Dynamics Of Mechanical Systems Research Articles

The braking car problem: A challenging and stimulating test bench for beginning mechanical engineering students

Introductory courses of physics should provide engineering students – especially mechanical engineering students – with a working knowledge of the laws of conservation of mechanical quantities, plus the capability of analyzing the kinematics and dynamics of simple mechanical systems (for instance, rolling wheels, which are a basic component of innumerable machines). Moreover, introductory courses of physics should teach the principle of relativity of classical mechanics which – within limits – allows to switch from an inertial reference frame to another. Experience proves that this is not always the case. The braking car problem is a challenging exercise which stimulates the ingenuity of beginning mechanical engineering students with its paradoxical nature. At the same time, the problem stress-tests their understanding of the basic tenets of mechanics and thermodynamics, preparing them for more advanced technical topics such as gears, cams, hydraulic machines, jet propellers.

Oscillator with variable mass excited with non-ideal source

In this paper dynamics of a non-ideal mechanical system which contains a motor, which is a non-ideal source, and an oscillator with slow time variable mass is investigated. Due to the insufficient energy of the energy source the one degree-of-freedom oscillator has an influence on the motion of the motor. The system is modeled with two coupled second order equations with time variable parameters where the motor torque is assumed as a linear function of angular velocity. The equations are transformed into four first order differential equations. An analytical procedure for obtaining the approximate averaging equations is developed. Based on these equations the amplitude-frequency relations are determined. In the paper the equations of motion of the non-ideal mass variable oscillatory system are solved numerically, too. The approximate analytical solutions are compared with numerically obtained ones. The difference is negligible. In the paper the qualitative analysis of the model is done. It is shown that due to mass variation the number and the position of the ‘almost’ steady-state positions are varying. By increasing or decreasing of mass the number of almost steady-state positions is varying. Based on the obtained results it is suggested to develop the control method for motion in the non-ideal mass variable oscillatory system.

Time finite element based Moreau‐type integrators

SummaryWith the postulation of the principle of virtual action, we propose, in this paper, a variational framework for describing the dynamics of finite dimensional mechanical systems, which contain frictional contact interactions. Together with the contact and impact laws formulated as normal cone inclusions, the principle of virtual action directly leads to the measure differential inclusions commonly used in the dynamics of nonsmooth mechanical systems. The discretization of the principle of virtual action in its strong and weak variational form by local finite elements in time provides a structured way to derive various time‐stepping schemes. The constitutive laws for the impulsive and nonimpulsive contact forces, ie, the contact and impact laws, are treated on velocity‐level by using a discrete contact law for the percussion increments in the sense of Moreau. Using linear shape functions and different quadrature rules, we obtain three different stepping schemes. Besides the well‐established Moreau time‐stepping scheme, we can present two alternative integrators referred to as symmetric and variational Moreau‐type stepping schemes. A suitable benchmark example shows the superiority of the newly proposed integrators in terms of energy conservation properties, accuracy, and convergence.

Applications of the Lie symmetries to complete solution of a bead on a rotating wire hoop

The existence of Lie symmetries in differential equations can generate transformations in the dependent and independent variables and obtain new equations that may be easier to integrate. In particular, in some situations, one can reduce the order and it is possible to obtain first integrals. Thus, this article presents the application of the fundamental Lie theorem to obtain the complete solution of a classical nonlinear problem of the dynamics of mechanical systems: the bead on a rotating wire hoop. From the first integral obtained with the Lie symmetry generators, the exact solution can be found with the aid of the Jacobi elliptic functions.

XI International scientific and technical conference ”Applied Mechanics and Dynamics Systems”"

PREFACEThe object of the scientific and technical conference "Applied Mechanics and System Dynamics" is the analysis of the current state, trends and prospects for the development of applied mechanics and system dynamics with the aim of improving technology and production and creating new-generation equipment.The conference addresses topical issues of development and research on the problems of mechanical engineering, strength and dynamics of mechanical systems.

