Energy dissipation of a vibrating Timoshenko beam considering support and material damping

This paper studies the effect of boundary conditions, via end-fixity and damping, on the overall damping capacity of a flexibly supported cantilever under the condition of steady-state vibrations. The effect of the beam's length to depth ratio is accounted for through the use of Timoshenko beam theory. The cases of a cantilever having a flexible viscously damped support and a cantilever-support system having a combination of structural support damping and beam material damping are focused upon. Comparisons are made with the results of other investigators.     

The elastically supported Timoshenko beam subjected to an axial force and a moving load

A solution for the flexural vibration of an elastically supported Timoshenko beam which is subjected to an axial force and a moving transverse load is obtained. The influences of the axial force and the load velocity on the beam response are studied and the characteristics of the various resonances are examined. The results are also compared with those by the Euler beam theory.     

Combined analytical and numerical solution for an elastically supported Timoshenko beam to a moving load

A combined analytical and numerical method is presented to get a response for an elastically supported Timoshenko beam to a moving load. The analytical steady-state solution as a particular solution is established and summed with the numerically calculated homogeneous solution. A steady-state solution is sought analytically through the direct application of the Fourier transform to the moving step load. It is shown to be a compact formula composed of exponential and sinusoidal functions depending on the load velocity. The homogeneous solution is established numerically to cancel out the discontinuities and the inconsistent boundary and initial conditions of the steady-state solution. The discontinuities produced by the steady-state solution are removed using the physical characteristics related to the bar wave. Some response curves are shown to compare the beam motions at different load velocities.     

A model management systems approach to manufacturing systems design

Manufacturing systems design involves the solution of a complex series of interrelated problems. This complexity will increase in the future as manufacturing practices change to meet increased global competition. Research within manufacturing systems design has mainly been focused on finding improved models for solving particular problems, or extending existing modeling techniques. This has resulted in numerous modeling tools being available to support manufacturing systems design. However, little research work has been carried out into consolidating the existing theories and models. As a result, a large body of this work has not been applied in industry.Model management has evolved as a research area which investigates methods for storing, modifying, and manipulating models. This article describes a prototype model management system for manufacturing systems design. The objective here is not to develop another decision support system for manufacturing design, but to illustrate, through the development of a prototype system, a number of key ideas of how concepts from the area of model management systems can be used to support manufacturing systems design. The prototype model management system utilizes the structured modeling framework and uses an extended version of the structured modeling language. An important aspect of the prototype model management system is the incorporation of the model development task, thus allowing the system to be easily updated and adapted. The prototype system was evaluated using a range of queueing network models for manufacturing systems design.     

An approach to the problem of damage identification in an elastic rod based on the Timoshenko beam model

The solution to the problem of damage identification in a cantilever based on minimization of a special functional of the discrepancy between the solution (eigenfrequencies and vibration modes) that was obtained analytically based on the Timoshenko beam model and using other methods, in particular, finite-element analysis (FEA), is presented. The results of the numerical calculations of the position and depth of a cut in a cantilever are compared with the data of the full-scale experiment, which verified the high degree of their reliability. The advantages of the proposed model as compared to FEA and the well-known model of A.D. Dimoragonas, which lie in the higher efficiency of calculations and the reliability of the reconstruction of the shapes of different vibrational modes of a damaged structure, are demonstrated. Owing to these advantages, the model can be used in optimization algorithms and applied for teaching neural networks. The correlation between the efficiency of damage identification and the position of the points of exciting load application on a tested structure is revealed. The proposed method for identification of damage can be used in systems that are intended for the diagnosis of aviation and building structures.     

Application of residuals from regression of experimental mode shapes to locate multiple crack damage in a simply supported reinforced concrete beam

The objective of the study was to propose an effective, simple and reliable technique to determine the location of triple-crack damage in a simply-supported reinforced concrete beam using the method of mode shape regression. The study required simply supported finite element reinforced concrete beam models to be constructed with one as control and another as the test beam with predetermined triple-cracks along the length of the beam. The technique necessitated the performance of linear and Eigen analyses on the control beam, and nonlinear analysis on the beam with triple-cracks. Residuals obtained from regression of the mode shape using the Chebyshev series rational on the modal frequencies and transformation and application into the fourth order centered finite divided difference formula were used. The use of the regressed mode shapes for the reinforced concrete beam model showed large residuals around the areas of the crack damage. The results showed that the method was successful in determining the locations of the triple cracks and was comparable with other techniques proposed by other researchers in terms of its simplicity and reliability.     

