This thesis investigates the impact of vibration isolators on circuit boards during harsh vibrationenvironments that occur when they are mounted on the wings of a fighter jet. To examine thisphenomenon, a mathematical model and a simulated model were developed to determine theresonant frequencies of the circuit board under various boundary conditions. Subsequently, theresonant frequencies of the circuit board were validated through experimental tests, allowing forthe establishment of the material properties of the circuit board. In order to prevent structuralfailure, this thesis employs α-gel dampers as the damped attachments for the circuit board.These vibration isolators belong to the category of silicone gel dampers and were evaluatedthrough experimental vibration testing. The two employed vibration isolators are denoted asmodels A1 and A2, exhibiting respective damping ratios of 0.1 and 0.05. By utilizing thesevibration isolators during the experimental vibration tests, the structure demonstrated resilienceagainst natural frequency coupling, thereby preventing failure. / Den här masteruppsatsen undersöker effekten av vibrationsisolatorer på kretskort under detuffa vibrationsmiljöer som sker vid vingarna på ett stridsflyg. För att undersöka detta såanvänds en matematisk modell samt en simulerad modell för att hitta resonansfekvensernaför kretskorten vid olika randvillkor. Resonansfrekvenserna från modellerna jämfördes medresonansfrekvenserna som kom tillhanda efter vibrationsprover och med dem så kunde ävenmaterialegenskaperna bestämmas. För att unvika kollaps av strukturen användes α-geldämpare till kretskorten. Dessa dämpare är gjorde av silikongel och utvärderades genomexperimentella vibrationsprover. Dessa vibrationsisolatorer var av modell A1 och A2 ochkorresponderande modell hade dämpningsförhållande 0.1 respektive 0.05. Genom att användadessa vibrationsiolatorer under de experimentella virbationstesterna så undvek strukturenkollaps genom att resonansfrekvenserna inte triggades.

Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. The present work starts from a review of the development and analysis of four basic types of beam theories: the Euler-Bernoulli, Rayleigh, Shear and Timoshenko and goes over to a study of flexural-torsional coupled vibration analysis using basic beam theories. In obtaining natural frequencies, orthogonal polynomials used in the Rayleigh-Ritz method are studied as an efficient way of getting results. The study is also performed for both non-rotating and rotating beams. Orthogonal polynomials and functions studied in the present work are : Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the eigenfunctions of a pinned-free uniform beam, and the special trigonometric functions used in conjunction with Hermite cubics. Studied cases are non-rotating and rotating Timoshenko beams, bending-torsion coupled beam with free-free boundary conditions, a cantilever beam, and a rotating cantilever beam. The obtained natural frequencies and mode shapes are compared to those available in various references and results for coupled flexural-torsional vibrations are compared to both previously available references and with those obtained using NASTRAN finite element package. / Master of Science

The deterioration of the nation's civil infrastructure has prompted the investigation of numerous solutions to offset the problem. Some of these solutions have come in the form of innovative materials for new construction, whereas others have considered rehabilitation techniques for repairing existing infrastructure. A relatively new system that appears capable of encompassing both of these solution methodologies is the Sandwich Plate System (SPS), a composite bridge deck system that can be used in both new construction or for rehabilitation applications. SPS consists of steel face plates bonded to a rigid polyurethane core; a typical bridge application utilizes SPS primarily as a bridge deck acting compositely with conventional support girders. As a result of this technology being relatively new to the bridge market, design methods have yet to be established. This research aims to close this gap by investigating some of the key design issues considered to be limiting factors in implementation of SPS. The key issues that will be studied include lateral load distribution, dynamic load allowance and deck design methodologies. With SPS being new to the market, there has only been a single bridge application, limiting the investigations of in-service behavior. The Shenley Bridge was tested under live load conditions to determine in-service behavior with an emphasis on lateral load distribution and dynamic load allowance. Both static and dynamic testing were conducted. Results from the testing allowed for the determination of lateral load distribution factors and dynamic load allowance of an in-service SPS bridge. These results also provided a means to validate a finite element modeling approach which would could as the foundation for the remaining investigations on lateral load distribution and dynamic load allowance. The limited population of SPS bridges required the use of analytical methods of analysis for this study. These analytical models included finite element models and a stiffened plate model. The models were intended to be simple, but capable of predicting global response such as lateral load distribution and dynamic load allowance. The finite element models are shown to provide accurate predictions of the global response, but the stiffened plate approach was not as accurate. A parametric investigation, using the finite element models, was initiated to determine if the lateral load distribution characteristics and vibration response of SPS varied significantly from conventional systems. Results from this study suggest that the behavior of SPS does differ somewhat from conventional systems, but the response can be accommodated with current AASHTO LRFD bridge design provisions as a result of their conservativeness. In addition to characterizing global response, a deck design approach was developed. In this approach the SPS deck was represented as a plate structure, which allowed for the consideration of the key design limit states within the AASHTO LRFD specification. Based on the plate analyses, it was concluded that the design of SPS decks is stiffness-controlled as limited by the AASHTO LRFD specification deflection limits for lightweight metal decks. These limits allowed for the development of a method for sizing SPS decks to satisfy stiffness requirements. / Ph. D.

