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The paper reports an algorithm to analytically solve one of the problems in the mechanics of elastic bodies, which is associated with studying the natural vibrations of a composite two-stage plate whose concave part is smoothly aligned with the part of a constant thickness. We have defined patterns for stating the boundary and transitional conditions, which should be taken into account when considering the natural vibrations of a two-stage plate.The ratios have been obtained, which make it possible to study the distribution of deflections and determine the values of amplitudes of the curved vibrations of the plate. It was noted that the modes of vibrations are based on the symmetry and factorization methods that we had developed and refined earlier. Specifically, it has been found that the deflections can be explored through expressions that are derived through the sum of relevant solutions to two linear second-order differential equations with variable coefficients.Based on the proposed approach, a system consisting of eight homogeneous algebraic equations has been defined, which allowed us to build a frequency equation for the plate rigidly fixed along the inner contour and free along the outer contour. We have determined the values for the plate’s natural frequencies for the first three modes of natural vibrations. Moreover, in order to verify and expand a set of plates of different configurations, the plates with two types of concave in their variable part have been considered. The new approaches and the ratios based on them could be useful for the further advancement of methods for solving similar problems in mathematical physics on natural values. A practical implementation is the problems about the vibrations of plates with variable thickness and of different modes, Приведен алгоритм аналитического решения одной из задач механики упругих тел, которая связана с изучением собственных колебаний составной двухступенчатой пластинки, где вогнутая часть плавно сочетается с частью постоянной толщины. Определены особенности формулирования граничных и переходных условий, которые необходимо учитывать при рассмотрении собственных колебаний двухступенчатой пластинки.Получены соотношения, которые позволяют изучить распределение прогибов и определить значения амплитуд изгибных колебаний пластинки. Отмечено, что формы колебаний построены на основе разработанных и развитых ранее авторами методов симметрии и факторизации. В частности найдено, что прогибы можно исследовать через выражения, которые определяются через сумму соответствующих решений двух линейных дифференциальных уравнений второго порядка с переменными коэффициентами.На основе предложенного подхода определена система из восьми однородных алгебраических уравнений, которая позволила построить частотное уравнение для пластинки жестко закрепленной по внутреннему контуру и свободной по внешнему контуру. Определены значения собственных частот пластинки для первых трех форм собственных колебаний. Причем в качестве апробации и расширения набора пластинок разной конфигурации рассмотрены пластинки с двумя видами вогнутости в их переменной части. Новые подходы и полученные на их основе соотношения могут быть полезными для дальнейшего развития методов решения подобных задач математической физики на собственные значения. Практическим воплощением этого есть задачи о колебаниях пластинок переменной толщины разной формы, Наведено алгоритм аналітичного розв’язку однієї з задач механіки пружних тіл, що пов'язана з вивченням власних коливань складеної двохступеневої пластинки, в якій увігнута частина плавно сполучається з частиною постійної товщини. Окреслено особливості формулювання граничних і перехідних умов, які необхідно дотримуватись при розгляді власних коливань двохступеневої пластинки.Отримано співвідношення, які дозволяють вивчити розподіл прогинів і визначити значення амплітуд згінних коливань пластинки. Зазначено, що форми коливань побудовано на основі положень розроблених та розвинутих раніше авторами методів симетрії та факторизації. Зокрема знайдено, що прогини можна дослідити через вирази, які визначаються через суму відповідних розв’язків двох лінійних диференціальних рівнянь другого порядку зі змінними коефіцієнтами.На основі запропонованого підходу визначено систему з вісьмох однорідних алгебраїчних рівнянь, яка дозволила побудувати частотне рівняння для пластинки, що жорстко закріплена за внутрішнім контуром і є вільною на зовнішньому контурі. Знайдено значення власних частот пластинки для перших трьох форм власних коливань. Причому, задля апробації та для розширення набору пластинок різної конфігурації, розглянуто пластинки з двома видами ввігнутості у їх змінній частині.Нові підходи та отримані на їх основі співвідношення можуть бути корисними для подальшого розвитку методів розв’язку подібних задач математичної фізики на власні значення. Практичним уособленням цього є задачі про коливання пластинок змінної товщини різної форми

The article presents higher vibration modes accounting method to evaluate system seismic resistance by nonlinear static method. As part of the study, in order to verify the proposed method for finding the inertial forces modified system series of dynamic and static calculations was performed. Proposed inertial forces modified system can be applied for seismic resistance estimation of system with elastomeric supports. The results difference varies within 12%.

