neuromuscular balance system; this time-delay increase has been shown [5] to be an important factor contributing to the loss of balance. However, commercial balance boards used to help improve individual’s balance deficiencies do not utilize time-delay as a tunable parameter. In order to systematically study stiffness and time-delay induced instabilities in standing posture, we developed an active balance board system with controllable torsional board stiffness, as well as an added controllable feedback time-delay of the torsional board. Using this dynamical system we confirmed the presence of two distinct mechanisms of instability: insufficient stiffness leading to tipping posture and excessive time-delays leading to limit cycle oscillations. We expect that this active balance board will allow for the early identification of an increased fall-risk, especially for subjects with extended time-delays and could help provide insights into how the human postural system adapts to various environments.

Highly Tunable Electrothermally Actuated Arch Resonator

This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of electrothermally actuated MEMS arch beams. The beams are made of silicon and are intentionally fabricated with some curvature as in-plane shallow arches. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared to the experimental data and results of a multi-physics finite-element model. A good agreement is found among all the results. The electrothermal voltage is applied between the anchors of the clamped-clamped MEMS arch beam, generating a current that passes through the MEMS arch beam and controls its axial stress caused by thermal expansion. When the electrothermal voltage increases, the compressive stress increases inside the arch beam. This leads to increase in its curvature, thereby increases the resonance frequencies of the structure. We show here that the first resonance frequency can increase up to twice its initial value. We show also that after some electro-thermal voltage load, the third resonance frequency starts to become more sensitive to the axial thermal stress, while the first resonance frequency becomes less sensitive. These results can be used as guidelines to utilize arches as wide-range tunable resonators.

Modeling and Simulation of a Wind Turbine Gear Set With Hydrodynamic Bearings Attached to an Induction Generator

This work presents the numerical modeling and simulation of a wind turbine gearset with hydrodynamic bearings and an induction generator. Transmissions based on epicyclic gear trains applied to wind turbines have some advantages, i.e., compactness, robustness and low maintenance requirement. The early stages of the development of such mechanism need numerical results in order to design it properly. The complexity of this machine requires a multidisciplinary approach to model and simulate a system comprising of mechanical, fluid and electrical components. The bearing model is integrated to the kinetics of the gearbox, allowing a precise evaluation of the journal bearing’s movements. Through a multidisciplinary multibody dynamics software, the gearbox dynamics, the bearing behavior and the induction generator are calculated in a single system. The numerical solution of the hydrodynamic lubrication problem of a finite bearing is achieved using the finite element method. The hydrodynamic bearing and the induction generator are implemented as a user module in MBDyn software, which makes them available to model and simulate other types of rotating machinery. Simulations of two different conditions showed a better damping property when compared to rolling bearings, in this gearset.

A Regularized Contact Model for Multibody System Simulation

Simulation of large-scale multibody systems with unilateral contacts requires formulations with which good computational performance can be achieved. The availability of many solver algorithms for Linear Complementarity Problems (LCP) makes the LCP-based formulations a good candidate for this. However, considering friction in contacts asks for new friction models compatible with this kind of formulations. Here, a new, regularized friction model is presented to approximate the Coulomb model, which allows to formulate the multibody system dynamics as a LCP with bounds. Moreover, a bristle approach is used to approximate the stiction force, so that it improves the numerical behaviour of the system and makes it able to handle redundancy coming from the friction interfaces. Several examples using a 3D wheel model has been carried out, and the proposed friction model shows a better approximation of the Coulomb model compared to other LCP-based formulations.