Vibration analysis of a simply supported beam under moving mass based on moving finite element method

In this paper, a moving finite element (MFE) method is proposed to perform the dynamic analysis of a simply supported beam for a moving mass (MM). The MFE method treats the moving mass as a moving part of the entire system, so that the transverse inertial effects caused by the moving mass may easily be taken into account. The solution to the beam’s dynamic behaviors including its displacement is obtained via a Newmark-β method; the effects of the velocity and weight of the MM on the beam’s dynamic behaviors are further discussed. The numerical examples show that the inertial effects of the MM significantly affect the transverse responses of the simply supported beam.     

Vibration analysis of a simply supported beam under moving mass based on moving finite element method

In this paper, a moving finite element (MFE) method is proposed to perform the dynamic analysis of a simply supported beam for a moving mass (MM). The MFE method treats the moving mass as a moving part of the entire system, so that the transverse inertial effects caused by the moving mass may easily be taken into account. The solution to the beam’s dynamic behaviors including its displacement is obtained via a Newmark-β method; the effects of the velocity and weight of the MM on the beam’s dynamic behaviors are further discussed. The numerical examples show that the inertial effects of the MM significantly affect the transverse responses of the simply supported beam.     

Analytical approach to robust design of nonlinear mechanical systems

The robustness of mechanical systems is influenced by various factors. Their effects must be understood for designing robust systems. This paper proposes a model for describing the relationships among functional requirements, structural characteristics, design parameters and uncontrollable variables of nonlinear systems. With this model, the sensitivity of systems was analyzed to formulate a system sensitivity index and robust sensitivity matrix to determine the importance of the factors in relation to the robustness of systems. Based on the robust design principle, an optimization model was developed. Combining this optimization model and the Taguchi method for robust design, an analysis was carried out to reveal the characteristics of the systems. For a nonlinear mechanical system, relationships among structural characteristics of the system, design parameters, and uncontrollable variables can be formulated as a mathematical function. The characteristics of the system determine how design parameters affect the functional requirements of the system. Consequently, they affect the distribution of system performance functions. Nonlinearity of the system can facilitate the selection of design parameters to achieve the required functional requirements.     

现代设计理论方法在机械系统设计中的应用

阐述了传统机械系统设计方法和机械系统的现设计理论方法的特征;在传统机械系统设计的基础上提出了机械系统动态设计的概念、方法、目的等;并介绍了机械系统的建模方法及动态设计方法;提出对机械系统进行动态优化设计的方法。     

快速测量技术在机械设计中的应用

以摩托车外形设计为例，介绍快速测量技术的具体应用，概述了快速测量技术给机械设计领域带来的变化。特别是对机动车设计带来的较大变革。     

The mechanical analysis of a mass-spring load supported on a beam system

The static deflection and dynamic characteristics of a mass-spring system supported on beam systems are investigated in this paper. In statics, it shows that the maximum deflection is reduced considerably when a clamped-free beam is replaced by a beam system which consists of a primary beam one end of which is clamped and the other end is supported by a subsidiary beam. The addition of a subsidiary beam leads to axial forces in both beams, the primary one in tension and the subsidiary in compression. The dynamic characteristic shows that the natural frequency of the mass-spring system decreases. In some cases it becomes imaginary, because buckling occurs in the subsidiary beam. This means that the effects of the addition of a subsidiary beam are not always of a positive nature, with respect to the stiffness of the whole system. At low frequencies, the response of the mass is larger than that of the mass supported on a motionless foundation. At high frequencies the dynamic characteristics of the foundation influence the vibration of the mass only a little; i.e. it moves as if the foundation were motionless.     

Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems

The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli–Euler single-span beams carrying a number of spring-mass system and Bernoulli–Euler multi-span beams carrying multiple spring-mass systems are plenty, but that of Timoshenko multi-span beams carrying multiple spring-mass systems with axial force effect is fewer. This paper aims at determining the exact solutions for the first five natural frequencies and mode shapes of a Timoshenko multi-span beam subjected to the axial force. The model allows analyzing the influence of the shear and axial force effects and spring-mass systems on the dynamic behavior of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The calculated natural frequencies of Timoshenko multi-span beam by using secant method for non-trivial solution for the different values of axial force are given in tables. The mode shapes are presented in graphs.     

