ABSTRACT. This is a report about the simulation study of a lightweight rover being separated from a larger spacecraft in vicinity of a small Solar system body. Monte Carlo simulation and statistical analysis estimate the rate of requirement violation depending on uncertain rover and separation mechanism parameters. During the rover development phase, the full Monte Carlo analysis is only done with a simplified model. The first iterations show relatively high probability of non-compliance with requirements. Model refinement and more precise hardware values lead to the final assessment that separation meets the requirements within a ∼ 2 σ region. A more detailed model serves for analysis of selected samples during the development phase. For this model, a full Monte Carlo analysis is only done close to the end once the parameter ranges are fixed, mostly for time reasons. This more detailed analysis in general confirms the ∼ 2 σ requirement meeting. The main difference with the simplified model is the much larger number of outliers, a few of which also violate the allocated volume for the rover in proximity of the mothership.

ABSTRACT. EELS-DARTS is a simulator designed for autonomy development and analysis of large degree of freedom snake-like robots for space exploration. A detailed description of the EELS-DARTS simulator design is presented. This includes the versatile underlying multibody dynamics representation used to model a variety of distinct snake robot configurations as well as an anisotropic friction model for describing screw-ice interaction. Additional simulation components such as graphics, importable terrain, joint controllers, and perception are discussed. Methods for setting up and running simulations are discussed, including how the snake robot’s autonomy stack closes the commands and information loop with the simulation via ROS. Multiple use cases are described to illustrate how the simulation is used to aid and inform robot design, autonomy development and field test use throughout the project’s life cycle. A validation analysis of the screw-ice contact model is performed for the surface mobility case. Lastly, an overview of simulation use for planning operations during a recent field test to the Athabasca Glacier in Canada is discussed

ABSTRACT. Although many good luthiers exist and they build excellent instruments some instruments even stick out of these high quality instruments and some luthiers, like Antonio Torres or Antonio Stradivari for example, have received almost irrefutable iconic status. To many musicians their instruments are unrivaled and real myths have grown around them. Naturally many attempts were made to copy those instruments as closesly as possible just to find out that these copies hardly sound like the original. These audible differences can be attributed largely to the natural variability of the woods used in instruments of identical manufacture, and it is known that professional musicians can distinguish even seemingly identical instruments only by their sound.

We present a methodology that allows the replication of reference instruments based on their vibrational characteristics rather than solely on their geometry. It allows building instruments that sound alike rather than merely look the same as geometric copies do. This is achieved by compensating unavoidable differences in vibrational properties between reference and replica caused by the natural variability of the wood through specific geometric adaptions. The challenge of such an approach is to reliably and non-destructively identify material parameters of the reference in order to be able to predict the necessary geometry modifications before the replica is built. One novel contribution is that we experimentally validated computer models to quantitatively predict the effects of material and design variations. This is apowerful new tool to systematically improve instruments, or to minimize scattering in series production of instruments.

As summarized in this contribution we first focus on matching the vibrational response of individual elements of a guitar, namely the soundboard. Two soundboards made from spruce with initially equal geometry and Torres bracing were manufactured. One is defined as reference soundboard while the other represents the copy to which eventually geometric modifications are applied. The eigenfrequencies and eigenmodes, identified with experimental modal analysis, are used to compare the soundboards. Although the same tonewood from the same batch was used the relative difference of the first few eigenfrequencies is about 5% initially due to the natural variability of the tonewood. A detailed and experimentally validated numerical finite element model of the soundboards is developed to predict suitable geometry modifications that can reduce the difference of eigenfrequencies between the soundboards. The individual heights of the different braces are chosen as the geometric parameters to influence the modal behavior of the soundboards. This numerical model is used as a virtual prototype that allows to find suitable modifications to significantly reduce the differences between the two soundboards’ lowest eigenfrequencies. In order to efficiently solve the optimization problem, model order reduction is utilized. Finally, the mean difference in eigenfrequencies of the first couple of modes decreased to 2.5%, solely by changing the height of four braces by about 1mm.