A method for detecting excitations leading to the damage of the gears and bearings working surfaces has been developed by means of experimental study of the dynamic characteristics of the metro tunnel escalator drive gearbox in normal and bad performance. The technique is based on the acquisition and analysis of low and high resolution spectra. The technique is tested during the analysis of vibration spectra of a standard three-stage, four-shaft tunnel escalator drive gearbox. The vibration analysis was performed using the kinematic excitation frequencies generated by the gears and rolling bearings in the zones of resonance vibrations of the gearbox elements. According to the results of the analysis, the presence of variable stiffness of the teeth in one of the gears and damage of the inner ring of the ball bearing of the intermediate shaft cover is established., На основании экспериментального исследования динамических характеристик редуктора привода эскалатора метрополитена в исправном и поврежденном состояниях разработана методика определения возмущений, которые приводят к повреждениям рабочих поверхностей зубчатых колес и подшипников. Методика базируется на получении и анализе спектров низкой и высокой разрешающей способности. Методика апробирована на анализе спектров вибраций стандартного трёхступенчатого, четырёх-валового редуктора привода туннельного эскалатора. Анализ вибраций проводился по частотах кинематического возмущения, сгенерированного зубчатыми передачами и подшипниками качения в зонах резонансных колебаний элементов редуктора. По результатах анализа установлено наличие сменной жесткости зубцов в одном из зацеплений и повреждения внутреннего кольца шарикоподшипника крышки промежуточного вала., На основі експериментального дослідження динамічних характеристик редуктора приводу ескалатора метрополітену у справному та пошкодженому станах розроблено методику виявлення збурень, що призводять до пошкодження робочих поверхонь зубчастих коліс і підшипників. Методика базується на отриманні та аналізі спектрів низької та високої роздільної здатності. Методика апробована на аналізі спектрів вібрацій стандартного трьохступеневого, чотирьохвалового редуктора приводу тунельного ескалатора. Аналіз вібрацій проводився за частотами кінематичного збурення, генерованого зубчастими передачами і підшипниками кочення в зонах резонансних коливань елементів редуктора. За результатами аналізу встановлено наявність змінної жорсткості зубців у одного з зачеплень та пошкодження внутрішнього кільця кулькового підшипника кришки проміжного валу.

[ES] El contacto rueda/carril es un problema complejo, altamente no-lineal y cuyo carácter fuertemente no-estacionario se revela crucial en fenómenos de alta frecuencia en el ámbito ferroviario, como el desgaste ondulatorio o los chirridos (o squeal) debidos a la acción del freno o al trazado de curvas cerradas. Las ecuaciones que rigen su comportamiento definen zonas de adhesión y de deslizamiento en modelos de elementos de contorno. La zona de adhesión viene determinada por las tracciones tangenciales (variables de estado del sistema), mientras que la de deslizamiento introduce la velocidad de deslizamiento o slip de cada elemento de contorno como nuevas variables de estado en el sistema de ecuaciones. La distinta naturaleza de ambos conjuntos de ecuaciones dificulta la continuidad de la solución, dando curvas de tracción tangencial en forma de dientes de sierra como errores de índole numérica. A la complejidad ya expuesta se le añade la dependencia del coeficiente de fricción con el slip, cuyo comportamiento decreciente actúa como amortiguamiento negativo que reenergiza el sistema, pudiendo contribuir a inestabilidades que pueden asociarse al squeal. Su carácter no-lineal supone pues una dificultad añadida para los solvers numéricos comerciales. Se propone la implementación de un solver robusto y eficiente que permita abordar el problema de contacto no-estacionario considerando fricción variable, fundamental para el desarrollo de modelos de interacción rueda/carril en el dominio de la alta frecuencia., [CA] L’objectiu del present treball de fi de màster és l’estudi de la inestabilitat que es produeix en el contacte roda-rail. Per fer-ho, es desenvolupen models abstractes per analitzar les dues teories principals qu expliquen l’origen físic de la inestabilitat: la basada en el pendent del coeficient de fricció, falling friction i l’acoblament geomètric. Tots dos són capaços d’explicar la inestabilitat que es produeix, i la seua anàlisi es realitza a través del criteri de Lyapunov i dels autovalors del sistema físic associat a cada model de l’estudi. També es duu a terme un estudi minuciós dels paràmetres del problema per estudiar-ne la influència a l’estabilitat del sistema. Finalment, l’efecte conjunt de les dues causes es discuteix breument., [EN] The objective of this master’s thesis is the study of the instability occurring in wheelrail contact. To do so, abstract models are developed to analyze the two main theories on the explanation of the phenomenon, the one based on the slope of the coefficient of friction, and the geometric coupling. Both can explain the instability that occurs, and their analysis is done through the Lyapunov criterion and the real part of the eigenvalues of the physical system associated with each model of the study. A thorough study of the parameters of the problem to study its influence and how they affect the stability of the system in each case has also been carried out. Finally, the joint effect of both causes is briefly discussed.

This paper introduces a method to identify the bending modes of vibration of railway tracks by using a laser Doppler vibrometer (LDV) mounted on a moving platform. Two sets of experiments were conducted at Transportation Technology Center Inc. (TTCI) in Pueblo Colorado, in order to validate the proposed method. First, the bending vibration modes were identified using the signals collected from a rail span (rail section between two consecutive sleepers) by accelerometers under moving car excitation. Then, vibration measurements from rail spans were obtained by using an LDV mounted on the moving railcar. All tests were carried out at four different rail car speeds: 8km/h (5 mph), 16km/h (10 mph), 35km/h (22 mph), and 45km/h (28 mph). To find LDV signal segments corresponding to rail spans, a novel approach based on the sleeper passing frequency is introduced. Comparison of the results from both sets of tests demonstrated good agreement for all speeds.

