Dynamics Of Mechanical Systems Research Articles

CREEP AND ELECTRICAL PROPERTIES OF CARBON NANOTUBE YARNS FOR LONG-TERM APPLICATIONS

One of the primary challenges to turning CNTs into commercial applications is the feasibility to manufacture macroscopic structures that mirror the extraordinary properties of individual CNTs. CNT yarns (CNTY) are an alternative to overcome this challenge. However, most yarn-like structures are exposed to dynamic systems, like creep and/or fatigue, and limited studies are published predicting their behavior. Therefore, the current study aimed to assess the behavior of CNTYs under creep situations and establish a relationship with their electrical properties. Five layers of CNTs were drawn from the MWCNT forest, placed one on top of the other, and scrolled into a 250 mm yarn, that was later twisted to 2000 twists m−1. Afterward, these CNTYs were densified with acetone. Creep experiments were performed with a sustained load of 50, 70, and 80 % of the YBL. The yarn behavior seen during creep experiments was unexpected, which, although partial breakage of the yarn was seen, it sustained the creep load much for longer periods. The mechanism proposed for the phenomenon includes CNT alignment and void elimination at first, followed by partial CNT sliding, with breakage of van der Waals forces. As the creep load continues, CNTs are able to rebind to their neighbors and recover their strength before total failure. Mechanical gripping due to friction is also occurring between nanotubes which favors a strength increase. This behavior indicates that there is a regeneration of van der Waals forces occurring among the CNTs, which recovers the strength of the yarn under constant load, increasing creep lifespan. The time to failure obtained under creep load is about 9, 10, and 11 days to failure for CNTYs at 50, 70, and 80 % of YBL, respectively. Raman results showed that ID/IG ratio remained the same after mechanical loads, which indicates that no structural modification is seen in the CNTs when static and/or dynamic mechanical systems are imposed on the yarn. The electrical conductivity of a CNTY is improved after the mechanical tests, increasing by 5.9 and 6.7% after static tensile and creep, respectively. The improvement of electrical conductivity is attributed to densification, which leads to an enhancement of the intertubes contact area among the nanotubes within the yarn.

Measurements-based constrained control optimization in presence of uncertainties with application to the driver commands for high-speed trains

The railway world is undergoing major changes. The advent of new technologies allows us to rethink the train system and face new challenges, but one must not forget all the ecological constraints that are now accentuated by the increase in energy costs. This paper focuses on the optimization of the driver commands to limit the energy consumption of the trains under punctuality and security constraints. This problem falls within the framework of control optimization problems for nonlinear dynamic mechanical systems in the presence of constraints and uncertainties. A four-step approach is then proposed in this paper to solve this problem: (1) the introduction of simplified and fast-to-evaluate models to model the nonlinear dynamic behavior of the train and its energy consumption; (2) the identification in a Bayesian formalism of the parameters on which these models depend from on-track measurements on commercial trains; (3) the reformulation of the optimization problem so that it integrates the uncertainties related to an imperfect knowledge of these estimated parameters; (4) the resolution of the optimization problem using evolutionary algorithms. The main specificity of this work lies in the fact that not only the objective function to be minimized, here the energy consumed by the train, is impacted by the uncertainties, but also the admissibility constraints of the solution, here punctuality and operating safety. The integration of the uncertainties in the search for the control function is thus not trivial and requires several original adaptations in order to make the final optimization problem well posed.

Numerical accuracy of principal geodesic analysis on the sphere in director‐based dynamics of hybrid mechanical systems

AbstractWe aim at nonlinear model order reduction (MOR) in hybrid mechanical systems by means of Principal Geodesic Analysis (PGA) on the Riemannian manifolds S2 (the sphere) and SO(3) (the rotation group). MOR requires highly accurate and efficient implementations of the logarithm maps and the resulting lifts across multiple branches. However, in our cases these maps have singularities due to periodicity. In this work we focus on the logarithm and lift maps for the sphere S2. We conduct detailed numerical experiments on mechanical systems to achieve maximal accuracy in spite of the singularities.