Dynamics and cutting stability of the dynamically loaded worktable subjected to simply supported conditions

This paper aims to explore the dynamic characteristics and cutting stability of a surface grinder. In simulated grinding, the dynamically loaded worktable is described by the Euler–Bernoulli beam theory. In the model, the elastic worktable has both ends simply supported on a movable and massless rigid base. The analysis of the dynamics and stability of the worktable is complex due to the operating worktable being dynamically loaded in variable positions. With the Lagrange energy method combined with the assumed mode expansion method, the system dynamic equations are derived and a state space model for the dynamically loaded worktable subjected to simply supported conditions is developed. In this study, the maximum negative real part of the overall dynamic compliance and the limiting depth of cut are used as indicators to assess the structural static and dynamic performance of the worktable in various positions. The effects of worktable damping, contact stiffness, and damping between the tool and the workpiece on the system performance are studied. Based on the regenerative chatter and stability theory, the 3D stability lobes diagram is analyzed to optimize the maximum depth of cut at the highest available spindle speed. The cutting stability is verified by comparing the results obtained in the time domain analysis with the stability lobe diagram. The procedure illustrated in this study to improve the dynamics performance of a surface grinder can also be implemented in a similar fashion for many machine tool applications.     

振劝时效技术机理

为配合国家经贸委技术进步与装备司推广应用《振动时效技术》,从本期开始,我们将陆续刊登有关此项技术的以下内容：振动时效技术机理;振动时效技术标准制修订动态;振动时效技术的应用与验证;振动时效技术在企业实际应用中所获得经济效益等。在对振动时效技术介绍的同时,本刊还将与机械科学研究院共同开展有关此项技术、设备的咨询和组织召开振动时效技术的现场演示活动,希望关心此项技术推广和应用的广大企业能够积极参加此项活动。     

A study of the fundamental frequency characteristics of eccentrically and concentrically simply supported stiffened plates

The paper investigates the fundamental frequency characteristics of eccentrically and concentrically simply supported stiffened supported plates. As a first stage, a numerical procedure for the computation of the fundamental frequency is presented. The strain energy of the assembled plate/stiffener elements is derived in terms of generalized in- and out-of-plane displacement functions and Mathematical Programming is then used to determine the lowest natural frequency. The prediction of the described algorithm is verified with other numerical procedures like finite-element, finite-strip and finite-difference methods. Results are then presented showing the influence of the plate/stiffener geometric parameters on the fundamental frequency of the structure with various concentric and eccentric stiffening configurations.     

Examining the trend in loss of flexural stiffness of simply supported RC beams with various crack severity using model updating

The flexural stiffness of simply supported cracked reinforced concrete beams was determined by model updating. The beams were 150 mm wide, 250 mm deep and 2200 mm long. Different FE models were created which include a datum and models with a single crack at three different locations along the length of the beam. The mode shape equation was obtained by using non-linear regression. The equation used in the regression was the generalized solution of transverse vibration of a prismatic beam. Local flexural stiffness, EI, at each coordinate point was derived by substituting the regressed data by using the centered-finite-divided-difference formula. Experimental modal analysis was performed on a control beam and beams with load-induced cracks at predetermined loading. Results from FE analyses showed the trend in the loss of stiffness was similar to the results obtained on the experimental beams. The more severe the damage, the higher the loss of stiffness and the loss patterns are similar for damage at different locations along the beam. The updating technique is able to indicate the trend in the loss of stiffness as a result of cracks of varying severity in the RC beams showing good agreement with experimental results.     

Sensitivity to noise of interspike intervals produced by an impacting vibrating beam

We use experimentally recorded time series of impact times to calculate the interspike intervals of an impacting oscillator. Using the interspike intervals we analyse the dynamics and especially the periodicity exhibited by the oscillator. We evaluate the effect of noise in the measurements and how this is reflected in the interspike intervals and the subsequent analyses. We compare experimental data against results produced numerically.     

Mode-shape determination in the synthesis of lumped-parameter vibrating systems

A method of mode-shape determination is presented which, when used in conjunction with an appropriate procedure for synthesizing dynamical systems, provides a ready means of designing lumped-parameter systems which vibrate at a prescribed natural frequency.