Введение: статья посвящена математическим моделям для исследования чувствительности колебаний рабочих лопаток энергетических турбомашин на основе метода конечных элементов и также выполнен численный анализ колебаний и чувствительности академических лопаточных структур. Исследование математического моделирования при анализе чувствительности лопатки позволяет значительно уменьшить число дорогостоящих экспериментальных исследований, необходимых для проектирования лопаточных структур энергетических турбомашин, а также сократить время проектирования и увеличить надежность лопаток и облопаченных дисков. Материалы и методы: в данной статье для исследования влияния расстройки параметров на долговечность рабочих колес турбомашин с учетом анализа чувствительности используется метод конечных элементов с применением конечного элемента ТЕТ10 из программного комплекса ANSYS WORKBENCH. Объектом исследования в работе является академическое рабочее колесо компрессора высокого давления с 10-ю лопатками. Результаты и обсуждение: в настоящей работе проведены результаты числено-экспериментального анализа чувствительности лопаток, расчета собственных и вынужденных колебаний академических рабочих колес турбомашин с расстройкой параметров и также показаны преимущества анализа чувствительности лопаток при исследовании долговечности лопаточных структур. Заключение: в данной работе предложен численный анализ чувствительности частот собственных колебаний лопаток облопаченного диска компрессора к внесению дополнительной массы конструкции. На основе анализа чувствительности можно получить уменьшение уровней напряжений и изменение частот колебаний на операционных диапазонах скоростей вращения компрессоров турбомашин, а также увеличить долговечность лопаточных рабочих колес., Introduction: the article is devoted to mathematical models for studying the sensitivity vibrations of the bladed rotor power turbomachines based on the finite element method, and also numerical analysis vibrations and sensitivity of academic bladed structure is carried out. The research of mathematical modeling in sensitivity analysis blades allows you to significantly reduce the number of expensive experimental studies required for the design bladed structures of power turbomachines, as well as reduce the design time and increase the reliability of the bladed disk. Materials and methods: this article uses finite element method and finite element TET10 from ANSYS WORK-BENCH software package to research effect of mistuning parameter on the durability of bladed disk turbomachines with sensitivity analysis. The object of research is an academic high-pressure compressor bladed disk with 10 blades. Results and discussion: in the present work, we performed the results of numerical and experimental sensitivity analysis blades, calculation of natural and forced vibrations of academic bladed disk turbomachines with mistuning parameter, and also this article shows the advantages of analyzing sensitivity of blades in the study of the durability bladed structures. Conclusion: in this paper, we propose a numerical sensitivity analysis of the natural vibration frequencies compressor bladed disk with bringing additional mass into the structure. Based on the sensitivity analysis, it is possible to obtain a reduction in stress levels and change in vibration frequencies at the operating speed ranges of turbomachines, as well as to increase the durability of bladed disks.

The dynamic behavior of tubular steel wind turbine towers is investigated, with emphasis on discussing how the effort to avoid resonance of the soil-foundation-tower system, by keeping its eigenfrequencies outside specific ranges around the rotor (1P) and blade-passing (3P) frequencies, influences tower optimization. For modern, tall towers avoidance of resonance becomes critical compared to other structural design checks, such as buckling and fatigue. Considering that the rotor and blades have predefined mass and rotation frequencies, the tower’s fundamental frequencies should be controlled considering the cross-sectional properties of the tower as well as the flexibility of its foundation. The objective of the optimization problem formulated in this work is to reduce tower weight, while satisfying the resonance and buckling criteria and considering restrictions pertaining to fabrication, transportation and erection. The vibration modes and frequencies of a 120m tall tower are determined via detailed as well as simplified finite element models, with the latter proving to be sufficiently accurate. The dependence of the tower’s vibration frequencies on the soil and foundation is also investigated. The numerical models are introduced into the high performance optimization computing platform (HP-OCP), to obtain an optimum distribution of tower shell thickness over the height.

[ES] Los engranajes planetarios son usados en un amplio rango de sectores como el automovilísti-co, el de los aerorreactores o el de los aerogeneradores, debido fundamentalmente a su alta densidad de potencia y grado de compacidad. Para sacar partido a la ventaja de los engrana-jes helicoidales en términos de menores esfuerzos, evitando la absorción de fuerzas axiales por parte de los cojinetes, los engranajes helicoidales dobles representan una solución viable. Con el propósito de estudiar el comportamiento dinámico de tales sistemas de engranajes, se desarrolla un modelo analítico paramétrico para obtener las frecuencias naturales y modos de vibración de engranajes planetarios con número variable de satélites y distinta geometría. Tal modelo incluye la posibilidad de definir errores comunes de fabricación y ensamblado, como excentricidades en el planeta o en la corona, errores de posicionamiento de los satélites y errores en la geometría. Se evalúan, a través del modelo desarrollado, la excitación y el comportamiento dinámico de un engranaje de cinco satélites, empleado en el banco de en-sayo de engranajes del Gear Research Centre. Los resultados obtenidos se comparan con las medidas experimentales de las aceleraciones en el banco de ensayo, para validar el mo-delo analítico., [EN] Planetary gear sets are used in a wide range of applications such as in the automotive sector, aircraft engines and wind turbines due to the high-power density and compactness. To utilize the advantage of helical gears in terms of less mesh excitation but to avoid a bearing ar-rangement for absorbing axial forces, double-helical gear sets represent a suitable solution. In terms of comfort and operational safety, it is mandatory to investigate the dynamic behavior of such gearboxes. For this purpose, a parametric analytical model to calculate the eigenfre-quencies and eigenmodes of planetary gear sets with variable planet number and gear geom-etry will be developed. This model includes the possibility to define common manufacturing and assembly errors, such as eccentricities of sun gear, ring gear or carrier, planet positioning errors and gear geometry errors. The excitation and vibration behavior of a double-helical planetary gear set with five planets, that is also used in the FZG (Gear Research Centre) planetary gearbox back-to-back test rig, will also be evaluated with the developed model. Calculation results are compared with experimental measurement of the acceleration from the test rig to validate the analytical model.