A study on the energy dissipation mechanism of dynamic mechanical systems with particle dampers by using the novel energy method

A study on the energy dissipation mechanism of dynamic mechanical systems with particle dampers by using the novel energy method

Fractional-order model and experimental verification of granules-beam coupled vibration

Granular media generally exhibit fluid phase, solid phase, or two coexisting phases, and the mechanism of the phase transition is not clear enough. Therefore, unlike the airflow-structure or fluid–structure coupled vibrations, the granules-structure coupled vibrations have not yet been theoretically modeled, and the interest in such coupled vibrations, which has just started in recent years, is mainly focused on experiments and simulations. In order to develop a theoretical model of the coupled vibrations of granular media and beam structures, in this paper, a novel concept called the inertia-viscous effect is introduced in terms of terminology and mathematical expression, and surprisingly, its constitutive relation can be summarized in a unified framework based on fractional calculus, together with Hooke spring, Newtonian dashpot, and Abel sticky pot. Furthermore, the existence of this effect in the granules-beam coupled vibrations is experimentally confirmed, and more importantly, the effect is more suitable for modeling by fractional-order derivatives rather than the conventional integer-order ones due to the frequency-dependent characteristics of the effect. Based on this, the theoretical model of the granules-beam coupled vibrations and the associated parameters identification procedure are successfully developed, in which a fractional-order model is proposed to describe the additional dynamic load (ADL) of the granular media on the beam. The numerical and experimental results suggest that the system response can be accurately predicted by the developed theoretical model without the computational cost as in the discrete element methods, which is the main contribution of this work. Finally, the effectiveness and robustness of the developed theoretical model are further verified by the results of numerous parametric experiments, and importantly, by combining these results with the analytical results, the mechanism of ADL is revealed, thus providing insights for modeling coupled vibrations between other engineering structures and granular media. From another perspective, this work can also be seen as a novel application of fractional calculus in the dynamics of mechanical systems.

Dynamic Ramsey Theory of Mechanical Systems Forming a Complete Graph and Vibrations of Cyclic Compounds

Ramsey theory constitutes the dynamics of mechanical systems, which may be described as abstract complete graphs. We address a mechanical system which is completely interconnected by two kinds of ideal Hookean springs. The suggested system mechanically corresponds to cyclic molecules, in which functional groups are interconnected by two kinds of chemical bonds, represented mechanically with two springs k1 and k2. In this paper, we consider a cyclic system (molecule) built of six equal masses m and two kinds of springs. We pose the following question: what is the minimal number of masses in such a system in which three masses are constrained to be connected cyclically with spring k1 or three masses are constrained to be connected cyclically with spring k2? The answer to this question is supplied by the Ramsey theory, formally stated as follows: what is the minimal number R(3,3)? The result emerging from the Ramsey theory is R(3,3)=6. Thus, in the aforementioned interconnected mechanical system at least one triangle, built of masses and springs, must be present. This prediction constitutes the vibrational spectrum of the system. Thus, the Ramsey theory and symmetry considerations supply the selection rules for the vibrational spectra of the cyclic molecules. A symmetrical system built of six vibrating entities is addressed. The Ramsey approach works for 2D and 3D molecules, which may be described as abstract complete graphs. The extension of the proposed Ramsey approach to the systems, partially connected by ideal springs, viscoelastic systems and systems in which elasticity is of an entropic nature is discussed. “Multi-color systems” built of three kinds of ideal springs are addressed. The notion of the inverse Ramsey network is introduced and analyzed.

Drivetrain Response Prediction Using AI-Based Surrogate and Multibody Dynamics Model

Numerical models, such as multibody dynamics ones, are broadly used in various engineering applications, either as an integral part of the preliminary design of a product or simply to analyze its behavior. Aiming to increase the accuracy and potential of these models, complex mechanisms are constantly being added to existing methods of simulation, leading to powerful modelling frameworks that are able to simulate most mechanical systems. This increase in accuracy and flexibility, however, comes at a great computational cost. To mitigate the issue of high computation times, surrogates, such as reduced order models, have traditionally been used as cheaper alternatives, allowing for much faster simulations at the cost of introducing some error to the overall process. More recently, advancements in Artificial Intelligence have also allowed for the introduction of Artificial Intelligence-based models in the field of surrogates. While still undergoing development, these Artificial Intelligence based methodologies seem to be a potentially good alternative to the high-fidelity/burden models. To this end, an Artificial Intelligence-based surrogate comprised of Artificial Neural Networks as a means of predicting the response of dynamic mechanical systems is presented in this work, with application to a non-linear experimental gear drivetrain. The model utilizes Recurrent Neural Networks to accurately capture the system’s response and is shown to yield accurate results, especially in the feature space. This methodology can provide an alternative to the traditional model surrogates and find application in multiple fields such as system optimization or data mining.

