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This chapter deals with some simplest nonlinear problems of the statics, stability, and vibrations of deformable systems.

Under transversal vibration, the local slippage on the thread and bearing surfaces is typically nonlinear and its gradual accumulation with vibration cycles contributes to the loosening of threaded fasteners. The classical Iwan model is used widely to model the nonlinearity of contact interface, but not appropriate for analyzing the local slippage accumulation on the thread and bearing surfaces. In this paper, we proposed modified Iwan model to represent the nonlinear local slippage behavior. The acting forces on the internal thread were decomposed into three component forces along different directions. The effect of each component on the local slippage accumulation was analyzed theoretically based on the modified Iwan model. It was found that the cyclic component force along the radial direction dominates the local slippage accumulation of thread surface and other two cyclic component forces have no effects on it. Then, we also analyzed the local slippage accumulation on the bearing surface using the modified Iwan model and developed a thorough understanding on loosening mechanism. Based on the loosening mechanism, we proposed that the key to preventing local slippage accumulation and sustained loosening was to inhibit the slippage or relative motion occurring on the thread surface along the radial direction. Thus, several novel thread structures were designed for resisting loosening based on above findings. Finally, their superior anti-loosening abilities were validated by FEA method.

On the basis of set of experimental tests a universal experimental relation for determination of natural transversal frequencies of short bulky bars with free ends is established. It is shown that the relation totally corresponds to approximate solution of the notorious differential equation obtained by Timoshenko for transversal vibration of stubby beams. The relation gives an opportunity for brief calculation of the transversal natural frequencies of stubby beams by avoiding complex and hard algorithms of vibration analysis. The achieved relation can be successfully used for control purposes of robot arms articulation, etc. An option of new differential equation for stubby both ends pinned beams transversal vibration is discussed.

International audience; In the European Union, timber is used in structural applications and must be graded with a Conformité Européene (CE) mark. To achieve standard, machine strength grading is used. A common technology for these machines is based on using the vibrational response of each wood board to estimate the timber modulus of elasticity and modulus of rupture. The first Eigen frequency is usually used to predict these mechanical properties. However, in heterogeneous wood species such as oak, this parameter is less correlated with mechanical properties. The current study proposes two new methods based on an extended exploitation of the vibrational response that predicts oak wood mechanical properties. The first method was based on the mechanical parameters deduced from several Eigen frequencies that were chosen with regards to a stepwise regression. The second method was based on the full vibrational spectrum and used a partial least squares method. The first method slightly improved the prediction of the modulus of elasticity compared with the first Eigen frequency in edgewise transversal vibration. Both methods significantly improved the prediction of the modulus of rupture.

A cable-driven parallel manipulator is a manipulator whose end-effector is driven by a number of parallel cables instead of rigid links. Since cables always have more flexibility than rigid links, a cable manipulator bears a concern of possible vibration. Thus, investigation of vibration of cable manipulators caused by cable flexibility is important for applications requiring high system stiffness or bandwidth. This paper provides a vibration analysis of general 6-DOF cable-driven parallel manipulators. Based on the analysis of the natural frequencies of the multibody system, the study demonstrates that a cable manipulator can be designed stiff enough for special applications like the cable-manipulator based hardware-in-the-loop simulation of contact dynamics. Moreover, under an excitation, a cable may vibrate not only in its axial direction, but also in its transversal direction. The paper also analyzes the vibration of cable manipulators caused by cable flexibilities in both axial and transversal directions. It is shown that the vibration of a cable manipulator due to the transversal vibration of cables can be ignored comparing to that due to the axial flexibility of cables.

The equation of free transverse vibration of beams with two sections of partially distributed mass is derived and its exact solution has been obtained. Experimental data for a cantilever beam are given to verify the computational results. Using a cantilever beam as an example, some interesting features of changes of natural frequencies with mass length and position are described. The method is finally generalized for the case of beams with multiple spans of distributed mass.

The present study reports numerical experiments performed on the determination of the fundamental frequency of transverse vibration of orthotropic plate of uniform thickness and discontinuously varying thickness.

This note presents a simple, general methodology for dealing with the orthotropic structural elements when vibrating in their fundamental mode

The present paper deals with the application of the Rayleigh Schmidt method for the determination of the fundamental frequency coefficient, for rectangular anisotropic plates

The present study deals with a doubly connected membrane, fixed at outer radius and inner radius.

Rectangular plates with two opposite simply supported edges and linearly varying thickness only in one direction are studied, and the natural frequencies of the transverse vibrations are investigated

The mono chain ropeway system for orchard cargo transportation is subjected to vibration, impact and alternating load. To ensure the safe use of the ropeway, it is necessary to determine the modal parameters and transversal vibration characteristics of the structure as this will give indications on which frequencies should be avoided. The tri-axial accelerometers were introduced to the experimental study. With a response surface methodology design, the experimental results indicate that the transversal vibration frequency of the axially moving chain decreases with the growth of the transport speed. The same tendencies as observe in the effects of load weight on the transversal vibration frequency. The evolution of the transversal vibration frequency can be described as increasing when the initial tension increased in the forced nonlinear vibrations. This study is a foundation for the transversal vibration control of the mono chain ropeway system.