机械多体系统碰撞动力学的对称性和守恒量研究

To provide a powerful new tool for quantitative and qualitative analysis of collision dynamics in complex mechanical multibody systems, the symmetry theory in modern analytical mechanics was introduced into the study of mechanical multibody external collision dynamics. Firstly, the Euler-Lagrange equation of collision dynamics was derived based on the momentum method; secondly, the group theory was introduced, then, according to the invariance principle, the condition equations for the Noether symmetry and the Lie symmetry were obtained and the corresponding conserved quantity form was got, which made possible an effective approach to the analytic integral theory for dynamic equations. Finally, the collision dynamics of a planar open-loop 2-connecting-rod mechanism was taken as an example for application and analysis. Research shows that deeper mechanical laws and motion characteristics of mechanical multibody system collision dynamics can be obtained by means of symmetries and conserved quantities, and the results also lay a theoretical foundation for more precise dynamic optimal design and advanced control.

Comparative study of the use of numerical methods in the solution of dynamic mechanical systems

Comparative study of the use of numerical methods in the solution of dynamic mechanical systems

Mechanics of Humanoid Robot

The effects of mechanical system dynamics are often disregarded in the design process of humanoid robots. Sophisticated control methods may compensate for some limitations of the mechanical structu...

Dynamic Mechanical Compression of Chondrocytes for Tissue Engineering: A Critical Review.

Articular cartilage functions to transmit and translate loads. In a classical structure–function relationship, the tissue resides in a dynamic mechanical environment that drives the formation of a highly organized tissue architecture suited to its biomechanical role. The dynamic mechanical environment includes multiaxial compressive and shear strains as well as hydrostatic and osmotic pressures. As the mechanical environment is known to modulate cell fate and influence tissue development toward a defined architecture in situ, dynamic mechanical loading has been hypothesized to induce the structure–function relationship during attempts at in vitro regeneration of articular cartilage. Researchers have designed increasingly sophisticated bioreactors with dynamic mechanical regimes, but the response of chondrocytes to dynamic compression and shear loading remains poorly characterized due to wide variation in study design, system variables, and outcome measurements. We assessed the literature pertaining to the use of dynamic compressive bioreactors for in vitro generation of cartilaginous tissue from primary and expanded chondrocytes. We used specific search terms to identify relevant publications from the PubMed database and manually sorted the data. It was very challenging to find consensus between studies because of species, age, cell source, and culture differences, coupled with the many loading regimes and the types of analyses used. Early studies that evaluated the response of primary bovine chondrocytes within hydrogels, and that employed dynamic single-axis compression with physiologic loading parameters, reported consistently favorable responses at the tissue level, with upregulation of biochemical synthesis and biomechanical properties. However, they rarely assessed the cellular response with gene expression or mechanotransduction pathway analyses. Later studies that employed increasingly sophisticated biomaterial-based systems, cells derived from different species, and complex loading regimes, did not necessarily corroborate prior positive results. These studies report positive results with respect to very specific conditions for cellular responses to dynamic load but fail to consistently achieve significant positive changes in relevant tissue engineering parameters, particularly collagen content and stiffness. There is a need for standardized methods and analyses of dynamic mechanical loading systems to guide the field of tissue engineering toward building cartilaginous implants that meet the goal of regenerating articular cartilage.

Features of dynamics of mechanical system with self-synchronizing vibroexciters near resonance

The paper describes some features of behavior of a mechanical system with self-synchronizing vibroexciters. The influence of friction torque in the bearings of vibroexciters rotors on their self-synchronization has been established by means of experimental research and mathematical simulation. Both the causes and frequency ranges of gaps in frequency responses has been found out. Further modification of the previously proposed algorithm for resonant tuning has expanded working regimes limits of the control system and improved resonant tuning stability.

Flexagon grid: a novel method of creating dynamic spatial forms based on the synthesis of tritetraflexagons

In this paper, we describe the method for the formation of spatial mechanical structures of flexagon grids, which aims to improve the technical and constructive qualities of dynamic mechanical systems and enrich the design practice of designers and artists with new materials that harmoniously combine both technical and expressive properties. This method can be regarded as an attempt to respond to the social demand of the modern consumer to surround himself with objects and things of a new reality that, due to the introduction of a dynamic component, at a qualitatively new, including aesthetic level, would satisfy his need for visual and physical comfort. The described structures can be appropriately focused on the improvement of the shape-forming and aesthetic qualities of design products, architectural forms and, in general, the filling of the object-spatial environment with objects with a dynamic component in its functionality and aesthetics. Flexagon grids must be attributed to spatial and plastic solutions, implemented in the framework of the kinetic direction in design and art, with the underlying idea of shape movement.