A novel dynamic dry friction model for applications in mechanical dynamical systems

This work presents a novel continuously differentiable, dynamic dry friction model, with dependence on normal contact force, slip velocity, and static and dynamic coefficients of friction. The state-of-the-art, Brown and McPhee friction model depends on transitional velocity, which is an empirical parameter. A limitation with this model is that there is no generic approach to select the optimal value for the transitional velocity for a certain application. The simulation results presented in this work highlight the sensitivity of friction force with transitional velocity in Brown and McPhee’s model to obtain smooth solutions, which are supportive in control system applications. It is because control systems require jitter-free signals in order to save costs on low-pass filters. The proposed model overcomes such empirical dependence on transition velocity through a combination of an iterative methodology and an empirical parameterization. In this article, a comprehensive analysis of the proposed friction model and the contributing parameters is carried out. The algorithm to implement the proposed friction model is elaborated. The proposed friction model is then simulated and compared against Brown and McPhee’s model. using a stick-slip benchmark problem. Furthermore, the proposed force model is applied to two spatial multibody systems formulated using index 0 tangent space differential-algebraic equations. The results demonstrate how the proposed friction model can be employed in dynamical mechanical systems. The independence on transitional velocity in the proposed friction model is observed to be effective for obtaining smooth solutions that make it suitable for control system applications.

The discretization method and multi-contact force model on 3D cylindrical clearance joint for multibody dynamics of spatial mechanical system

The discretization method and multi-contact force model on 3D cylindrical clearance joint for multibody dynamics of spatial mechanical system

IMPROVING EFFICIENCY OF SSCA KIDYM DYNAMICS PROGRAM MODULE BY USING AUTOMATICALLY GENERATED DLL-PROCEDURE AND BY OTHER MEANS

The paper presents the results of research on the significant increase in the speed of solving the problems of the dynamics of discrete mechanical systems of an arbitrary form with arbitrary links by a special system of computer algebra (SSCA) KiDyM. In particular, an algorithm for determining the parameters of the additional rotation of the central coordinate systems (CS) of solid bodies in the presence of a non-diagonal inertia tensor to transform them into the main central SCs, in which Euler's equations have the simplest form, is implemented. The main central moments of inertia of the body are determined. A simpler description of SC transformations of robot links with open kinematic chains is proposed. It consists in a separate description of the positions of the SC of the links and the positions of the center of mass and the central SC in relation to the SC of the link. This approach leads to localized description of the kinematics of the mechanism and complete information about the inertial parameters of the link, such as mass, inertia tensor, position of the central SC. The possibility of errors in model descriptions is thereby reduced. On the example of the model of the lower limbs of an human like robot, the gain in the number of machine operations of this description is shown. The use of the software-generated DLL procedure for saving the mathematical model of the system is analyzed in detail. If necessary, it is loaded from an external medium (disk) into the computer's memory during numerical integration. For this purpose, a special procedure has been created in SSCA KiDyM, which transforms the internal representation of analytical expressions of the computer algebra system into program code in C++, calls the appropriate compiler, which creates and saves the DLL-procedure on the disk. In the numerical integration block, the system can load it and calculate the right-hand sides of the Cauchy form of the dynamic equations by the Runge-Kutta procedure. The time gain of this integration method compared to direct calculations of formula trees in PC memory for various tasks is shown. The time gain increases with the increase in the complexity of the mechanical system. A criterion for automatically switching such an algorithm depending on the amount of C++ code in the DLL procedure is proposed.

