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RESUMO Por ser um material anisotrópico e heterogêneo, o uso racional da madeira em estruturas requer o conhecimento de uma série de propriedades físicas e mecânicas. Parte das propriedades é obtida com o uso de equipamentos de grande porte, geralmente encontrados em poucos centros de pesquisas. A vibração transversal consiste em um método de ensaio não destrutivo utilizado na determinação da rigidez da madeira, em função agilidade proporcionada na realização dos ensaios. Essa pesquisa objetivou, com base na obtenção de dezessete propriedades entre físicas e mecânicas da madeira de Mandioqueira [Ruizterania albiflora (Warm.) Marc. -Berti, Vochysiaceae], espécie pouco conhecida na literatura nacional e internacional, avaliar a indicação de uso e relacionar suas propriedades físicas (estabilidade dimensional) e mecânicas (resistência e rigidez) com a densidade aparente e com a frequência natural do ensaio de vibração transversal por meio de modelos de regressão. Os resultados indicam o uso da madeira de Mandioqueira em estruturas, por apresentar propriedades equivalentes ou superiores às propriedades de outras comumente utilizadas na construção civil. Dos modelos de regressão, foram notadas fracas correlações entre a densidade e a frequência natural com as propriedades físico-mecânicas avaliadas, resultando em estimativas de baixa precisão. Entretanto, resultados mais abrangentes requerem maior número de espécies, e consistirão em objetivos de pesquisas futuras. ABSTRACT As it is an anisotropic and heterogeneous material, the rational use of wood in structures requires knowledge of a series of physical and mechanical properties. Part of the properties is obtained with the use of large equipment, generally found in a few research centers. Transverse vibration consists of a non-destructive test method used to determine the stiffness of the wood, due to the agility provided in carrying out the tests. This research aimed, based on obtaining seventeen physical and mechanical properties of Mandioqueira wood [Ruizterania albiflora (Warm.) Marc.- Berti, Vochysiaceae], a little known species in national and international literature, evaluate the indication of use and relate its properties physical (dimensional stability) and mechanical (strength and stiffness) to the apparent density and to the natural frequency of the transversal vibration test by means of regression models. The results indicate the use of Mandioqueira wood in structures, as it has properties equivalent or superior to the properties of others commonly used in civil construction. From the regression models, weak correlations were observed between density and natural frequency with the evaluated physical-mechanical properties, resulting in low precision estimates. However, more comprehensive results require a greater number of species, and will consist in the objectives for future research.

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

Method of loss coefficients calculation from mechanical quality factors of transversal vibration modes is presented. Theoretical formulae are derived for the contour mode of thin square plate and width extensional mode of a thin rectangular plate. Mechanical quality factors are expressed as a function of loss coefficients for ceramic with known Poisson’s ratio. Measured impedance spectra are compared with calculations and used for the characterization of losses on lead-free BCZT and lead-based PZT piezoelectric ceramics. Full set of loss coefficients active for planar vibration modes is characterized on a single sample. Mechanical quality factor at resonance is the same for the contour extensional mode of a thin square plate and for the width extensional mode of a thin rectangular plate. Loss coefficients reach the biggest values for the piezoelectric losses, followed by the dielectric and elastic losses. Our results show that the BCZT ceramics have losses of the same magnitude as soft PZT ceramic.

This paper presents general solution of boundary value problem for constant cross-section Timoshenko beams with four typical boundary conditions. The authors have taken into consideration rotational inertia and shear strain by using the theory of influence by Cauchy function and characteristic series. The boundary value problem of transverse vibration has been formulated and solved. The characteristic equations considering the exact bending theory have been obtained for four cases: the clamped boundary conditions; a simply supported beam and clamped on the other side; a simply supported beam; a cantilever beam. The obtained estimators of fundamental natural frequency take into account mass and elastic characteristics of beams and Timoshenko effect. The results of calculations prove high convergence of the estimators to the exact values which were calculated by Timoshenko who used Bessel functions. Characteristic series having an alternating sign power series show good convergence. As it is shown in the paper, the error lower than 5% was obtained after taking into account only two first significant terms of the series. It was proved that neglecting the Timoshenko effect in case of short beams of rectangular section with the ratio of their length to their height equal 6 leads to the errors of calculated natural frequency: 5%÷12%.

Proposing technological innovations in the investigation of the structure and behaviour of wood is important to optimize its use. The assimilation of methods diffused in other areas, such as particle image velocimetry (PIV), can allow a rich range of information for different aspects. The aim of this study was to estimate the Young’s modulus using the PIV technique, independently of the wood density. The Young modulus value was obtained by universal testing machine, transversal vibration and PIV technique. Cedrela spp. and Eucalyptus cloeziana wood specimens were analyzed and their Young modulus were compared and correlated. The PIV technique presented mean Young’s modulus values statistically equal to those of the universal testing machine. The standard error of prediction from PIV approach was 0.46 and 0.97 GPa for Young’s modulus estimates for Cedrela spp. and Eucalyptus cloeziana wood, respectively.

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.