Influence of Airway Secretion on Airflow Dynamics of Mechanical Ventilated Respiratory System.

Secretions in the airways of mechanical ventilated patients are extremely dangerous to patients' health. In recent studies, the continuous constant airflow is adopted, however, it is not consistent with a clinical situation. To study respiratory airflow dynamic characteristics with secretion in the airways, a mathematical model based on clinical mechanical ventilation is established in this paper. To illustrate the secretion's influence on the airflow dynamics of mechanical ventilated respiratory system, three key parameters which are cross section area ratio of secretion/ pipe, air-secretion contact area, and secretion viscosity are involved in the study. Through the experimental study, the accuracy and dependability of the model are confirmed. By the simulation study, we find that: based on the model which combines two airways and two model lungs, when one of the airways was covered with secretion, the maximum pressure of the model lung which is attached to the end of this airway maintains constant when the cross section area ratio is less than 66 percent, and then it tends to decline sharply with the ratio increasing, but it remains constant with the augment of air-secretion contact area, the maximum flow declines both with the increasing of cross section area ratio and air-secretion contact area. Furthermore, as for the other airway, the maximum pressure of the model lung has no significant changes with the augment of area ratio and air-secretion contact area, however, along with the increasing of area ratio and air-secretion contact area, the maximum flow rises up. Moreover, the secretion viscosity has barely any influence on airflow dynamics. According to our analysis results, we conclude that the cross section area ratio of secretion/pipe has bigger influence on airflow dynamic characteristics than air-secretion contact area and secretion viscosity. This paper lays the foundation for the further study of efficacy and safety in mechanical ventilation and the secretion clearance of mechanical ventilated patients. In addition, the mathematical model proposed in this paper can also be referred to study on the secretion movement in human airways.

Computational analysis of nonlinearities within dynamics of cable-based driving systems

This paper deals with computational nonlinear dynamics of mechanical systems containing some flexural parts within the actuating scheme, and, especially, the situations of the cable-based driving systems were treated. It was supposed both functional nonlinearities and the real characteristic of the power supply, in order to obtain a realistically computer simulation model being able to provide very feasible results regarding the system dynamics. It was taken into account the transitory and stable regimes during a regular exploitation cycle. The authors present a particular case of a lift system, supposed to be representatively for the objective of this study. The simulations were made based on the values of the essential parameters acquired from the experimental tests and/or the regular practice in the field. The results analysis and the final discussions reveal the correlated dynamic aspects within the mechanical parts, the driving system, and the power supply, whole of these supplying potential sources of particular resonances, within some transitory phases of the working cycle, and which can affect structural and functional dynamics. In addition, it was underlines the influences of computational hypotheses on the both quantitative and qualitative behaviour of the system. Obviously, the most significant consequence of this theoretical and computational research consist by developing an unitary and feasible model, useful to dignify the nonlinear dynamic effects into the systems with cable-based driving scheme, and hereby to help an optimization of the exploitation regime including a dynamics control measures.

Visualized simulation and design method of mechanical system dynamics based on transfer matrix method for multibody systems

The transfer matrix method for multibody systems is a new method with very high computational speed developed in recent 20 years for studying multibody system dynamics. By combining transfer matrix...

A methodology for areal modeling of structural dynamics based on a Takagi–Sugeno fuzzy system

For simulation analysis and controller design mathematical models are necessary. This also applies to characterize the structural dynamics of mechanical systems, but current modeling approaches are limited to describe a restricted amount of predefined geometric points. A procedure to model the mechanical behavior of an arbitrary point along a line or within a surface area is missing. We propose a novel method to tackle this issue, by adapting Takagi–Sugeno Fuzzy Systems and combining them with the general linear description of mechanical systems. The presented method consists of two paths, each designed to meet a specific purpose, subject to numerical complexity and representation aberration. In the end, both cases lead to nonlinear differential equations, which provide a continuous estimation of the properties of an area. The accuracy and performance of our approach is verified by different experimental and simulation setups. One specific example is a galvanometer laser scanner, for which the new method is inevitable for a precise system modeling.