The extension of this approach to full guitars requires adaptions in several areas. First, mode shapes need to be considered in the cost function of the shape optimization. In order to do so it is very advantageousto have finite element meshes whose nodes remain consistent across geometric variations of the domain, instead of re-meshed discretizations, because it allows to directly compare mode shapes. This is achieved by using mesh morphing approaches which will be presented. An advantageous feature of the presented morphing strategies is that they allow to increase the manifold of geometric variations, since high-level parameters like arcs, polynomials, etc. are used to define the geometry, i.e. the contour of the instrument. One problem arising from the increased possibilities to alter geometry is the increasing dimensionality of the optimization domain, making it increasingly difficult to extract a reasonably accurate and efficient parameterized reduced order numerical model by affine approaches. We will present an approach in which the dependency of the high-level parameters (which determine the overall geometic changes) are mapped to the element level, such that each finite element depends on all design parameters. The advantage of this approach is that all element-specific dependencies can be formulated symbolically and this symbolic relationship carries over to the assembled finite element matrices. This in turn allows a very efficient model order reduction, hence a very efficient and precise symbolically parameter-dependent model order reduced numerical model. The approach will be presented for hexahedral elements.

ABSTRACT. NASA is pursuing a sustainable human habitat on the Moon using In-Situ Resource Utilization (ISRU) to harness natural resources like minerals and ice water for oxygen, fuel, and construction materials. For efficient regolith extraction and transport, NASA is testing the Regolith Advanced Surface Systems Operations Robot (RASSOR) and similar designs. RASSOR uses two counter-rotating bucket drums on opposite arms to minimize reaction force, allowing a lightweight design. The rover raises its drums to travel and unloads by rotating the drums in opposite directions. The drums also aid in navigating steep terrain. Autonomous policies are being developed to reduce power consumption and improve traction. While Gazebo has been used for lunar environment simulations, it lacks support for deformable terrain modeling. Project Chrono, an open-source multi-physics simulation platform, addresses this by providing a framework for simulating the rover's interaction with lunar terrain at various fidelity levels and an interface to ROS2 autonomy stack. 

ABSTRACT. A tethered system represents a flexible multi-body system in which components and bodies such as a mothership, probes and equipment, are connected by flexible tether cable. When using such a system, it is assumed that the mothership moves harmonically while changing the tether length. This can cause the system resonance while being affected by ' the spaghetti problem', which is the problem involves the instability with oscillations of a flexible body. In this study, the effects of small vibrations of the mother ship on a tethered system during changing the tether length are studied and the indicators for these phenomena are proposed.

ABSTRACT. The wings of recent regional jet tend to have high aspect ratio to reduce induced drag. Because of the high aspect ratio configuration with lightweight, the wings undergo large deformations induced by aerodynamic forces. In addition, such high aspect ratio wings experience very high wing root bending moment when they encounter gust. To alleviate the gust response, a folding wing concept was proposed. When designing the high aspect ratio wings with the folding wing mechanism, a multibody simulation considering geometric nonlinearity is necessary. Owing to the slenderness of the high aspect ratio wing, geometrically nonlinear beam formulations are suitable for the simulation. In this study, two geometrically nonlinear beam formulations are compared in multibody simulations. One is absolute nodal coordinate formualtion (ANCF) and the other is strain-based beam formulation (SBBF). The major difference of them is that ANCF has a constant mass matrix, while SBBF has a constant stiffness matrix.

ABSTRACT. A new formulation for rigid bodies with unilateral interactions is presented. A rigid body is represented with an alternative formulation: an equimomental system of four point masses rigidly connected through constant distance constraints. In this work, the forward dynamics problem is addressed, in which the motion of the rigid body is determined by solving the dynamics formulation under given loads. The simulation problem involves two main parts. First, the dynamics problem involving momentum/velocity updates is solved using the point mass model. Once the velocities of the point masses are determined, the kinematics problem is solved using the rigid body representation, ensuring that the rigid body condition is met. The validity of this new formulation is proved in this work for unilateral contact and friction problems.

