Numerical and experimental investigation of a vibration system with non-ideal vibration source

An excitation force that is not influenced by the system's states is said to be an ideal energy source. In real situations, a direct and feedback coupling between the excitation source and the system must always exist. This manifestation of the law of conversation of energy is known as Sommerfeld Effect. In the case of obtaining a mathematical model for such system, additional equations are usually necessary to describe the vibration sources and their coupling with the mechanical system. In this work, a cantilever beam and a non-ideal electric DC motor that is fixed to the beam free end is analyzed. The motor has an unbalanced mass that provides excitation to the system proportional to the current applied to the motor. During the motor's coast up operation, as the excitation frequency gets closer to the beam first natural frequency and if the drive power increases further, the DC motor speed remains constant until it suddenly jumps to a much higher value (simultaneously the vibration amplitude jumps to a much lower value) upon exceeding a critical input power. It was found that the Sommerfeld effect depends on some system parameters and the motor operational procedures. These parameters are explored to avoid the resonance capture in Sommerfeld effect. Numerical simulations and experimental tests are used to help insight this dynamic behavior.

Análise dinâmica não-linear de um sistema não-ideal, utilizando amortecedor magneto-reológico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Controle das propriedades dinâmicas de sistemas mecânicos através da utilização de molas inteligentes

Pós-graduação em Engenharia Mecânica - FEIS

Análise de ordem de uma bancada experimental aplicada ao estudo de rotores

In this work the main concepts to apply to dynamic signal analysis technique for rotating machines known as order analysis, discussing their characteristics and applying it on an experimental test rig. It aims to characterize the dynamic behavior of experimental test rig in run up and run down tests, it's operational speed range and the identification of the critical speed of shaft rotation. The results of the critical speed and stationary natural frequency of the shaft are discussed

Análise de ordem de uma bancada experimental aplicada ao estudo de rotores

In this work the main concepts to apply to dynamic signal analysis technique for rotating machines known as order analysis, discussing their characteristics and applying it on an experimental test rig. It aims to characterize the dynamic behavior of experimental test rig in run up and run down tests, it's operational speed range and the identification of the critical speed of shaft rotation. The results of the critical speed and stationary natural frequency of the shaft are discussed

Conditions for the validity of the quantum Langevin equation

From microscopic models, a Langevin equation can, in general, be derived only as an approximation. Two possible conditions to validate this approximation are studied. One is, for a linear Langevin equation, that the frequency of the Fourier transform should be close to the natural frequency of the system. The other is by the assumption of "slow" variables. We test this method by comparison with an exactly soluble model and point out its limitations. We base our discussion on two approaches. The first is a direct, elementary treatment of Senitzky. The second is via a generalized Langevin equation as an intermediate step.

Prediseño de modelos a escala para el estudio de fenómenos dinámicos de interacción suelo-estructura en aerogeneradores off-shore sobre monopilotes

Máster Universitario en Eficiencia Energética (SIANI)

Sulla progettazione in zona sismica di strutture dotate di dissipatori fluido-viscosi: proposta di una metodologia