Nowadays, the guitar is one of the most popular musical instruments all over the world. We can find a great number of models with a wide range of acoustic quality, depending on the way the guitar has been built. The guitar luthiers need to know how to control certain acoustic attributes depending on the type of instrument they want to make. Currently, most luthiers check these acoustic features by analysing the vibration modes and trying to tune them to certain frequencies. To analyse these modes, one of the most used techniques is to analyse the spectrum of the impulsive response by recording a guitar tapped just below its bridge. Although the vibration modes are very important for the final sound of the guitar, there are many more elements that affect the different characteristics that compose the timbre. In this master thesis, developed in the context of the company MIIL–Musical Instruments Innovation Lab, we have created a computing tool named GIRAS-Guitar Impulse Response Analysis Software. This software allows us to record impulsive responses of guitars, using the technique explained above, and analyse them to obtain new acoustic parameters in addition to the vibration modes, with the aim that these can be used to define the timbre of the instrument. The acoustic parameters we have extracted from the impulsive response have been: the vibration modes, attack time, decay time, vibration sensitivity, centroid, low-to-high frequency ratio and MFCC. To verify if all these computations are related to any timbre feature of the guitar, a small experiment has been made using 5 classical guitars and 4 guitarists, where each of the guitarists had to evaluate the timbre of the guitars according to certain characteristics such as attack, sustain, intelligibility, warmness, balance, volume and dynamic range. After measuring these 5 guitars with our programme, the results are that there are some parameters such as the vibration modes, the attack time, the decay time and the low-to-high frequency ratio, which are clear about their influence on the timbre, and others in which a deeper research and an improvement of the methodology followed is needed to know if they can help to describe the timbre. The most important conclusion of this project is that we have created a software that makes much easier the research on the guitar timber.

A mathematical model of parametric oscillations in the planetary wheel gearboxes (PWG) of the trolley buses has been developed. The model takes into account the cyclic deformations of a thin-walled rim and teeth in the meshing of the epicycle with the satellites. The differential equation of the oscillations of the epicycle is reduced to the form of the Mathieu-Hill equations with variable periodic coefficients. On the basis of the Ains-Strett diagram, regions of instability of parametric oscillations of the "criteria element" – a thin-walled epicycle for spur and helical gears are determined, taking into account the influence of gaps in the gears. The ranges of values of the critical velocities of the trolley buses corresponding to the manifestation of the first three parametric resonances of the PWG epicycle in the structure of the traction bridges of the 1st and 3rd generations of well-known manufacturing companies are established. The criterion of the vibration stability of the epicycle is substantiated, the calculated values of the probabilities of parametric resonances are established. Theoretically, the positive effect of helical engagement in PWG has been confirmed, which provides a minimum depth of hardness pulsation, a narrowing of the instability region of parametric oscillations of the epicycle, reduces the probability of nucleation and development of fatigue cracks., Разработана математическая модель параметрических колебаний в планетарных колесных редукторах (ПКР) троллейбусов. Модель учитывает циклические деформации тонкостенного обода и зубьев в зацеплении эпицикла с сателлитами. Дифференциальное уравнение колебаний эпицикла приведено к виду уравнений Матье-Хилла с переменными периодическими коэффициентами. На основании диаграммы Айнса-Стретта определены области неустойчивости параметрических колебаний "критериального элемента" – тонкостенного эпицикла для прямозубых и косозубых передач с учетом влияния зазоров в зацеплениях. Установлены диапазоны значений критических скоростей движения троллейбусов, соответствующие проявлению первых трех параметрических резонансов эпицикла ПКР в составе конструкций ведущих мостов 1-го и 3-го поколений известных фирм-производителей. Обоснован критерий виброустойчивости эпицикла, установлены расчетные значения вероятности параметрических резонансов. Теоретически подтвержден положительный эффект от применения косозубого зацепления в ПКР, что обеспечивает минимальную глубину пульсации жесткости, сужение области неустойчивости параметрических колебаний эпицикла, уменьшает вероятность зарождения и развития усталостных трещин.