ABSTRACT. The contact-impact analysis focuses on the short period contact that results in a change in the direction of a body’s velocity. In the finite element method, an adequate expression of the contact stress for discretized spatial fields should be formulated to obtain accurate results. In general, the penalty method is a popular approach for fulfilling the impenetrability condition. It regularizes the impulsive response of the contact stress and generates the contact stress using nonphysical springs on the contact surfaces. Thus, an arbitrary stiffness parameter should be defined, and the simple representation of the contact stress can reduce the implementation difficulty and computational cost. The penalty method with a large stiffness penalty accurately constrains the contact conditions and reduces temporal potential energy loss by decreasing the penetration. However, in the explicit finite element method, the stability is pushed to its limit at the same time, and it requires a smaller time step to satisfy the stability condition. To alleviate this difficulty, the bi-penalty method was proposed and showed that the stability can be conserved by a mass penalty term in the one-dimensional contact case. This method is an extension of the penalty method, which utilizes the idea of the penalty method to the mass term. This study proposes a novel bi-penalty method for general contact-impact cases with conserved stability. The method is demonstrated to show and prove the effectiveness and stability in 1D, 2D, and 3D contact cases.

ABSTRACT. We exercise implicit formulations for the modeling and enforcing of mechanical contact constrains in a finite element setting. The mortar finite element method is used with weighted kinematic quantities to enforce non-penetration and frictional constraints. That method has been shown to yield favorable results, both in terms of finite element and algorithmic convergence. Those mortar methods may be enforced in a Lagrangian fashion, with explicit system Lagrange multipliers, or by regularizing methods such as the augmented Lagrange approach with Uzawa iterations. While these two methods can successfully enforce dual mortar contact equations, they exhibit different convergence behavior and amenity to iterative preconditioning techniques. These aspects are discussed and initially analyzed in this work.  

ABSTRACT. Robotic contact manipulations of objects are central elements in many applications. Insuch tasks, a robotic arm applies forces to an object at certain contact points to movethe object to a desired position or along a trajectory. The aim of this work is to deviseand implement an algorithm based on Reinforcement Learning (RL) to move a rectangular objectto a desired configuration along a designed trajectory by employing a three-link robotic arm. Traditional control methods arechallenging to implement due to the complex geometry of the object and the unknowncontact dynamics, particularly friction. Reinforcement Learning overcomes this by eliminating the need forsophisticated control gain tuning, allowing the robot to adapt to randomized scenarios. Residual policy learning \cite{silver2018residual} is utilized as a joint torque augmentation to ensure the end effector has the appropriate contact points and forces throughout the contact operation. The results indicate that residual policy learning significantly improves the accuracy of the object’s translation and rotation during the pushing process.

ABSTRACT. In this report, we investigate whether a recurrent neural network (RNN) can be used to act as a virtual sensor and thus provide additional information for the control strategy. Estimators are currently used in control engineering, but they require a very detailed understanding of the model and are therefore difficult to create. In order to realise the thrust model, training data is created using a well-validated simulation model. From the time series created, the thrust force currently acting on the rotor surface is to be recognised on the basis of the last 200 time steps. In our case, the RNN is made up of several LSTM memory cells. The advantage of simulation is that all the required data is available and can be utilised. So the first tests were carried out with ideal initialisation and the past time steps of the thrust force were used to estimate the current thrust force.  As a result, the estimated and original thrust correlated very strongly. Since in reality the thrust force is not measurable and therefore cannot be initialised ideally, the initialisation vector was filled with zeros and is updated with the last estimated thrust at each time step. The results of the models look very promising and show that it is possible to use them as estimators of the thrust force.

ABSTRACT. Bicycles as non-holonomic dynamic systems exhibit non-trivial behavior that is statically unstable but can achieve self-stabilization at moderate speeds. The classical Whipple model, which conceptualizes a bicycle as a multibody system of four rigid bodies enables in-depth research into bicycle dynamics, but poses significant computational challenges due to its complexity. This paper addresses these challenges by developing a surrogate model based on the reduced dynamics of a Whipple bicycle.