A damage assessment methodology for structural systems using transfer learning from the audio domain

Neural network-based strategies require balanced training datasets to avoid creating unreliable classification and prediction models. While these strategies are commonly used to model the dynamics of structural and mechanical systems, the imbalanced composition of monitoring data is a fundamental challenge for damage assessment in structural systems. The monitoring data often contain abundant observations from structures in their normal operating conditions (undamaged state) and small and partial information from systems in the damaged state. Therefore, the model, trained by adopting deep learning approaches, tends to show an ill-conditioned nature, limited to specific structures in a narrow range of damage conditions.The current study presents a damage assessment strategy that overcomes the limitations of unbalanced datasets. To improve the model’s ability to distinguish between different health conditions, informative features are utilized to facilitate the differentiation of multiple classes according to the frequency content of vibration signals. The model acquires this ability by learning from a rich dataset of human voices (source domain), where low-level features that denote the vibration traits of human waveforms are extracted. Subsequently, this knowledge is transferred to the features of a target domain that has limited data for damage detection.The proposed methodology relies on creating an informative feature extractor training a Time-Delay Neural Network (TDNN) using a collection of human voice recordings. Cepstral and pitch features derived from the speech data are used as input features for the TDNN. This network is used to derive low-level features at intermediate layers of the network, called “x-vectors”. These features store non-case-dependent information about the frequency content of the signals and depict the ability to distinguish between different classes according to a change in the frequency content of the investigated system. This is not a unique attribute of the original audio source domain, and it can be employed to help differentiate categories for any vibrating system where a modification in the frequency content is representative of a transition between classes, including the structural and mechanical systems. Because of the generalization trait of the x-vector, they can be employed to construct a Probabilistic Linear Discriminant Analysis model able to classify various damage classes considering vibration measurements obtained from a different system, i.e., a structural system (target domain).Initially, the simulated acceleration response from the 12-degree of freedom structure are analyzed to affirm the effectiveness of the framework. Then, the method is further validated by using the field data of the Z24 bridge, to evaluate its reliability in real-world applications.

Long-time principal geodesic analysis in director-based dynamics of hybrid mechanical systems

In this article, we investigate an extended version of principal geodesic analysis for the unit sphere S2 and the special orthogonal group SO(3). In contrast to prior work, we address the construction of long-time smooth lifts of possibly non-localized data across branches of the respective logarithm maps. To this end, we pay special attention to certain critical numerical aspects such as singularities and their consequences on the numerical accuracy. Moreover, we apply principal geodesic analysis to investigate the behavior of several mechanical systems that are very rich in dynamics. The examples chosen are computationally modeled by employing a director-based formulation for rigid and flexible mechanical systems. Such a formulation allows to investigate our algorithms in a direct manner while avoiding the introduction of additional sources of error that are unrelated to principal geodesic analysis. Finally, we test our numerical machinery with the examples and, at the same time, we gain deeper insight into their dynamical behavior.

Closed Form Constraint Equations Used to Express Frictionless Slip of Multibody Systems Attached to Finite Elements—Application to a Contact between a Double Pendulum and a Beam

This paper focuses on the numerical modeling of the dynamics of mechanical systems. Robots that can inspect high-voltage lines inspired this research. Their control systems must anticipate potential grab positions appropriately. We intend to formulate equations dedicated to the numerical description of the robot/cable contact. The investigated problem is not straightforward, since parts of the modeled systems are numerically inhomogeneous. They consist of multibody and finite element components. These components interact with each other only through frictionless point contact. We limit the present investigation to the mathematical modeling of these frictionless point connections. According to the model-adopted assumption, the location of the contact point is invariant in the multibody structure, but it is variable in the finite elements part. Unlike the classically used models (i.e., spring/damper models of elastic contacts), we focus on constraint equations. We present and discuss their details in this paper. Following the presence of the constraint equations, their associated Lagrange multipliers appear in the dynamics equations of the two sub-models. The main feature/result of the presently proposed method is the closed form of the coordinate-portioning formulae, proposed in this paper, employed to eliminate the dependent coordinates and the constraint-associated Lagrange multipliers. To verify the applicability of the proposed elimination methodology, we test its use in a dedicated numerical example. During the test, we limit the investigation to a frictionless connection between a double pendulum and a beam. The results confirm that the proposed methodology allows us to model the investigated frictionless contact. We shall underline a vital property, that the proposed elimination method is universal, and thus one can easily extend/modify the above methodology to operate with other multibody/finite element contacts.