CHAPTER 1:FLUID-VISCOUS DAMPERS In this chapter the fluid-viscous dampers are introduced. The first section is focused on the technical characteristics of these devices, their mechanical behavior and the latest evolution of the technology whose they are equipped. In the second section we report the definitions and the guide lines about the design of these devices included in some international codes. In the third section the results of some experimental tests carried out by some authors on the response of these devices to external forces are discussed. On this purpose we report some technical schedules that are usually enclosed to the devices now available on the international market. In the third section we show also some analytic models proposed by various authors, which are able to describe efficiently the physical behavior of the fluid-viscous dampers. In the last section we propose some cases of application of these devices on existing structures and on new-construction structures. We show also some cases in which these devices have been revealed good for aims that lies outside the reduction of seismic actions on the structures. CHAPTER 2:DESIGN METHODS PROPOSED IN LITERATURE In this chapter the more widespread design methods proposed in literature for structures equipped by fluid-viscous dampers are introduced. In the first part the response of sdf systems in the case of harmonic external force is studied, in the last part the response in the case of random external force is discussed. In the first section the equations of motion in the case of an elastic-linear sdf system equipped with a non-linear fluid-viscous damper undergoing a harmonic force are introduced. This differential problem is analytically quite complex and it’s not possible to be solved in a closed form. Therefore some authors have proposed approximate solution methods. The more widespread methods are based on equivalence principles between a non-linear device and an equivalent linear one. Operating in this way it is possible to define an equivalent damping ratio and the problem becomes linear; the solution of the equivalent problem is well-known. In the following section two techniques of linearization, proposed by some authors in literature, are described: the first technique is based on the equivalence of the energy dissipated by the two devices and the second one is based on the equivalence of power consumption. After that we compare these two techniques by studying the response of a sdf system undergoing a harmonic force. By introducing the equivalent damping ratio we can write the equation of motion of the non-linear differential problem in an implicit form, by dividing, as usual, for the mass of the system. In this way, we get a reduction of the number of variables, by introducing the natural frequency of the system. The equation of motion written in this form has two important properties: the response is linear dependent on the amplitude of the external force and the response is dependent on the ratio of the frequency of the external harmonic force and the natural frequency of the system only, and not on their single values. All these considerations, in the last section, are extended to the case of a random external force. CHAPTER 3: DESIGN METHOD PROPOSED In this chapter the theoretical basis of the design method proposed are introduced. The need to propose a new design method for structures equipped with fluid-viscous dampers arises from the observation that the methods reported in literature are always iterative, because the response affects some parameters included in the equation of motion (such as the equivalent damping ratio). In the first section the dimensionless parameterε is introduced. This parameter has been obtained from the definition of equivalent damping ratio. The implicit form of the equation of motion is written by introducing the parameter ε, instead of the equivalent damping ratio. This new implicit equation of motions has not any terms affected by the response, so that once ε is known the response can be evaluated directly. In the second section it is discussed how the parameter ε affects some characteristics of the response: drift, velocity and base shear. All the results described till this point have been obtained by keeping the non-linearity of the behavior of the dampers. In order to get a linear formulation of the problem, that is possible to solve by using the well-known methods of the dynamics of structures, as we did before for the iterative methods by introducing the equivalent damping ratio, it is shown how the equivalent damping ratio can be evaluated from knowing the value of ε. Operating in this way, once the parameter ε is known, it is quite easy to estimate the equivalent damping ratio and to proceed with a classic linear analysis. In the last section it is shown how the parameter ε could be taken as reference for the evaluation of the convenience of using non-linear dampers instead of linear ones on the basis of the type of external force and the characteristics of the system. CHAPTER 4: MULTI-DEGREE OF FREEDOM SYSTEMS In this chapter the design methods of a elastic-linear mdf system equipped with non-linear fluidviscous dampers are introduced. It has already been shown that, in the sdf systems, the response of the structure can be evaluated through the estimation of the equivalent damping ratio (ξsd) assuming the behavior of the structure elastic-linear. We would to mention that some adjusting coefficients, to be applied to the equivalent damping ratio in order to consider the actual behavior of the structure (that is non-linear), have already been proposed in literature; such coefficients are usually expressed in terms of ductility, but their treatment is over the aims of this thesis and we does not go into further. The method usually proposed in literature is based on energy equivalence: even though this procedure has solid theoretical basis, it must necessary include some iterative process, because the expression of the equivalent damping ratio contains a term of the response. This procedure has been introduced primarily by Ramirez, Constantinou et al. in 2000. This procedure is reported in the first section and it is defined “Iterative Method”. Following the guide lines about sdf systems reported in the previous chapters, it is introduced a procedure for the assessment of the parameter ε in the case of mdf systems. Operating in this way the evaluation of the equivalent damping ratio (ξsd) can be done directly without implementing iterative processes. This procedure is defined “Direct Method” and it is reported in the second section. In the third section the two methods are analyzed by studying 4 cases of two moment-resisting steel frames undergoing real accelerogramms: the response of the system calculated by using the two methods is compared with the numerical response obtained from the software called SAP2000-NL, CSI product. In the last section a procedure to create spectra of the equivalent damping ratio, affected by the parameter ε and the natural period of the system for a fixed value of exponent α, starting from the elasticresponse spectra provided by any international code, is introduced.