In this study, a precision motion stage, whose design utilizes a single shaft supported from the bottom by an air bearing and voice coil actuators in complementary double configuration, is evaluated for its dynamic properties, motion accuracy, and potential machining force response, through modal testing, laser interferometric metrology, and spectral analysis, respectively. Modal testing is carried out using two independent methods, which are both based on impact hammer testing. Results are compared with each other and with the predicted natural frequencies based on design calculations. Laser interferometry has been used with varying optics to measure the geometric errors of motion. Laser interferometry results are merged with measured servo errors, estimated thermal errors, and the predicted dynamic response to machining forces, to compile the error budget. Overall accuracy of the stage is calculated as peak-to-valley 5.7 μm with a 2.3 μm non-repeatable part. The accuracy measured is in line with design calculations which incorporated the accuracy grade of the encoder scale and the dimensional tolerances of structural components. The source of the non-repeatable errors remains mostly equivocal, as they fall in the range of random errors of measurement in laser interferometry like alterations of the laser wavelength due to air turbulence.

U ovom se radu predlože teoretska metoda koja omogućuje određivanje oblika titranja okvirnih AB građevina s identičnim katovima ili s prvim ili zadnjim katom različitim od ostalih. Kao rezultat istraživanja, tablično su prikazani svi prirodni oblici titranja građevina s dva do deset identičnih katova. Ti se rezultati mogu proširiti na veći broj katova (više od deset). Predlaže se i matematička metoda za određivanje karakterističnih koeficijenata polinoma za posebnu trodijagonalnu matricu, A theoretical method allowing determination of vibration modes for RC frame structures with identical floors, or with either the first or the last floor differing from other floors, is proposed in the paper. As a result of the research, all natural vibration modes for buildings with two to ten identical storeys are presented in a table. These results can be extended to include a greater number of floors (more than ten). A mathematical method for determining characteristic polynomial coefficients of a specific tridiagonal matrix is also proposed.

Trabalho final de mestrado elaborado no Laboratório Nacional de Engenharia Civil (LNEC) para a obtenção do grau de mestre em Engenharia Civil pelo Instituto Superior de Engenharia de Lisboa no âmbito do protocolo de cooperação entre o ISEL e o LNEC A reabilitação de estruturas tem vindo a assumir uma importância crescente, nomeadamente por razões económicas. Para caracterização do estado de degradação das estruturas existentes utilizam-se preferencialmente métodos não invasivos, assumindo especial relevância os ensaios de vibração ambiente que permitem determinar os principais parâmetros modais, com base nos denominados métodos de identificação modal. Os parâmetros modais (frequências próprias, amortecimentos e modos de vibração) estão diretamente relacionados com as reais condições de conservação/deterioração das estruturas, pois dependem das suas características de rigidez, massa e amortecimento. Os métodos de identificação modal dividem-se em duas categorias principais, métodos no domínio da frequência e métodos no domínio do tempo, abordando-se neste trabalho apenas os métodos no domínio do tempo. Quanto aos métodos no domínio do tempo, apresenta-se inicialmente o denominado Método da Máxima Verosimilhança (MMV), implementado, neste caso, apenas para sistemas completamente observados. No caso de sistemas parcialmente observados implementou-se, o método Covariancedriven, Stochastic Subspace Identification method (SSI-Cov). Neste trabalho foram inicialmente implementados, em MATLAB, os referidos métodos no domínio do tempo, MMV e SSI-Cov, os quais foram testados na análise de estruturas simples do tipo edifícios de N pisos, considerando situações de estruturas completamente observadas. Posteriormente o método SSI-Cov foi aplicado a casos de estruturas simples, mas considerando situações de estruturas parcialmente observadas. Por fim, o método SSI-Cov é testado na barragem do Cabril, primeiro com base em registos gerados numericamente, recorrendo a um modelo de elementos finitos da barragem (considerando excitação do tipo ruído branco) e, em seguida, o método é utilizado para a análise de registos reais de vibrações medidas na barragem do Cabril, com um sistema de monitorização de vibrações em contínuo, instalado em obra desde 2008. The rehabilitation of structures is becoming increasingly important, for economic reasons. In order to characterize the degradation state of existing structures, non-invasive methods are preferred. Ambient vibration tests are used to determine the main modal parameters, based on the so-called modal identification methods. Modal parameters (own frequencies, damping and vibration modes) are directly related to the actual conditions of conservation / deterioration of the structures, since they depend on their characteristics of rigidity, mass and damping. The methods of modal identification are divided into two main categories - methods in the frequency domain and time-domain methods, being the latter, i. e., time-domain methods, the only ones used in this work. As for the methods in the time domain, the so-called Maximum Likelihood Method (MLM) is initially introduced, implemented in this case only for fully observed systems. In the case of partially observed systems, the Covariance-driven, Stochastic Subspace Identification method (SSI-Cov) was implemented. This work is divided into two phases. In a first phase, the time domain methods MLM and SSICov in MATLAB are implemented, in order to study simple structures, such as N-storey buildings, in cases of completely observed structures. Subsequently, the SSI-Cov method is applied to simple structures, but considering these as partially observed. Finally, and as a main objective, this work intends to contribute to the development and use of the modal identification methods of structures in large dams, in the time domain, in the perspective of their use in the analysis of vibrations, due to environmental excitation. Thus, the SSI-Cov method is tested on the Cabril dam, based on numerically generated records, using a finite element model of the dam (considering white noise type excitation), and then the method is used for the analysis of actual vibration records measured at the Cabril dam, with a continuous vibration monitoring system, installed on site since 2008. N/A