Обобщенная задача динамического уравновешивания и перспективные направления ее применения

The paper considers the generalized problem of the machines and mechanisms dynamic balance in terms of ensuring the given laws of altering reactions in the selected links. Representation of equations of the mechanical systems dynamics in the form of differential algebraic equations was used making it possible to obtain mathematical models of the nonlinear mechanical systems dynamics with the arbitrary structure of kinematic and force connections. With this approach, the constraint reactions are determined by algebraic equations from the system coordinates. The problem solution is based on changing the bonds selected reactions due to the impact on reactions in the other selected bonds by adding non-stationary terms to the selected bonds equation. Conditions for rigorous solution of the optimal control problem for a mechanical system are shown for the integral quality criterion not explicitly containing the control functions. The method is aimed at numerical models of the mechanical systems widely used in the programs for dynamic analysis of the coupled systems of bodies. Test examples are provided for manipulator, anthropomorphic robot and controlled suspension of a transport vehicle. The method was realized in the software package for simulating the controlled motion dynamics of the coupled systems of bodies.

Correspondence between Dicke-model semiclasscial dynamics in the superradiant dipolar phase and the Euler heavy top

Analytic expression is found for the frequency dependence of the transmission coefficient of a transmission line inductively coupled to the microwave cavity with the superradiant condensate. Sharp transmission drops reflect the condensate's frequencies spectrum. These results pave the way to direct detection of emergence of the superradiant condensates in quantum metamaterials. Results are based on the analytic solutions of the nonlinear semiclassical dynamics of the superradiant photonic condensate in the Dicke model of an ensemble of two-level atoms dipolar coupled to the electromagnetic field in the microwave cavity. In the adiabatic limit with respect to the photon degree of freedom, the system is approximately integrable with evolution being expressed via Jacobi elliptic functions of real time. Depending on the coupling strength, the semiclassical coordinate of the superradiant condensate in the ground state either oscillates in one of the two degenerate minima of the condensate's potential energy or traverses between them over the saddle point. An experimental setup for measuring of the breakdown of the normal phase of the Dicke model via coupling to the transmission line is proposed. A one-to-one mapping of the semiclassical motion of the superradiant condensate on the nodding of unstable Lagrange ``sleeping top'' also turns the Dicke model into an analog device for modeling the dynamics of mechanical systems.

Study on Characteristics of Acoustic Emission b Value of Coal Rock with Outburst-Proneness under Coupled Static and Dynamic Loads

In this paper, a rock dynamic and static triaxial mechanical test system is adopted to conduct triaxial compression failure acoustic emission test on coal rock with outburst-proneness. The purpose is to study the evolution law of the acoustic emission (AE) b value of coal rock under static and dynamic load of varying frequencies. The test results show that the dynamic load disturbance will accelerate the instability failure process of coal rock, that the average stress level/ultimate strain of coal rock decline/rises correspondingly with the increasing dynamic load frequency. Moreover, the overall AE b value after dynamic load disturbance is relatively low, and the higher the dynamic load frequency, the larger the decrease in the b value. In addition, as the dynamic load frequency increases, the AE ringing count and AE energy show a trend of first increasing and then decreasing, and they are negatively correlated with the evolution characteristics of the acoustic emission b value. Furthermore, the change rule of AE b value is closely related to the instability and failure process of coal rock. A second-stage of the overall b value of acoustic emission shows a “cliff jumping type” decrease dip angle or “fault cliff type” decrease dip angle indicates the imminent failure of coal rock, which can be used as an evaluation index for real-time monitoring of dynamic disasters of coal rock with outburst-proneness.

A Dynamic Response Analysis of Vehicle Suspension System

Automotive engineering is a very important branch of design and development in mechanical engineering devoted to vehicle manufacturing. It demands solid knowledge focusing on the kinematics and dynamics of mechanical systems, either using structural analysis or modelling techniques. In this manuscript, a model based on the application of the fundamentals of the static and dynamic behaviour of the suspension system of a bus vehicle is developed. Therefore, a set of mathematical equations is expanded following the structural dynamic formulations to obtain an analytical solution on natural frequencies and the displacement under an external load. The problem is also solved using the Finite Element Method (FEM) to confirm the analytical results. Equivalent material parameters and boundary conditions were used for the FEM simulation. This work aims to propose a methodology based on modal analysis with a simplified model to predict the dynamic response of an automotive structure.