Operational Modal Analysis: the CEME Skywalk at UBC, Vancouver

Slender and lighter footbridges are becoming more and more popular to meet the transportation demand and the aesthetical requirements of the modern society. The widespread presence of such particular structures has become possible thanks to the availability of new, lightweight and still capable of carrying heavy loads material . Therefore, these kind of structure, are particularly sensitive to vibration serviceability problems, especially induced by human activities. As a consequence, it has been imperative to study the dynamic behaviour of such slender pedestrian bridges in order to define their modal characteristics. As an alternative to a Finite Element Analysis to find natural frequencies, damping and mode shape, a so-called Operational Modal Analysis is a valid tool to obtain these parameters through an ambient vibration test. This work provides a useful insight into the Operational Modal Analysis technique and It reports the investigation of the CEME Skywalk, a pedestrian bridge located at the University of British Columbia, in Vancouver, Canada. Furthermore, human-induced vibration tests have been performed and the dynamic characteristics derived with these tests have been compared with the ones from the ambient vibration tests. The effect of the dynamic properties of the two buildings supporting the CEME Skywalk on the dynamic behaviour of the bridge has been also investigated.

Planetary Gear Modal Vibration Experiments and Correlation against Lumped-Parameter and Finite Element Models

Experimental modal analysis techniques are applied to characterize the planar dynamic behavior of two spur planetary gears. Rotational and translational vibrations of the sun gear, carrier, and planet gears are measured. Experimentally obtained natural frequencies, mode shapes, and dynamic response are compared to the results from lumped-parameter and finite element models. Two qualitatively different classes of mode shapes in distinct frequency ranges are observed in the experiments and confirmed by the lumped-parameter model, which considers the accessory shafts and fixtures in the system to capture all of the natural frequencies and modes. The finite element model estimates the high-frequency modes that have significant tooth mesh deflection without considering the shafts and fixtures. The lumped-parameter and finite element models accurately predict the natural frequencies and modal properties established by experimentation. Rotational, translational, and planet mode types presented in published mathematical studies are confirmed experimentally. The number and types of modes in the low-frequency and high-frequency bands depend on the degrees of freedom in the central members and planet gears, respectively. The accuracy of natural frequency prediction is improved when the planet bearings have differing stiffnesses in the tangential and radial directions, consistent with the bearing load direction. (C) 2012 Elsevier Ltd. All rights reserved.

Investigating the Effects of Various Crowd Characteristics on the Dynamic Properties of an Occupied Structure

One of the challenges for structural engineers during design is considering how the structure will respond to crowd-induced dynamic loading. It has been shown that human occupants of a structure do not simply add mass to the system when considering the overall dynamic response of the system, but interact with it and may induce changes of the dynamic properties from those of the empty structure. This study presents an investigation into the human-structure interaction based on several crowd characteristics and their effect on the dynamic properties of an empty structure. The dynamic properties including frequency, damping, and mode shapes were estimated for a single test structure by means of experimental modal analysis techniques. The same techniques were utilized to estimate the dynamic properties when the test structure was occupied by a crowd with different combinations of size, posture, and distribution. The goal of this study is to isolate the occupant characteristics in order to determine the significance of each to be considered when designing new structures to avoid crowd serviceability issues. The results are presented and summarized based on the level of influence of each characteristic. The posture that produces the most significant effects based on the scope of this research is standing with bent knees with a maximum decrease in frequency of the first mode of the empty structure by 32 percent atthe highest mass ratio. The associated damping also increased 36 times the damping of the empty structure. In addition to the analysis of the experimental data, finite element models and a two degree-of-freedom model were created. These models were used to gain an understanding of the test structure, model a crowd as an equivalent mass, and also to develop a single degree-of-freedom (SDOF) model to best represent a crowd of occupants based on the experimental results. The SDOF models created had an averagefrequency of 5.0 Hz, within the range presented in existing biomechanics research, and combined SDOF systems of the test structure and crowd were able to reproduce the frequency and damping ratios associated with experimental tests. Results of this study confirmed the existence of human-structure interaction andthe inability to simply model a crowd as only additional mass. The two degree-offreedom model determined was able to predict the change in natural frequency and damping ratio for a structure occupied by multiple group sizes in a single posture. These results and model are the preliminary steps in the development of an appropriate methodfor modeling a crowd in combination with a more complex FE model of the empty structure.