The vibration of robot joint reducer is the main factor that causes vibration or motion error of robot system. To improve the dynamic precision of robot system, the cycloid ball transmission used in robot joint is selected as study object in this paper. An efficient dynamic modelling method is presented—lumped stiffness method. Based on lumped stiffness method, a translational–torsional coupling dynamics model of cycloid ball transmission system is established. Mesh stiffness variation excitation, damping of system are all intrinsically considered in the model. The dynamic equation of system is derived by means of relative displacement relationship among different components. Then, the natural frequencies and vibration modes of the derivative system are presented by solving the associated eigenvalue problem. Finally, the influence of the main structural parameters on the natural frequency of the system is analysed. The present research can provide a new idea for dynamic analysis of robot joint reducer and provide a more simplify dynamic modelling method for robot system with joint reducer.

Introducción: En el artículo se da una breve introducción al problema de las vibraciones de baja frecuencia, describiendo como éstas son generadas por el caminar humano y a su vez afectan la estructura del puente peatonal; y porque al final se ven traducidas en una molestia para los usuarios.Objetivo: El documento explica el método comúnmente usado por los ingenieros para la evaluación del efecto de las vibraciones y sus limitaciones, optando por desarrollar una técnica de modelado por computador que represente de manera más aproximada a la realidad el fenómeno de vibraciones de piso en puentes peatonales.Metodología: El estudio está compuesto por dos fases principales: 1) una revisión bibliográfica conceptual al tema de vibraciones de piso enfatizando en la Guía de Diseño No. 11 del Instituto Americano de Construcciones de Acero y 2) se desarrolla el modelo por computador que a su vez comprende: definición de variables, elaboración del modelo dinámico de la estructura, calibración del modelo, evaluación de los parámetros objeto de estudio, análisis de resultados y conclusiones.Resultados: Consecuentemente y conforme con las etapas preliminares se obtienen los resultados de la aceleración para diferentes frecuencias y para diferentes grados de amortiguamiento, observando que el puente de estudio es potencialmente susceptible entre los rangos de 4 a 8 HZ; y que, al entrar resonancia, la estructura presenta una aceleración pico muy superior al umbral para la comodidad humana recomendada en puentes peatonales. Conclusiones: Al respecto se aprecia cómo con el uso de buenas técnicas de modelación y de elementos finitos pueden llegar a obtenerse resultados confiables y que acompañen de manera directa el proceso de diseño de estructuras en este caso puentes peatonales. Introduction− The present article is aimed to present a brief introduction of the issues related to the low frequency vibrations, by indicating human walk-ing as its relevant source which affecting structures of the footbridges and are turned into inconveniences to the pedestrian traffic.Objective−The main objective of this research paper is to explains the most common methods used by engineers for the evaluation of the vibrations and their effects as well as their limitations, furthermore a computer modeling technique was developed in order to approach it to the reality of the phenom-enon of vibrations in pedestrian bridges. Methodology−The present work was divided into main phases: The first phase was a conceptual bibliographical review of the subject of floor vibrations by focusing on the use of the Design Guide No. 11 of the American Institute of Steel Constructions, with regard to the second phase it had to do with the developing of a computer model which included a definition of variables, the elaboration of a dynamic model of the structure, the calibration of the model, the evaluation of the parameters under study and the analysis of results and conclusions. Results−Consequently, and according to the preliminary stages, the results of the acceleration were obtained to different frequencies and to different de-grees of damping by observing that the chosen sample was potentially suscep-tible between four and eight Hz ranges, hence when resonances took place the mentioned structure presented a peak acceleration above the threshold recom-mended by human beings comfort related to pedestrian bridges. Conclusions−To conclude it can be said that through the appropriate model-ing techniques and finite elements convenient and reliable results should be accomplish that leading the design process of structures as pedestrian bridges.