On establishing equations of motion of mechanical vibration systems placed on moving bases

The first author has been teaching the postgraduate course, “The Dynamics of Mechanical Systems” in The ITU Faculty of Mechanical Engineering for nearly 20 years. He has observed that students frequently have problems in obtaining the equations of motion of the vibrating systems which were placed on moving bases. Starting from this observation, he has found that the homework stated below, which was given to the students occasionally, was very helpful in learning the subject. The main idea of the homework is the derivation of the equations of motion, with the help of formulating the Lagrange’s equations with respect to a moving set of axis for a vibration system with two degrees of freedom which consists of a horizontal table rotating with a constant angular velocity around a vertical axis. The students were also asked to solve the same problem with a different method of their choice and to determine the reaction forces as well. We want to share this problem with the reader, which we have assessed as very instructive and appropriate from the viewpoint of applicability of different methods.

Relativistic coupling of internal and centre of mass dynamics in classical and simple bound quantum mechanical systems

Although special relativity and quantum mechanics revolutionised physics in the early 20th century, the consequences of combining these two theories are still being explored a hundred years later, usually using the formidable theoretical machinery of quantum field theory. However, a formalism accessible to undergraduates has been recently developed which shows how the centre of mass and internal dynamics of classical and quantum systems is relativistically coupled with interesting consequences. Here we explore some of the implications of this coupling, first classically, where we find that the dynamics of the system is time dilated when moving relative to another inertial frame. We then apply the dynamics to a quantum 2-level atom bound in a one-dimensional infinite potential well, and show that the coupling produces collapses and revivals in quantum interference. This example provides an illustration of how the combination of special relativity and quantum mechanics can be studied in situations familiar to most undergraduates.

Dynamic Simulation of the Harvester Boom Cylinder

Based on the complete dynamic calculation method, the layout, force, and strength of harvester boom cylinders were designed and calculated. Closed simulations for the determination of the dynamic responses of the harvester boom during luffing motion considering the cylinder drive system and luffing angle position control have been realized. Using the ADAMS mechanical system dynamics analysis software, six different arm poses were selected and simulated based on the cylinder as the analysis object. A flexible model of the harvester boom luffing motion has been established. The movement of the oil cylinder under different conditions were analyzed, and the main operation dimensions of the harvester boom and the force condition of the oil cylinder were obtained. The calculation results show that the dynamic responses of the boom are more sensitive to the luffing acceleration, in comparison with the luffing velocity. It is seen that this method is very effective and convenient for boom luffing simulation. It is also reasonable to see that the extension of the distance of the bottom of the boom is shortened by adjusting the initial state of the boom in the working process, which can also effectively reduce the workload of the boom—thus improving the mechanical efficiency.

Stabilization of Internal Dynamics of Underactuated Systems by Periodic Servo-Constraints

The model-based motion control of underactuated, multiple degree-of-freedom, complex multibody systems is in focus. Underactuated mechanical systems possess less number of independent control inputs than degrees-of-freedom. The main difficulty in their control is caused by the dynamics of the uncontrolled part of the system. The complexity of multibody systems makes the dynamical and control formulation difficult. The direct application of traditional control techniques available in the literature can lead to unstable dynamic behavior in many cases. In order to avoid instability, these general methods are usually adapted for specific problems in an intuitive way. Here, we present a direct, more algorithmic approach, and propose the use of periodic servo-constraints to overcome stability problems and enhance the dynamic behavior. An exact, stability analysis-based method is also proposed for tuning the control parameters. A stability analysis procedure is developed which is directly applicable for investigating the dynamics of mechanical systems described by dependent coordinates and mathematically formulated as a set of algebraic differential equations.

An Experimental Approach Based on Electronic Circuits for Verifying Dynamic Mechanical Behavior of a Harmonically Forced System with Clearances

Two electronic circuits are designed according to the dynamical model of a harmonically forced system with clearances by both conventional approach and SC-CNN strategy. Dynamics of the piecewise smooth mechanical system, in low forcing frequency domain, is investigated by double-parameter simulation analysis and experiment conducted on these two electronic circuits. The outputs of the designed circuits are well consistent with the numerical results of the mechanical model, which validates the experimental approach.