Dysregulation of intracellular pH in the failing heart.

Despite significant advances in the therapeutic armamentarium, heart failure (HF) remains a deadly disease. Metabolic derangement occurs in HF, with a decrease in the overall ATP synthesis and alterations in substrate utilization. Our recent studies demonstrate beat-to-beat intracellular acidification, namely “intracellular pH (pHi) transient”, in cardiomyocytes, which is coupled to the contraction, myofilament ATP hydrolysis, and mitochondrial electron transport chain function, essential for ATP synthesis. However, the regulation of pHi in HF cardiomyocytes remains less understood. We hypothesize that pHi and pHi transients in HF cardiomyocytes may be subjected to dysregulation as a response to metabolic changes in HF.A HF mouse model was generated using transverse aortic constriction for eight weeks. We quantified pHi and sarcomere lengths simultaneously in single ventricular myocyte. We demonstrate that the baseline pHi and pHi transients are significantly reduced in HF cardiomyocytes compared to sham. Moreover, there are significant cell-to-cell variabilities in pHi and pHi transients in the HF mouse model. Similar alterations were observed in a rabbit model with pressure- and volume-overload induced HF. The phasic pHi during cardiac contraction dovetails with the prevailing dynamic electrical, Ca2+ and mechanical systems defining the heart as an efficient pump. Indeed, the dynamic acidification of pHi may serve as negative feedback to provide the needed relaxation during cardiac contraction. Therefore, the reduced amplitude in pHi transients may significantly contribute to the decrease in lusitropy in HF, well documented in HF. Our study demonstrates dysregulated cardiac pHi and pHi transients in HF ventricular myocytes with significantly increased variabilities. The abnormal pHi and pHi transients suggest significant dysregulation of acid-base balance in HF, which may contribute to cardiac dysfunction. Our study may help to unravel new therapeutic strategies targeting pHi and pHi transients to ameliorate cardiac dysfunction in the failing heart.

Approximate Symmetries and Conservation Laws for Mechanical Systems Described by Mixed Derivative Perturbed PDEs

This article focuses on developing and applying approximation techniques to derive conservation laws for the Timoshenko–Prescott mixed derivatives perturbed partial differential equations (PDEs). Central to our approach is employing approximate Noether-type symmetry operators linked to a conventional Lagrangian one. Within this framework, this paper highlights the creation of approximately conserved vectors for PDEs with mixed derivatives. A crucial observation is that the integration of these vectors resulted in the emergence of additional terms. These terms hinder the establishment of the conservation law, indicating a potential flaw in the initial approach. In response to this challenge, we embarked on the rectification process. By integrating these additional terms into our model, we could modify the conserved vectors, deriving new modified conserved vectors. Remarkably, these modified vectors successfully satisfy the conservation law. Our findings not only shed light on the intricate dynamics of fourth-order mechanical systems but also pave the way for refined analytical approaches to address similar challenges in PDE-driven systems.

O Stohastičkim procesima u dinamici planetarnih prenosnika

In addition to the theoretical analysis of the nonlinear dynamics of dissipative mechanical systems with the possibility of stochastic and chaotic processes, the paper also includes a numerical experimental example of a planetary transmission. The most common non-linear effects of operation and their influence on the behavior of the planetary gear as a system were analyzed. A simplified model of planetary gears as dissipative dynamic systems whose operation is a complex dynamic process with different effects was considered. These operating effects can appear in many different ways and can be the cause of stochasticity in the operation of the planetary gear. A numerical analysis of planetary gear lubrication was made, as one of the effects of stochasticity, where turbulent damping occurs. The turbulent damping force, due to oil splashing, is taken to be proportional to the second power of the angular velocity of the sun gear. Based on the experiment, it is concluded that the phase space in this system is not preserved and the system is dissipative because the trajectories spiral down into a certain singularity.