Dynamics Of Mechanical Systems Research Articles

Stochastic dynamics of mechanical systems with impacts via the Step Matrix multiplication based Path Integration method

AbstractIn this work we propose the Step Matrix Multiplication based Path Integration method (SMM-PI) for nonlinear vibro-impact oscillator systems. This method allows the efficient and accurate deterministic computation of the time-dependent response probability density function by transforming the corresponding Chapman–Kolmogorov equation to a matrix–vector multiplication using high-order numerical time-stepping and interpolation methods. Additionally, the SMM-PI approach yields the computation of the joint probability distribution for response and impact velocity, as well as the time between impacts and other important characteristics. The method is applied to a nonlinear oscillator with a pair of impact barriers, and to a linear oscillator with a single barrier, providing relevant densities and analysing energy accumulation and absorption properties. We validate the results with the help of stochastic Monte-Carlo simulations and show the superior ability of the introduced formulation to compute accurate response statistics.

Frequency-response curves for rate-independent hysteretic mechanical responses of complex shape

We illustrate the performances of a brand new hysteretic model, recently proposed and denominated VRM+D, to characterize the nonlinear response of mechanical systems endowed with quite complex hysteretic behaviors. To this end, we combine the VRM+D with a continuation procedure based on Poincaré maps developed by Lacarbonara et al. in 1999. In this way, the steady-state response, as well as stability and bifurcation, of a large class of mechanical systems can be analyzed. In particular, we show the effectiveness of the VRM+D, in conjunction with the Poincaré map-based continuation procedure, in accurately predicting periodic solutions of the above-mentioned systems independently of the form of the hysteresis loop shapes. Furthermore, we draw some general considerations on the potential applications of the proposed approach in different fields of engineering to get an improved understanding of the dynamics of hysteretic mechanical systems subjected to cyclic loading.

Выделение гироскопических инерционных сил из центробежных и кориолисовых инерционных сил

The purpose of the study is to identify in the equations of dynamics of mechanical systems generalized gyroscopic inertial forces, consisting of a part of centrifugal and Coriolis inertial forces, indica¬ting the bodies whose movements form these forces. The methods of research refer to mechanics of body systems, systems analysis and robotics. The results of the study allow us to write out general formulas for calculating generalized centrifugal, Coriolis and gyroscopic inertial forces through partial derivatives on generalized coordinates from elements of the matrix of inertial coefficients in the expression of kinetic energy of arbitrary mechanical system. In the process of analyzing these formulas for systems of bodies with an open tree structure, such as orbital stations with manipulators on board or walking vehicles in the single-supported walking phase, the bodies whose movements affect the occurrence of the listed inertial forces are highlighted. For robot manipulation systems we present examples of the equations of dynamics, in which all possible inertial forces are highlighted and the bodies that form them are indicated. Conclusion. Singling out the gyroscopic forces allows you to simplify the formula for calculating the power consumption of drives, because the power of these forces is zero. This fact, in particular, allows to simplify the expression of the minimizing functional in the problem of energy optimal control. The isolated centrifugal forces can be used to realize program motions of some bodies of manipulators with polar, cylindrical, spherical and angular coordinate systems without expenditure of power consumed by their drives.

Efficient and robust estimation of many-qubit Hamiltonians

Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in developing quantum technologies. We propose an efficient protocol based on the estimation of the time-derivatives of few qubit observables using polynomial interpolation for characterizing the underlying Hamiltonian dynamics and Markovian noise of a multi-qubit device. For finite range dynamics, our protocol exponentially relaxes the necessary time-resolution of the measurements and quadratically reduces the overall sample complexity compared to previous approaches. Furthermore, we show that our protocol can characterize the dynamics of systems with algebraically decaying interactions. The implementation of the protocol requires only the preparation of product states and single-qubit measurements. Furthermore, we improve a shadow tomography method for quantum channels that is of independent interest and discuss the robustness of the protocol to various errors. This protocol can be used to parallelize the learning of the Hamiltonian, rendering it applicable for the characterization of both current and future quantum devices.