The natural dynamics are not ideal or linear. To understand their complex behavior, we needs to study the nonlinear dynamics in more simple models. This thesis is consist of two main setups. Both setups are simplified models for the behavior occurs in the complex systems. We studied in both systems the same nonlinear dynamics such as higher-harmonics, sub-harmonics, solitary waves,...etc. In Chapter (2), the propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly in influenced by dispersion. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of FPU equation, describing a chain of masses connected by nonlinear quadratic springs. The results can be extrapolated to other systems described by this equation. We studied theoretically and experimentally the generation and propagation of kinks in the system. We excite pulses at one boundary of the system and demonstrate the existence of kinks, whose properties are in very good agreement with the theoretical predictions, that is the equation that approaches, under the conditions of our experiments, the one corresponding to full model describing a chain of masses connected by magnetic forces. The results can be extrapolated to other systems described by this equation. Also, In the case of a lattice of finite length, where standing waves are formed, we report the observation of subharmonics of the driving wave. In chapter (3), we studied the propagation of intense acoustic waves in a multilayer crystal. The medium consists in a structured fluid, formed by a periodic array of fluid layerswith alternating linear acoustic properties and quadratic nonlinearity coefficient. We presents the results for different mathematicalmodels (NonlinearWave Equation,Westervelt Equation and Constitutive equations). We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g. cubic) nonlinearities, or extremely linear media. In chapter (4), the oscillatory behavior of a microbubble is investigated through an acousto-mechanical analogy based on a ring-shaped chain of coupled pendula. Observation of parametric vibration modes of the pendula ring excited at frequencies between 1 and 5 Hz is considered. Simulations have been carried out and show spatial mode, mixing and localization phenomena. The relevance of the analogy between a microbubble and the macroscopic acousto-mechanical setup is discussed and suggested as an alternative way to investigate the complexity of microbubble dynamics., La dinámica natural no es ideal ni lineal. Para entender su comportamiento complejo, necesitamos estudiar la dinámica no lineal en modelos más simples. Esta tesis consta de dos configuraciones principales. Ambas configuraciones son modelos simplificados de el comportamiento que se produce en los sistemas complejos. Estudiamos en ambos sistemas la misma dinámica no lineal como son la generación de armónicos superiores, los sub-armónicos, las ondas solitarias, etc. En elCapítulo (2), se estudia, tanto teórica comoexperimentalmente, la propagación de ondas no lineales en sistemas periodicos de partículas acopladas mediante fuerzas repulsivas. Se propone una configuración experimental simple, que consiste en una matriz de dipolos magnéticos acoplados. Inyectando armónicamente la señal en un extremo, excitamos ondas de propagación y demostramos diferentes regímenes de conversión de modos en armónicos, fuertemente influenciados por la dispersión. También se predice y se discute el fenómeno de dilatación acústica de la cadena. Los resultados se comparan con las predicciones teóricas de la ecuación FPU, describiendo una cadena de masas conectadas por muelles cuadráticos no lineales. Los resultados pueden ser extrapolados a otros sistemas descritos por esta ecuación. Estudiamos también teórica y experimentalmente la generación y propagación de kinks. Excitamos pulsos en la frontera del sistema y demostramos la existencia de kinks cuyas propiedades están en muy buen acuerdo con las predicciones teóricas, es decir, con la ecuación que aproxima bajo las condiciones de nuestros experimentos la correspondiente al modelo completo que describe un cadena de masas conectadas por fuerzas magnéticas. Los resultados pueden ser extrapolados a otros sistemas descritos por esta ecuación. Además, en el caso de una red finita, donde se forman ondas estacionarias, describimos la observación de subarmónicos del armónico principal. En el capítulo (3), estudiamos la propagación de ondas acústicas intensas en un cristal multicapa. El medio consiste en un fluido estructurado, formado por un conjunto periódico de capas fluidas con propiedades acústicas lineales alternas y coeficiente de no linealidad cuadrática. Presentamos los resultados de diferentes modelos matemáticos (ecuación de ondas no lineal, ecuación de Westervelt y ecuaciones constitutivas). Mostramos que la interacción entre la fuerte dispersión y la no linealidad conduce a nuevos escenarios de propagaciónde ondas. El proceso de distorsión de la onda clásica, típico de las ondas acústicas intensas en medios homogéneos, puede ser alterado de forma importante cuando los armónicos generados no linealmente se encuentran dentro o cerca del gap. Esto permite la posibilidad de diseñar un medio con el fin de obtener una forma de onda en particular. Ejemplos de esto incluyen el diseño demedios con no linealidad efectiva (por ejemplo, cúbica) o medios extremadamente lineales. En el capítulo (4), el comportamiento oscilatorio de una microburbuja se investiga a través de una analogía acusto-mecánica basada en una cadena en forma de anillo de péndulos acoplados. Se estudian los modos de vibración paramétrica del anillo pendular excitado a frecuencias entre 1 y 5 Hz. Se han llevado a cabo simulaciones que muestran la presencia de modos espaciales, mixtos y fenómenos de localización. Se discute la relevancia de la analogía entre una microburbuja y la configuración macroscópica acústico-mecánica y se sugiere como una vía alternativa para investigar la complejidad de la dinàmica de microburbujas., La dinàmica natural no és ideal ni tampoc lineal. Per entendre el seu comportament complex, es necessita estudiar la dinàmica no lineal dels models més simples. Aquesta tesi consisteix en l'estudi de dues configuracions principals, que són models simplificats del comportament que es produeix en els sistemes complexos. Estudiem en ambdós sistemes la mateixa dinàmica no lineal, com és la generació d'harmònics superiors, sub-harmònics, ones solitàries, etc. En el capítol (2), estudiem, tant teòrica com experimentalment, la propagació de les ones no lineals en sistemes periòdics de partícules acoblades mitjançant forces repulsives. Es proposa una configuració experimental simple, que consisteixen en una matriu de dipols magnètics acoblats. En conduint harmònicament la xarxa en un límit, excitemla propagació de les ones i demostrem diferents règims de conversió de modes en harmònics més alts, força influenciada per la dispersió. El fenomen de la dilatació acústica de la cadena també es prediu i es discuteix. Els resultats es comparen amb les prediccions teòriques que descriu una cadena de masses conectades per molls quadràtics no lineals. Els resultats es poden extrapolar a altres sistemes descrits per aquesta equació. Hem estudiat teòrica i experimentalment la generació i propagació de Kinks. Excitem polsos a la frontera del sistema i demostrem l'existència d'Kinks, les propietats desl quals estan en molt bon acord amb les prediccions teòriques, és a dir, de l'equació que aproxima sota les condicions dels nostres experiments la corresponent al model complet que descriu un cadena demasses connectades per forcesmagnètiques. Els resultats es poden extrapolar a altres sistemes descrits per aquesta equació. A més, en el cas d'una xarxa finita, on es formen ones estacionàries, descrivim l'observació de subarmónicos de l'harmònic principal. En el capítol (3), s'estudia la propagació d'ones acústiques intenses en un medi multicapa. El medi consisteix en un fluid estructurat, format per una matriu periòdica de capes de fluid amb l'alternança de propietats acústiques lineals i coeficient de no linealitat de segon grau. Es presenten els resultats per a diferents models matemàtics no lineals (equació d'ones no lineal, equació de Westervelt i les equacions constitutives). Es demostra que la interacciò entre la forta dispersió i no linealitat condueix a nous escenaris de propagació de l'ona. El procés de distorsió en formad'ona clàssica, típica de les ones acústiques intenses en medis homogenis, es pot alterar de manera significativa quan els harmònics generats de forma no lineal es troben dins o a prop del gap. Això obri la possibilitat de dissenyar unmedi per tal d'obtenir una forma d'ona particular. Exemples d'això inclouen el disseny delsmedis amb una no linealitat efectiva (per exemple cúbica), o medis extremadament lineals. En el capítol (4), el comportament oscilatori d'una micro-bombolla és investigat a través d' una analogia acústica-mecànica basada en una cadena en forma d'anell de pèndols acoblats. Es considera l'observació dels modes de vibració paramètriques de l'anell pendular excitat amb freqüències entre 1 i 5 Hz. S'han dut a terme simulacions que mostren la presència de moes espacilas, mixtes i fenòmens de localització. Es discuteix la relevància de l'analogia entre les microbambolles i la configuració macroscòpica acústica-mecànica i es suggereix una formaalternativa per a investigar la complexitat de la dinàmica demicrobombolles.

