Formulations in Advanced Dynamics of Mechanical Systems

In the study of the dynamics of mechanical systems with distributed parameters, the discretization of partial differential equations by the finite element method, finite difference method, or boundary element method is widely used. This makes it possible to simplify the analysis of dynamic processes by reducing it to solving a system of ordinary differential equations. The aim of this paper is to mathematically substantiate the method of direct discretization of long-dimensional elastic links as applied to free and forced longitudinal oscillations of a straight rod as a mechanical system with distributed parameters, and to investigate the convergence of the method in determining the natural frequencies and amplitudes of forced oscillations of mechanical systems. The method of direct discretization is considered in the application to a rod with distributed parameters, which performs longitudinal oscillations. It is shown that by mathematical discretization of the wave equation, the boundary value problem can be reduced to the analysis of oscillatory phenomena in a chain mechanical system of material points. The formulas for determining the masses of the inertial elements of the computational model and the stiffness coefficients of the elastic connections are given. The convergence of the method is investigated by determining the natural frequencies of oscillations of a rod with free ends, as well as with one end clamped and the other end free, and comparing the approximate results of calculations with the exact results. The effect of the number of degrees of freedom, rod length, and material density on the eigenfrequencies is investigated. It is found that to ensure sufficient accuracy for engineering practice in determining the three or four lowest natural frequencies, computational models with 8-10 degrees of freedom can be used. It is emphasized that the cross-sectional area of the rod does not affect the characteristics of the frequency spectrum of the mechanical system. The zero value of the lowest natural frequency of an elastic rod with free ends can be explained by the fact that this value corresponds not to the oscillatory but to the translational motion of a mechanical system that is not connected to the base. Forced longitudinal oscillations of an elastic rod, one end of which is clamped at the base and the other end is free, under power and kinematic excitation are considered. The amplitude-frequency characteristics of mechanical systems are constructed on the examples of the dependences of the movement amplitude of one of the material points and the amplitude of the longitudinal force in one of the elastic links of the computational model on the frequency of forced oscillations. Since the dissipation of the mechanical energy of the system during its oscillations is not taken into account, as the frequency of forced oscillations approaches one of the natural frequencies of the system, the movement amplitudes, as well as the amplitudes of internal forces, tend to infinity. The actual values of resonant amplitudes are not of practical interest, since resonant modes of operation are not expected for the vast majority of machine units. The scientific novelty of the results obtained is that the mathematical substantiation of the method of direct discretization of the rod in its application to its longitudinal oscillations, the creation of computational algorithms and the study of the convergence of the results of determining the natural frequencies and amplitudes of forced oscillations can be considered as a development of the computer methodology for the dynamic analysis of mechanical systems with distributed parameters. The practical significance and scope of further research of the results of this work are based on the wide possibilities of practical application of the direct discretization method in the study of dynamic processes in rather complex mechanical systems of such technical objects as drilling rigs, cranes, mine hoisting machines, conveyors, rotary kilns, etc. This is facilitated by the simplicity and computational efficiency of the method in solving problems of dynamics of both linear and nonlinear mechanical systems. The method can be applied in the study of both stationary and transient dynamic processes in machine units.

Multi-body contact in non-linear dynamics of real mechanical systems

Dynamics and Control of Machines

A fundamental study of noise generation in complex mechanical systems is undertaken. The objective of the study is the development of design guidelines for the prediction of mechanical system noise levels. Recently developed dynamical procedures are used to obtain the motions of linked mechanical systems with elastic elements and connection clearances. An analytical procedure for modeling the acoustical noise generated by complex mechanical systems is applied to a typical linked system, a four-bar mechanism. The far field acoustic pressure distribution is calculated and shown to be a function of many of the parameters under the control of the system designer. To aid the designer in producing quieter systems, acoustic design functions are developed. In particular, the system sound power and modal power efficiencies are found to be promising design tools.

Artificial intelligence and condition monitoring and diagnostics of systems are emerging, computer-based transdisciplines. The origins of the theoretical kernels of both transdisciplines can be traced to the last century, but the richly structured theories in the body of knowledge that supports the present work in the cognitive sciences and our recently achieved ability to make real-time decisions related to the operation and maintenance of modern, large-scale, complex mechanical systems are due, in large part, to the explosion of synergistic activity in systems thinking and computers which has occurred in the past three decades. In artificial intelligence one strives to make machines (usually, digital computers) do the sorts of things that the human mind does, including making decisions and problem solving, which is an essential element in condition monitoring and diagnostics as well. Thus there is a strong link between the two transdisciplines. A generic definition of artificialintelligence is given above; however, there is no universally accepted definition of the term conditionmonitoringanddiagnostics, either in its general form or in one of its specific forms, say, the condition monitoring and diagnostics of machines. Nevertheless, it is believed that most practitioners of the condition monitoring and diagnostics art would agree that the activities encompassed by the term can be characterized as a two-phase sequence of processes designed to monitor the condition of an operating, functioning system for the purpose of diagnosing faults in the system. Monitoring is a passive, system-specific, information and data gathering process. Diagnostics is an interactive decision-making process in which the unique, system-specific information and data obtained in the monitoring phase are used by a human or computer-based decision maker to decide if faults exist in the system, where they are located, their criticality and what advisory and/or corrective action should be taken. In the diagnostic phase, computer-based decision making (read ‘‘artificial intelligence’’) can be used to support decisions made by a human or to make and implement decisions automatically. Both cases are discussed here, using the condition monitoring and diagnostics of a gas turbine as an illustrative example.