The Variational Iteration Method for a Pendulum with a Combined Translational and Rotational System

Abstract The dynamic analysis of complex mechanical systems often requires the application of advanced mathematical techniques. In this study, we present a variation iteration-based solution for a pendulum system coupled with a rolling wheel, forming a combined translational and rotational system. Furthermore, the Lagrange multiplier is calculated using the Elzaki transform. The system under investigation consists of a pendulum attached to a wheel that rolls without slipping on a horizontal surface. The coupled motion of the pendulum and the rolling wheel creates a complex system with both translational and rotational degrees of freedom. To solve the governing equations of motion, we employ the variation iteration method, a powerful numerical technique that combines the advantages of both variational principles and iteration schemes. The Lagrange multiplier plays a crucial role in incorporating the constraints of the system into the equations of motion. In this study, we determine the Lagrange multiplier using the Elzaki transform, which provides an effective means to calculate Lagrange multipliers for constrained mechanical systems. The proposed solution technique is applied to analyse the dynamics of a pendulum with a rolling wheel system. The effects of various system parameters, such as the pendulum length, wheel radius and initial conditions, are investigated to understand their influence on the system dynamics. The results demonstrate the effectiveness of the variation iteration method combined with the Elzaki transform in capturing the complex behaviour of a combined translational and rotational system. The proposed approach serves as a valuable tool for analysing and understanding the dynamics of similar mechanical systems encountered in various engineering applications.

Launching ceremony of the International Society of Mechanical System Dynamics Convened in Beijing, China

Launching ceremony of the International Society of Mechanical System Dynamics Convened in Beijing, China

Coherent charge oscillations in a bilayer graphene double quantum dot

The coherent dynamics of a quantum mechanical two-level system passing through an anti-crossing of two energy levels can give rise to Landau-Zener-Stückelberg-Majorana (LZSM) interference. LZSM interference spectroscopy has proven to be a fruitful tool to investigate charge noise and charge decoherence in semiconductor quantum dots (QDs). Recently, bilayer graphene has developed as a promising platform to host highly tunable QDs potentially useful for hosting spin and valley qubits. So far, in this system no coherent oscillations have been observed and little is known about charge noise in this material. Here, we report coherent charge oscillations and T2*\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${T}_{2}^{*}$$\\end{document} charge decoherence times in a bilayer graphene double QD. The charge decoherence times are measured independently using LZSM interference and photon assisted tunneling. Both techniques yield T2*\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${T}_{2}^{*}$$\\end{document} average values in the range of 400–500 ps. The observation of charge coherence allows to study the origin and spectral distribution of charge noise in future experiments.

Influence of two kinds of clearance joints on the dynamics of planar mechanical system based on a modified contact force model

This study takes the slider-crank mechanism with revolute joint and translational joint as the research object and studies the contact force model of the clearance joint and the influence of the hybrid clearance joints on the nonlinear dynamic behavior of the mechanism. A modified contact force model is established based on the simplified elastic oscillator model, which can be used as a normal force in clearance joint. In the new contact force model, the component n of the indentation depth can be arbitrarily selected and it can support the calculation of contact force for both fully elastic recovery, non-elastic recovery and fully inelastic recovery. Based on the LuGre friction model, the tangential friction model of the clearance joint is given. Thus, the normal force and tangential force during the dynamic contact of the clearance joint are formed. Combining Lagrange’s equations of the first kind with the modified normal force and tangential friction force, the dynamic equations of the multi-body system with clearance joints are established. The Baumgarte stabilization method is used to improve the numerical stability. The correctness of the dynamic prediction model in the mechanism with clearance joint is verified by experiment. The dynamic analysis of the slider-crank mechanism with mixed clearance joints shows that the revolute clearance joint has a greater influence on the mechanism than the translational clearance, and the revolute clearance joint plays a leading role in the dynamic response.

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.