paper 806 ORAL; International audience; In this work an analytical model for the energy harvesting of an acoustic spherical sensor has been developed in the context to make it autonomous. Our spherical sensor is composed of two half-spheres of Plexiglas and a piezoelectric ring of PZ26 that can be used as exciter or sensor. For the analytical model, the piezoelectric ring was modeled using two primary modes of vibration: thickness and radial. For each mode, the ring is described by an equivalent electromechanical model which connects the mechanical part (forces and velocities) to the electrical part (voltage and current). The proposed paper theoretical model enables building a global electromechanical circuit in order to simulate the total harvested voltage response.

A reliable procedure to identify the dynamic behaviour of existing masonry buildings is described in the paper, referring to a representative case study: a historical masonry palace located in Benevento (Italy). Since the building has been equipped with a permanent dynamic monitoring system by the Department of Civil Protection, some of the recorded data, acquired in various operating conditions, have been analysed with basic instruments of the Operational Modal Analysis in order to identify the main eigenfrequencies and vibration modes of the structure. The obtained experimental results have been compared to the numerical outcomes provided by three detailed Finite Element (FE) models of the building. The influence of Soil-Structure Interaction (SSI) has been also introduced in the FE model by a sub-structure approach where concentrated springs were placed at the base of the building to simulate the effect of soil and foundation on the global dynamic behaviour of the structure. The obtained results evidence that subsoil cannot a priori be disregarded in identifying the dynamic response of the building.

The paper focuses on the vibration analysis of a vehicle equipped with two identical engines. Such solutions are encountered in practice when less power is needed for a vehicle for a certain period of time and then greater power the rest of the time. An example of this would be a mobile drilling rig. During transport (a relatively short period of time) only one engine operates and then, in service (most of the operating time), both engines operate. A characteristic of such an aggregate is the existence, within the transmission, of two identical engines. The existence of identical parts in mechanical systems leads to properties that allow the computations to be simplified in order to obtain suggestive and rapid results, with reduced computation effort. These properties refer to the eigenvalues and eigenmodes of vibration for these types of systems and have been stated and demonstrated in the paper. It also allows for a qualitative analysis of the behavior of the system in case of vibrations. The existence of these properties allows for easier calculation and shortening of the design time. The mechanical consequences of the existence of symmetries or identical parts have begun to be studied in more detail in the last decade (see references), and the work is part of these trends. The vibration properties of a transmission of a truck with two identical engines have been stated and proven and a real example is analyzed. Two 215 hp engines were used in the application. In order to establish a useful solution in practice, two constructive variants with a different clutch position in the transmission are analyzed in parallel.