The Edge-Glued Panel is produced using sawn wood, i.e., lumber, with or without butt joints and edge-glued lumber. It can be composed with one layer, but the most common is with three layers (two external longitudinal and one transversal). This panel is used in Europe for furniture and forms of concrete structures. The resin applied in the gluing is based on urea-formaldehyde and phenol-formaldehyde. Due to the importance of this panel, this research aims to analyze the use of Transversal Vibration techniques for EGP grading. For this purpose, twelve EGP panels of three layers were produced and tested in order to determine the modulus of elasticity and modulus of rupture in static bending and dynamic modulus. The results showed nonexistent correlations among the dynamic modulus of elasticity with EGP density and between the modulus of rupture in static bending with the dynamic modulus, providing just a good correlation between statistic and dynamic modulus of elasticity.

Resumo Aplicação de técnicas não-destrutivas pode auxiliar no processo de avaliação da madeira, não sendo necessária a extração de corpos-de-prova. Entre as técnicas de avaliação mecânica, destacam-se as técnicas não-destrutivas de ultra-som e de vibração transversal. Com o avanço no uso das técnicas não-destrutivas, tornou-se possível o desenvolvimento de novas tecnologias, entre as quais se destaca a técnica de ondas de tensão, que permite a obtenção de imagem tomográfica da madeira. O objetivo deste trabalho foi verificar a acuracidade das técnicas de vibração transversal e ultra-som comparativamente aos valores obtidos em ensaios estáticos e a obtenção de imagem tomográfica a partir do emprego de ondas de tensão para a espécie Eucalyptus citriodora. Os valores obtidos de coeficiente de determinação para as técnicas de ultra-som (R² = 0,76) e vibração transversal (R² = 0,80) são significativos, demonstrando que essas são importantes ferramentas para a inferência do módulo de elasticidade da madeira. Os resultados permitem também verificar que a imagem tomográfica obtida com o emprego de ondas de tensão possibilita estimar a porcentagem da área deteriorada com adequada confiabilidade. Abstract The application of nondestructive techniques can assist in timber evaluation, without the need to extract specimens. Two of the main mechanic evaluation techniques are the nondestructive techniques of ultrasound and transversal vibration . The evolution in the use of nondestructive techniques has led to the development of new technologies, particularly the stress-wave technique, which allows the obtention of tomographic images of timber. The purpose of this study was to verify the accuracy of the ultrasonic and transverse vibration techniques in comparison with the values obtained from static tests and tomographic images obtained through the use of stress waves for Eucalyptus citriodora. The values of the coefficient of determination for the ultrasonic technique (R 2 = 0.76) and for the transverse vibration technique (R 2 = 0.80) were significant, demonstrating that the ultrasonic and transverse vibration techniques are important tools for the nondestructive inference of the modulus of elasticity of timber. The results also show that the tomographic images obtained through the use of the stress-wave technique allow the percentage of deteriorated area of timber to be estimated with adequate reliability.

The stability of the mechanical equilibrium of a plane horizontal binary mixture layer with Soret effect in the presence of high frequency transversal vibration is studied. The asymptotic analysis for long-wave disturbances and the numerical solution of the spectral amplitude problem for cellular disturbance has shown that independently of properties of the binary mixture the effect of transversal vibration is always stabilizing. The critical values of Rayleigh number and the characteristics of critical disturbances are determined.

In ancient bows the grip of the bow was in the way of the arrow. The arrow needed to get round the bow while being accelerated; this phenomenon is called the ‘Archer's Paradox’. In the forties it was observed experimentally with high-speed cameras that the arrow vibrates in a horizontal plane perpendicular to the vertical median plane of the bow. These movements are started and controlled by the movements of the two points of contact with the bow, viz. the middle of the string in contact with the rear end of the arrow and the grip where the arrow slides along the bow. The latter contact imposes a moving-boundary condition. The numerically obtained results are satisfactorily in agreement with experimental data. The model can be used to estimate the drawing force of ancient bows of which only the contemporary arrows are available and also for the design of new archery equipment.

The Rayleigh-Ritz method using characteristic orthogonal polynomials has been applied to study the problem of transverse vibration of completely-free elliptic and circular plates of uniform thickness. A sequence of successive approximations has been generated to work out the frequencies and mode shapes. The process is continued until at least the first four frequencies converge to five significant digits. It has been found that the results agree completely with the known results for a circular plate. A comparison has also been made with some known experimental and theoretical results for an elliptic plate.

The Finite Element Method FEM can be used in the context of physics engineering education, particularly in nanotechnology training. Cantilevers and cantilevers arrays have been implemented as sensors within lots of applications. In the present paper, FEM was used to assess validity of basic models where cantilevers are used as mass sensors. Resonance frequency of a cantilever transversal vibration was found; this was a silicon one-side clamped cantilever. A number of minor mass elements Am was added on the cantilever's free side. Then in each case, a new resonance frequency was found; this led to obtain the Am values from shifts of resonance frequencies. Finally, those values were compared with CAD model values.

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)

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

Experimental studies were made on the curve of equal sensitivity of the human ear for vibration. In cases of vertical vibration obvious difference was observed as regards points representing equal sensitivity at low frequencies and at high frequencies. The curves were similar in cases of longitudinal vibration and of transversal vibration.

Solutions to the initial-boundary value problem for the nonlinear Kirchhoff equation are considered. Conditions on the initial data and nonlinear term are given so that the solutions to the problem under consideration do not exist for all t > 0. An estimate of the t -interval of existence of the solutions is obtained.