Fluid-Structure Coupling Effects on the Dynamic Response of Pump-Turbine Guide Vanes

Mechanical design have experienced a long process of development, the improvement of design method and optimization method have always been the pursuit of any designer. In recent years, introduction of CAD/CAE have increased greatly the speed of design and experiment, making mechanical design undergo a fundamental leap. However, the whole process: design-trial-improve- ment, still needs manual control to complete, designers still face the problem of complex repeating process. In views of this bottleneck, we will conduct parametric modeling on complex mechanical system in PRO/E, and let key parts import into ANSYS to be flexible .Then, we will build and analyze rigid-flexible mixture virtual prototyping in automatic dynamic analysis of mechanical systems. At last, we will integrate this process in ISIGHT3.5, exploring design-trial-improvement integrated optimization and simulation method through the optimization of the size of key parts of complex mechanical system.

In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are few reports in the field of mechanical nonlinear systems. So, can we apply Von Neumann entropy and Rényi entropy to study and analyze the dynamic behavior of macroscopic nonlinear systems? In view of the current lack of suitable methods to characterize the dynamics behavior of mechanical systems from the perspective of nonlinear system correlation, we propose a new method to describe the nonlinear features and coupling relationship of mechanical systems. This manuscript verifies the above hypothesis by using a typical chaotic system and a real macroscopic physical nonlinear system through theory and practical methods. The nonlinear vibration correlation in multi-body mechanical systems is very complex. We propose a full-vector multi-scale Rényi entropy for exploring the chaos and correlation between the dynamic behaviors of mechanical nonlinear systems. The research results prove the effectiveness of the proposed method in modal identification, system dynamics evolution and fault diagnosis of nonlinear systems. It is of great significance to extend these studies to the field of mechanical nonlinear system dynamics.

The designs of modern electronic technology are complex mechanical systems with many rigid bonds, and their microminiature in many cases has reached the physical limit of the dimensional, charge and energy quantization of components. For such mechanical systems, with non-classical methods for mechanics of fastening of separate structural elements, it is difficult to build a design model, simple enough and at the same time one that well reflects physical and dynamic properties. To ensure mechanical strength of interconnects and ultra-thin electronic components, it is necessary to determine the stress-strain state of structural elements. These reasons necessitate the use of numerical methods to calculate the dynamic parameters of the design of electronic equipment interconnections, which will improve the reliability of the developed tools that meet the requirements of regulatory technical documentation on mechanical characteristics, shorten the time and cost of their creation. Subject matter of this work is the study of beam deformation of constant cross section under the action of axial forces, bending moments and torque relative to the longitudinal axis. Goal this work is to determine the deformation of the elements of the structure of the devices using the stiffness matrix with a known vector of external forces. To achieve this goal, it is necessary to solve the following tasks: to consider the existing methods of description and analysis, which take into account the specificity of the structures and technological processes used to manufacture specific structures MEMS; explore the nature of these methods; calculate displacements and deformations using the finite element method; using the stiffness matrix to determine the deformation of the structural elements of the devices; to calculate the deformation of the beam of constant cross-section under the action of axial forces, bending moments and torque relative to the longitudinal axis. Conclusions: stiffness matrix, constructed using functional analysis, allows for the calculation of deformation of MEMS elements and electronic interconnect flexible.

Classical mechanics is mainly based on two mechanical principles, the principle of linear momentum (Isaac Newton) and the principle of angular momentum (Leonhard Euler). The principle of angular momentum implies that the time derivative of the angular momentum equals the sum of all torques, acting on the body. Concerning all types of education it is particularly important that theoretical basic principles are profoundly understood. This often enables to understand difficult mechanical systems by drawing parallels between complex mechanical systems and simple basic principles. One way to generate profound understanding of theoretical correlations is to use interesting experimental examples. In this paper, a teaching model is presented, which has the ability both to demonstrate the effects of the principle of angular momentum and to catch the attention of students. For this purpose, a remote-controlled model car was built carrying a high-speed gyroscope on its top. The gyroscope can cause that the car turns over to the inside of a turn against the centrifugal force. Even more, it is possible to drive in a circle on the inner tires of the RC vehicle.