This paper addresses these challenges by developing a surrogate model for the reduced dynamics of a Whipple bicycle. Our work refines the bicycle dynamics model by integrating dynamics reduction with surrogate modeling. We design an optimization routine for the surrogate model using skew subspace projection, quasi Monte-Carlo integration, and structure learning, allowing for efficient and accurate approximation of dynamic coefficients. The surrogate model reduced computational operations from 65,000 Flops to 192 Flops on average, resulting in a 30x acceleration in dynamic computation, while maintaining close approximation to the original dynamic coefficients.

We evaluate the surrogate model's application in various scenarios. Our approach significantly enhances real-time dynamic computation and stability control, allowing improved control applications and trajectory planning.

ABSTRACT. This study focusses on using an AI-based, data-driven surrogate model to estimate unknown parameters in mechatronic systems, focusing on the payload estimation at the end of a hydraulically actuated flexible boom. A feedforward neural network (FFN) was developed and trained using data from a commercial multibody software to predict unknown masses with high accuracy (98.5%). The study achieved promising results, with the FFN effectively predicting payload not included in the training set with minimal error. The findings suggest future research directions, including the estimation of variable payload and the use of automated hyperparameter tuning and comparing with extended Kalman filters, to enhance the AI-based control and maintenance of complex systems. Further investigations are needed to compare these AI methods with traditional model-based controllers.

ABSTRACT. This study proposes an automated hyperparameter-tuned deep neural network (DNN) designed to predict uncertain oscillations in systems, which are typically challenging for mobile machines and heavy equipment like excavators and spacecraft. The DNN utilizes a regression model, enhanced through automated hyperparameter tuning, to predict the behavior of these oscillations effectively. The key innovation involves using a feedforward neural network (FFN) configured through a random optimization algorithm to optimize variables such as the learning rate, number of layers, dropout, and activation function. The proposed DNN model demonstrates precise prediction of uncertain mass oscillations with high accuracy, quantified by a relative mean absolute error of 0.010, using simulation data from the Exudyn software.This advancement holds significant potential for enhancing control and structural health monitoring of machines and equipment, suggesting that further research could extend these methods to broader applications in multibody systems, control algorithms, and structural health monitoring.

ABSTRACT. This paper addresses the enhancement of remote operation for underwater construction robots through the development and integration of a digital twin. The digital twin model, developed using the recursive subsystem synthesis method, accurately predicts the robot's behavior in real-time. To address the challenge of simulating high-frequency contact forces during tasks like grinding and drilling, a deep neural network (DNN)-based meta-model was created to estimate tool forces. Experimental tests were conducted to collect data, including tool penetration, position, orientation, hydraulic actuator pressure, pressure differences in hydraulic motors, and IMU information of the cabin. This data was used to integrate the virtual tool force estimation model with the virtual robot model. Basic hydraulic motor models for the manipulator arm were also developed. The combined model's real-time simulation performance was evaluated, demonstrating the feasibility of accurate and efficient remote control in harsh underwater environments.

ABSTRACT. The generalized-α method is a Newmark-type integrator that has become a standard approach for the time integration of the equations of motion of multibody systems. An extension of generalized-α for multibody systems with a configuration space with Lie group structure has been proposed, which we refer to as Lie group generalized-α in the following. A primary motivation for the present study arises from recent investigations, showing that the conventional generalized-α method often achieves higher accuracy than Lie group generalized-α when simulating rigid multibody systems. In this work, we present improvements for the time integration of constrained multibody systems, using Lie group methods applied to Newmark-based time integration methods.