Investigation of Human-Structure Interaction Through Experimental and Analytical Studies

Vibration serviceability is a widely recognized design criterion for assembly-type structures, such as stadiums, that are likely subjected to rhythmic human-induced excitation. Human-induced excitation of a structure occurs from the movement of the occupants such as walking, running, jumping, or dancing. Vibration serviceability is based on the level of comfort that people have with the vibrations of a structure. Current design guidance uses the natural frequency of the structure to assess vibration serviceability. However, a phenomenon known as human-structure interaction suggests that there is a dynamic interaction between the structure and passive occupants, altering the natural frequency of the system. Human-structure interaction is dependent on many factors, including the dynamic properties of the structure, posture of the occupants, and relative size of the crowd. It is unknown if the shift in natural frequency due to humanstructure interaction is significant enough to warrant consideration in the design process. This study explores the interface of both structural and crowd characteristics through experimental testing to determine if human-structure interaction should be considered because of its potential impact on serviceability assessment. An experimental test structure that represents the dynamic properties of a cantilevered stadium structure was designed and constructed. Experimental modal analysis was implemented to determine the dynamic properties of the empty test structure and when occupied with up to seven people arranged in different locations and postures. Comparisons of the dynamic properties were made between the empty and occupied testing configurations and analytical results from the use of a dynamic crowd model recommended from the Joint Working Group of Europe. Data trends lead to the development of a refined dynamic crowd model. This dynamic model can be used in conjunction with a finite element model of the test structure to estimate the dynamic influence due to human-structure interaction due to occupants standing with straight knees. In the future, the crowd model will be refined and can aid in assessing the dynamic properties of in-service stadium structures.

Experimental Evaluation of the Influence of Human-Structure Interaction for Vibration Serviceability

The effects of human-structure interaction on the dynamic performance of occupied structures have long been observed. The inclusion of the effects of human-structure interaction is important to ensure that the dynamic response of a structure is not overestimated. Previous observations, both in service and in the laboratory, have yielded results indicating that the effects are dependent on the natural frequency of the structure, the posture of the occupants, and the mass ratio of the occupants to the structure. These results are noteworthy, but are limited in their application,because the data are sparse and are only pertinent to a specific set of characteristics identified in a given study. To examine these characteristics simultaneously and consistently, an experimental test structure was designed with variable properties to replicate a variety of configurations within a controlled setting focusing on the effects of passive occupants. Experimental modal analysis techniques were employed to both the empty and occupied conditions of the structure and the dynamic properties associated with each condition were compared. Results similar to previous investigations were observed, including both an increase and a decrease in natural frequency of the occupied structure with respect to the empty structure, as well as the identification of a second mode of vibration. The damping of the combined system was higher for all configurations. Overall, this study provides a broad data set representing a wide array of configurations. The experimental results of this study were used to assess current recommendations for the dynamic properties of a crowd to analytically predict the effects of human-structure interaction. The experimental results were used to select a set of properties for passive, standing occupants and develop a new model that can more accurately represent the behavior of the human-structure system as experimentally measured in this study.

Kalman Filter approaches on crane swing

The purpose of this study is to explore a Kalman Filter approach to estimating swing of crane-suspended loads. Measuring real-time swing is needed to implement swing damping control strategies where crane joints are used to remove energy from a swinging load. The typical solution to measuring swing uses an inertial sensor attached to the hook block. Measured hook block twist is used to resolve the other two sensed body rates into tangential and radial swing. Uncertainty in the twist measurement leads to inaccurate tangential and radial swing calculations and ineffective swing damping. A typical mitigation approach is to bandpass the inertial sensor readings to remove low frequency drift and high frequency noise. The center frequency of the bandpass filter is usually designed to track the load length and the pass band width set to trade off performance with damping loop gain. The Kalman Filter approach developed here allows all swing motions (radial, tangential and twist) to be measured without the use of a bandpass filter. This provides an alternate solution for swing damping control implementation. After developing a Kalman Filter solution for a two-dimensional swing scenario, the three-dimensional system is considered where simplifying assumptions, suggested by the two-dimensional study, are exploited. One of the interesting aspects of the three-dimensional study is the hook block twist model. Unlike the mass-independence of a pendulum's natural frequency, the twist natural frequency depends both on the pendulum length and the load’s mass distribution. The linear Kalman Filter is applied to experimental data demonstrating the ability to extract the individual swing components for complex motions. It should be noted that the three-dimensional simplifying assumptions preclude the ability to measure two "secondary" hook block rotations. The ability to segregate these motions from the primary swing degrees of freedom was illustrated in the two-dimensional study and could be included into the three-dimensional solution if they were found to be important for a particular application.

Abutments influence in the dynamic response of bridges

A simplified analytical model of a short span bridge is proposed. The inertial interaction effects of pier foundations and abutments has been included in order to evaluate the response sensitivities to different soil-structure interaction variables. The modification of natural frequency and damping properties is shown for typical short span bridges of the integral deck-abutment type for longitudinal vibrations or general bridges for the transverse ones.