Stability of motion is a central theme in the dynamics of mechanical systems. While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book starts with the treatise of the mathematical background on non-smooth analysis, measure and integration theory and an introduction to the field of non-smooth dynamical systems. The unilateral constraints are modelled in the framework of set-valued force laws developed in the field of non-smooth mechanics. The embedding of these constitutive models in the dynamics of mechanical systems gives rises to dynamical models with impulsive phenomena. This book uses the mathematical framework of measure differential inclusions to formalise such models. The book proceeds with the presentation of stability results for measure differential inclusions. These stability results are then applied to nonlinear mechanical systems with unilateral constraints. The book closes with the study of the convergence property for a class of measure differential inclusions; a stability property for systems with time-varying inputs which is shown to be highly instrumental in the context of the control of mechanical systems with unilateral constraints. While the book presents a profound stability theory for mechanical systems with unilateral constraints, it also has a tutorial value on the modelling of such systems in the framework of measure differential inclusions. The work will be of interest to engineers, scientists and students working in the field of non-smooth mechanics and dynamics.

A major goal in the control of complex mechanical systems such as advanced aircraft, spacecraft, and power plants is to achieve high performance with increased reliability, availability, component durability, and maintainability. The current state-of-the-art of control systems synthesis focuses on improving performance and diagnostic capabilities under constraints that often do not adequately represent the dynamic properties of the materials. The reason is that the traditional design is based upon the assumption of conventional materials with invariant characteristics. In view of high performance requirements and availability of improved materials, the lack of appropriate knowledge about the properties of these materials will lead to either less than achievable performance due to overly conservative design, or over-straining of the structure leading to unexpected failures and drastic reduction of the service life. The key idea of the research reported in this paper is that a significant improvement in service life can be achieved by a small reduction in the system dynamic performance. This requires augmentation of the current system-theoretic techniques for synthesis of decision and control laws with governing equations and inequality constraints that would model the properties of the materials for the purpose of damage representation and failure prognosis. The major challenge in this research is to characterize the damage generation process in a continuous-time setting, and then utilize this information for synthesizing algorithms of robust control, diagnostics, and risk assessment in complex mechanical systems. Damage mitigation for control of mechanical systems is reported in the two-part paper. The concept of damage mitigation is introduced and a continuous-time model of fatigue damage dynamics is formulated in this paper which is the first part. The second part which is a companion paper presents the synthesis of the open-loop control policy and the results of simulation experiments for transient operations of a reusable rocket engine.

Study on Immune Cloud Model Adapted to Complex Mechanical System Diagnosis

Modelling and simulation is of crucial importance for the understanding of system dynamics. In aircraft, simulation has been strong in the area of flight control. Modelling and simulation of the hydraulic systems has also a long tradition. The rapid increase in computational power has now come to a point where complete modelling and simulation of all the sub systems in an aircraft is not far away. This means new challenges in dealing with very complex multi domain systems. Of all the systems in an aircraft fluid power systems is one of the most difficult to handle from a numerical point of view. They are characterised by difficulties such as discontinuities, very strong non-linearities, stiff differential equations and a high degree of complexity. A considerable effort has therefore been made to develop methods suitable for simulation of such systems. This means that it is possible to simulate fluid power systems much more efficiently than before, and that a lot of systems can even be simulated in real time. The distributed modelling technique used, also makes it possible to partition the system for parallel processing. This means that it is possible to simulate much larger systems within reasonable time. It also is a valid paradigm for multi domain system. The rapid development in simulation methods and the general increase in hardware performance imply that simulations can be run thousands of times faster than just a few years ago. As a consequence, there is no longer such need to use very economic, more or less analytical methods. This means that design methods based on different kinds of numerical optimisation for system design, are becoming much more important.

Analysis of a variable displacement axial piston pump, as in other complex fluid power and mechanical systems, requires appropriate insight into three multidisciplinary domains, i.e. hydraulics, mechanics and tribology. In recent years, at FPRL, modelling of axial piston pumps has evolved in AMESim (one dimensional code) where a three dimensional mechanical approach has required generation of proprietary libraries leading to the evaluation of internal forces/reactions in all pump subsystems. Tribologic aspects in axial piston pumps modelling are also being investigated but AMESim, in this respect, does not appear as the appropriate computational environment. Consequently, a new approach has been initiated grounded on MSC.ADAMS. In this perspective, the paper details how the model has been developed through proprietary macros that automatically originate all pump subsystems parametrically and further apply required constraints and forces (springs, contacts and pressure forces). The ADAMS environment has also been selected due to co-simulation capabilities with AMESim. Accordingly, the paper elucidates how the entire modelling has been construed where hydraulics is managed in AMESim while ADAMS takes care of mechanics. As such this paper indicates an innovative methodology for the analysis of complex fluid power systems in the hope that, eventually, tribology will also fit into the scene.