ABSTRACT. HILS can be regarded as a kind of co-simulation technique that controls hardware components by real-time simulation based on measured data, and is widely used in automobile development. HILS needs to use the values from one step earlier when simulating with the data measured in the hardware section. In addition, delays occur during measurement due to communication between hardware and filtering of measurement signals. These factors reduce the accuracy and stability of HILS analysis. In this study, HILS based on time series forecasting using Long Short-Term Memory networks was investigated to reduce the effect of this delay. Experiments were conducted to evaluate the accuracy of the proposed method. In our conventional HILS, the analysis was performed using the measured value one step before. When the step time is extended up to 10 ms, the result differed from the result when the step size was set to 2 ms in conventional HILS. On the other hand, almost similar result was obtained by using of the time series forecasting even when the step time was set to 10 ms.

ABSTRACT. The paper investigates the real time computation of forward dynamics for planar serial chains on Graphic Processing Units (GPUs). Parallelizing dynamics on GPUs causes data bottlenecks due to sequential tasks, resulting in simulation latency. Using the Jacobian approach, the presented method shows a way to break recursiveness using previous time step calculations at cost of error. A comparison is made between speed-up obtainable for a fully parallel code and the amount of error generated during the simulation.

ABSTRACT. Powered robotic lower-limb exoskeletons have the potential to advance mobility and quality of life for individuals with physical impairments. In the current abstract, we discuss multibody dynamic modeling of a human wearing a lower-limb exoskeleton and interacting with their environment. Said models can then be adopted for design of model-based assistive control systems as well as performing “what-if” dynamic simulations, which can assess control safety and behaviour prior to human testing. The modeling approach emphasizes sagittal floating-base coordinates for both human and exoskeleton movements, integrating muscle torque generators (MTGs) for realistic human actuation without complex musculoskeletal geometry. Physical interactions among human, exoskeleton, and environment are captured through kinematic constraints and reset maps. Simulation studies on balance control featuring the model disseminated are consistent with the literature and suggest that model-derived feedback assistance improves the ability of users with reduced muscle strength to recover balance following a large perturbation.

ABSTRACT. This study explores the development of neural network-based control policies for autonomous robots, focusing on path following and obstacle avoidance. Utilizing the Autonomy Research Testbed (ART) and the Chrono simulation engine, we crafted two control strategies: an end-to-end imitation learning policy and a hybrid policy combining path following with a value function-based obstacle controller. Preliminary simulations validate both approaches, highlighting their respective efficiencies in managing complex navigation tasks. Future efforts will address transferring these policies to real vehicles, emphasizing the reduction of the sim-to-real performance gap.

ABSTRACT. We examine the applicability of Graph Neural Simulators (GNS), a data-driven model gaining traction for modeling terrain deformation. This report focuses on the training and inference aspects of GNS to assess its suitability for large-scale applications. Specifically, we train a GNS to replicate the dynamics of granular flow, as modeled by the Discrete Element Method (DEM). We document the data volume, computational resources, and time required for training. Additionally, we conduct a benchmark to evaluate the memory demands and computational speed of the GNS when applied to large domains. We suggest practical optimizations to enhance GNS usability and conclude with observations on its overall applicability.

ABSTRACT. Semi-analytical simulation methods have the potential to facilitate the integration of multibody simulationfor bicycle design and dimensioning. Operating loads measured at the system boundaries are applied as anexcitation to the bicycle within a multibody simulation to calculate accurate internal loads during complexdriving operations. However, a mandatory requirement for this method is the availability of measurementdata. To broaden the applicability of semi-analytical simulation methods, this paper investigates the transferabilityof measurement data sets to different bicycle structures. Given the impracticality of conductinga direct load comparison in the time domain due to time shifts, a comparison of total accumulated damageover a test track is conducted at validation points distributed along the structure.

ABSTRACT. Increased interest and development in unmanned aerial systems launched from various platforms and environments necessitates an accurate and efficient analysis of deployment capabilities and performance.  Traditional methods of modeling launch dynamics and fly out performance may be at a disadvantage when evaluating complex multi-body systems.  This work seeks to quantify the capabilities of two rigid body dynamic modeling methods, Newton-Euler and Kane's Method, when used to model multi-body launched unmanned aerial systems (UAS). In the first part of this work, both methods are used to develop a single rigid body, six degree of freedom model. This is used to verify the implementation and serves as a baseline case for comparison. In the second part of this work, rigid multi-body dynamic models using Newton-Euler and Kane's methods are developed.  These models evaluate the true multi-body, higher degree of freedom problem without the need to use prescribed motion, and use a simple aerodynamic model to capture the forces and moments with changing vehicle state.  Comparing the computational cost of each method shows that Kane's Method can be advantageous when evaluating complex multi-body systems.