A large number of papers and technical reports are available on the technically important problem of structural elements executing transverse vibrations and carrying concentrated masses. In general it is assumed that the attachment is perfectly rigid. On the other hand, a rather limited amount of published work is available when the mass is elastically connected to the structure. The system then exhibits a more complex behavior than in the case of rigid attachment. The present study deals with the solution of the title problem using the well-known normal mode, sinusoidal eigenfunction expansions.

In this paper a new control technique based on the LAC/HAC concept is proposed to suppress the vibration of flexible space structures. The new technique employs the mechanism to turn on or off the HAC part of the LAC/HAC system in such a manner as to suppress the spillover effects as quickly as possible. The control system designed by the new technique has global stability and is more effective than a pure LAC system, even when an ordinary LAC/HAC system results in failure because of spillover instability. To show the characteristic features of the new technique and how to implement the system, computer simulation examples are given. Finally, the technique is applied to the transversal vibration control of a cantilever beam to show its effectiveness and practicality.

This study addresses the determination of the fundamental frequency of the plate or slab when the edge x=a is free and the other three are subjected to all possible supported combinations. Eigenvalues are determined by using the optimized Rayleigh-Ritz and the finite element methods. Fil: Bambill, Diana Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina Fil: Rossit, Carlos Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina Fil: Laura, Patricio Adolfo Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina Fil: Rossi, Raul Edgardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina

The possibility of exciting horizontal parametric resonance vibration in a cable stayed footbridge as a result of a premeditated action of a group of people, or of crowd movement, is analysed. Large horizontal transverse vibration are caused by the vertical periodic synchronised movement of people, which is analogical to the movements of a person on a swing. The problem studied is how large a group of people is able to excite dangerous parametric transversal vibration in the system. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Transverse, axisymmetric vibrations of a rotating disk of uniform strength is studied. Closed-form solution for the equation of transverse motion is obtained in terms of confluent hypergeometric functions.

In this paper the author has shown the correct method of vibration analysis of solid elastic structure, taking an example in the problem of transversal vibration (in vertical plane) of continuous truss-bridge on many piers. He has also applied in this paper his long-cherished opinion as to the phase velocity of longitudinal progressing-wave in solid elastic bar, which was already reported in his previous paper, ' Phase Velocity of Longitudinal Impact Wave in Solid Elastic Bar ' in the Trans. of JSCE, No. 260, April, 1977.

In this study, we compared two vibration characteristics of a car below the resonant speed, in a case, used as a motor car, and in the other case, used as a trailer. In the case of a motor car, about a half of motor weight is assumed to be unsprung weight over the trailer one. Results of the studies are as follows : -1°The natural periods of the car are not significantly different in the two cases, in both the vertical and transversal vibrations. 2°As to the vertical vibration. (1) Under 70 km/h, the heavier the unsprung weight becomes, the larger the vibration increases. (2) From 70 to 82 km/h, there are no difference. As to the transversal vibration. (3) Under 65 km/h, the vibration is larger in the heavier unsprung weight. (4) From 65 to 75 km/h, there are no difference. (5) Over 75 km/h, the vibration is rather small in the heavier unsprung weight.

The writers studied experimentally the effect of the taper of tire treads on the vibration of railway cars, in cooperation with the Keihanshin Express Electric Railway Co., Ltd. The vibration of running cars was measured in both cases of 1/20-tapered conical tread and cylindrical tread, and the vibration charts are treated statistically. Results obtained are as follows : (1) Acceleration in the case of cylindrical treads are less in both vertical and transversal vibration. (2) In the vertical vibration, difference is a little. (3) But, in the transversal vibration, acceleration is about 7 : 5 when the car speed is over 80 kg/h.

大阪のある郊外電車で, 釣合ばねのこわさ, 心皿の形状を変え, また外輪の摩耗せる場合および削正せる場合につき, 走行中の振動の変化を研究したものである.その結果, 上下動は心皿および外輪の状態によつてあまり変化なく, その振動周期はわれわれの計算結果で説明できることがわかつた.また左右動は釣合ばねのこわさおよび心皿の形状によつてはあまり変化しないが, 外輪の摩耗状態によつて著しく変化すること, また測定された振動を蛇行動および各種の固有振動が重畳して表われるものとして説明できることがわかつた.左右動に対しては0.35s程度の車体の曲げ振動が非常に大きく表われ, 高速の100km/h程度で特に悪い影響を與える.これらを乗心地の点から見ると, 上下動はいわゆる"乗心地が