ABSTRACT. The occurrence of vibrations during a roller coaster ride can significantly impact the overall experience and contribute to material fatigue. Despite its relevance, understanding the root causes or accurately predicting these vibrations remains an unresolved challenge, introducing an element of unpredictability into the design process. In spite of improvements in track quality, relevant vibration levels are still present in modern roller coasters. The elasticity of the train components leading to oscillations due to the changing spatial trajectory and the excitation through rail irregularities are commonly regarded to simulate vibrations in roller coaster systems. Here, the impact of contact nonlinearities on the vibration response of these systems, accounting for friction forces owing to wheel-rail creepage –leading to transient self-excited oscillations– and the frequency modulation of the rigid modes of vibration, is studied. The results indicate that these nonlinearities play a central role in predicting the vibration spectrum in roller coaster systems, not captured by prevailing simpler multi-degree-of-freedom linear oscillator models. These findings are corroborated against real measurements.

ABSTRACT. Optical motion capture is highly dependent on the geometry of the underlying rigid body model, so obtaining as accurate a model as possible is of great importance. This paper shows an optimization method that performs the scaling together with the identification of other model parameters, such as rotation axes, by recording a few motions and solving a single large-scale nonlinear optimization problem. The combination of analytical derivatives and a sparse solver leads to a very efficient implementation, which which allows for fitting the model to the measured markers in a matter of seconds.

ABSTRACT. Adipogenic differentiation is the process of the differentiation of a stem cell into an adipose, or fat-storing, cell. A novel, physics-based, three-dimensional multibody dynamic model of a stem cell is presented that includes the nucleus, the cytoskeleton, the lipid droplets, the cellular envelope, and focal adhesion points. The cellular model proposes the hydrostatic pressure difference between the inside and outside of the cell as the mechanism of maintaining its structural integrity. Obtaining long-term dynamic simulation of cellular processes has been infeasible even with the employment of supercomputers. The scaling approach presented herien, based on the method of multiple scales (MMS), effectively separates the computational time from size and distribution of the cellular models' elements. Employing the scaling approach enables the production of the 14-day time history of this process on a desktop computer in less than 1 hour and 9 minutes.

ABSTRACT. About 44.1% of the patients suffering from oral and maxillary tumors had trismus syndrome (restricted mouth opening) six months after mandibulectomy. Patients with restricted mouth opening can use mandibular movement function trainer (MMFT) for jaw-opening training. However, existing MMFT cannot consider individual mandibular movement characteristics. Mandibular musculoskeletal modeling can reveal the patient-specific muscle recruitment patterns and temporomandibular joint (TMJ) impedance during jaw opening. In this paper, a human-machine coupling model was established based on flexible multibody dynamics, and it was further utilized to design the MMFT auxiliary forces of each patient.

ABSTRACT. This study leverages 3D human modeling and gait analysis using multibody dynamics to enhance the understanding of human locomotion. By integrating detailed biomechanical models with computational methods, it provides a comprehensive analysis of gait patterns, overcoming traditional limitations. The model segments the body into various rigid parts, connected by spherical joints, to simulate realistic movements. Accurate foot-ground contact dynamics are modeled using a Hertzian-based normal contact force with dissipated damping and a modified Coulomb friction model, with a CT scan of a complete foot improving precision. This advanced approach significantly enhances the fidelity of human movement simulation and offers potential for clinical applications in diagnosing and treating gait disorders.

ABSTRACT. Hydraulic machinery such as cranes and excavators are multidisciplinary systems that combine mechanics, hydraulics, and electronics. Their computer simulation often includes data fusion from real sensors using various information fusing techniques such as state and parameter estimations. Out of various methods, the error-state extended Kalman filter, also known as the indirect Kalman filter, is often used in the literature because of their high computational efficiency for multibody systems. However, their application to hydraulically actuated multibody systems utilizes a numerical approach and consequently, it affects to the computational efficiency.

The objective of this study is to introduce an efficient indirect Kalman filter that utilizes a semi-analytical approach in computing the state-transition matrix in the framework of hydraulic machinery. The introduced methodology is compared with the numerical approach available in the literature. As a case example, a hydraulic crane is considered, where the mechanics is modeled using the index-3 augmented Lagrangian-based semi-recursive formulation and the hydraulics is modeled using the classical lumped fluid theory. The two filters are compared based on the accuracy of the state estimations and the associated computational efficiencies.

ABSTRACT. Monitoring and control of advanced mechatronic systems requires precise data on the current state of the system. This often involves equipping the systems with appropriate sensors. However, measuring all variables is not always economically or technically viable, and their values must be computationally determined. State estimation is a method that merges prior knowledge of system behavior (the model) with observed behavior (measurements) to infer deeper system insights (virtual measurements). Within multibody systems, this prior knowledge typically includes the equations of motion of the system. However, these equations can sometimes be significantly offset by factors like unknown contact forces or undetermined mass properties. In such scenarios, the kinematic Kalman filter emerges as a robust alternative. This technique disregards the equations of motion as prior knowledge and instead utilizes acceleration data to drive the estimation. This work presents the key findings of the recently published work by the authors, where the kinematic Kalman filter approach is extended by substituting acceleration data with hydraulic pressure measurements and leveraging the established relationship between kinematics and hydraulic pressures.

ABSTRACT. Constrained dynamics problems naturally result in systems of Differential-Algebraic Equations, which can be reduced to the underlying systems of Ordinary Differential Equations using projection algorithms. Their linearization about a steady reference solution can be formulated as a generalized eigenproblem whose eigensolution represents the spectrum of the problem. The sensitivity of the eigensolution to specific parameters of interest of the original problem may provide useful insight into the system’s dynamic characteristics. Building on an original continuation approach for the update of the coordinate projection matrix, the sensitivity of the eigensolution is formulated and analyzed in analytical form for simple, yet very illustrative problems. 

ABSTRACT. Optimization of the dynamics of multibody systems is an active area of research with many important applications in different fields. Among many available optimization techniques, gradient methods are very versatile and popular; and one of its main ingredients is the computation of sensitivities. The point of departure is an objetive functional. This problem is typically solved employing a gradient method, that requires the computation of the gradient of the funcional respect the parameters; aplying the chain rule.  Sensitivity analysis of mechanisms exclusively composed by rigid bodies has been studied in many works of the literature. However, analysis dealing with flexible mechanisms are rarer. In this work we show the results of a sensitivity analysis of special systems, where the flexible parts are slender beams, that could be represented either by a nonlinear beam model or with solid elements.  The specific nonlinear beam model considered in this work is defined as a collection of n identical deformable 1D segments (only withstand tensile or compressive forces) with regular section moving in a three-dimensional Euclidean space. Each segment is defined by two nodes, and two consecutive segments share one node. The axial response of the beam is represented by the deformation of the segments and is governed by an hyperelastic potential. The bending response is represented by the misalignment of consecutive trusses and is governed by another potential. The sum of both potentials is an approximation of the strain energy of the beam.The approach with solid elements will explore the possibilities of performing the analytical derivatives in the isoparametric formulation of linear tetrahedra and/or bilinear hexahedra defining a beam. In both cases (beam or solid elements), the relevant proposal of this work is the analytical deduction of the sen- sitivities associated with the deformable parts, that are expected to improve the efficiency and accuracy of the computations.   A simple and physically intuitive approach based on a finite-difference method is used for validating the preliminary sensitivity results Some simple numerical examples are presented showing the performance of the proposed formulation.