A large structural weldment has been designed to serve as the new star tracker bridge for the Dark Energy Experiment upgrade to the Hobby-Eberly Telescope at McDonald Observatory. The modeling approach, analysis techniques and design details will be of interest to designers of large structures where stiffness is the primary design driver. The design includes detailed structural analysis using finite element models to maximize natural frequency response and limit deflections and light obscuration. Considerable fabrication challenges are overcome to allow integration of precision hardware required for positioning the corrector optics to a precision of less than 5 microns along the 4-meter travel range. This thesis provides detailed descriptions of the bridge geometry, analysis results and challenging fabrication issues. / text

Methods of determining natural frequencies of the D76D88, B76D88, A86E93, C86G90, C86L90 and C125L89 turbine wheel designs for various environmental conditions were investigated by application of Finite Element Analysis and beam theory. Modelling and simulation methods were developed ; the first method composed of 15 finite element simulations ; the second composed of 15 finite element simulations and a set of experimental frequency survey results; the third composed of 5 simulations , an incorporated mathematical model and a set of experimental frequency survey results. Each of these methods was designed to allow prediction of resonant frequency changes across a range of exhaust gas temperature and shaft rotational speed. For the new modelling and simulation methods, an analysis template and a plotting tool were developed using Microsoft Excel and MATLAB software. A graph showing a frequency-temperature-speed variations and a Campbell Diagram that incorporates material stiffening and softening effects across a range of rotational speeds was designed, and applied to the D76D88, B76D88, A86E93, C86G90, C86L90 and C125L89 turbine wheel designs. New design methodologies for turbine wheels were formulated and validated, showing a good agreement with a range of data points from frequency survey, strain-gauge telemetry and laser tip-timing test results. The results from the new design method were compared with existing single compensation factor methodology, and showed a great improvement in accuracy of prediction of modal vibration. A new nomenclature for the mode shapes of a turbocharger’s blade was proposed, designed and demonstrated to allow direct identification of associated mode shape. It is concluded that Finite Element Analysis combined with the frequency survey is capable of predicting changes in turbine natural frequencies and, when incorporated into the existing turbine design methodology, resulted in a major improvement in the accuracy of the predictions of vibration frequency.

The stability of the high-walls is one of the major concerns for open pit mines. Among the various factors affecting the stability of high-walls, blast vibrations can be an important one. In general, worldwide the established respective government regulations and industry standards are used as guidance to determine the maximum recommended levels of the peak particle velocity and frequency from the blast to avoid any effects on the structures around the mining project. However, most of the regulations are meant for buildings or houses and do not concern high-walls. This thesis investigates the response of high-walls under the effects of vibrations from mine blasting. In this research, the relationship between the high-wall response, the geometry of the slope, the frequency and the amplitude, of the ground vibration produced by blasting, is explored using numerical models in 3DEC. The numerical models were calibrated initially with data collected using seismographs installed in a surface mine operation and recording vibrations produced by an underground mine drill and blast operation. Once the calibration was accomplished, a parametric study was developed to explore the relationships between various parameters under study and its impact on the stability of high-walls.

Abstract The purpose of this study is to determine the exact natural frequencies and mode shapes of multi-span uniform and multi-step Euler-Bernoulli beams with various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, etc.) by using the matrix assembly method (MAM). To this end, the coefficient matrices for an intermediate pinned support, an intermediate concentrated elements, left-end support and right-end support of a beam are derived, first. Next, the overall coefficient matrix for the whole structural system is obtained by using the assembly technique of the finite element method. Finally, the natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions respectively. The effects of in-span pinned supports and various concentrated elements on the free vibration characteristics of the beam are also studied.

<p>Today’s bridge design work in many cases demands a trustworthy dynamic analysis instead of using the traditional dynamic amplification factors. In this thesis a reliable 3D Bernoulli-Euler beam finite element model of the New Årsta Railway Bridge was prepared for thorough dynamic analysis using in situ bridge monitoring for correlation. The bridge is of the concrete box girder type with a heavily reinforced and prestressed bridge deck. The monitoring system was designed for long term monitoring with strain transducers embedded in the concrete and accelerometers mounted inside the edge beams and at the lower edge of the track slab.</p><p>The global finite element model used the exact bridge geometry but was simplified regarding prestressing cables and the two railway tracks. The prestressing cables and the tracks were consequently not included and an equivalent pure concrete model was identified.</p><p>A static macadam train load was eccentrically placed on one of the bridge’s two tracks. By using Vlasov’s torsional theory and thereby including constrained warping a realistic modulus of elasticity for the concrete without prestressing cables and stiffness contribution from the railway tracks was found. This was allowed by comparing measured strain from strain transducers with the linear elastic finite element model’s axial stresses. Mainly three monitoring bridge sections were used, each of which was modelled with plane strain finite elements subjected to sectional forces/moments from a static macadam train load and a separately calculated torsional curvature.</p><p>From the identified modulus of elasticity the global finite element model was updated for Poisson’s ratio and material density (mass) to correspond with natural frequencies from the performed signal analysis of accelerometer signals. The influence of warping on the natural frequencies of the global finite element model was assumed small and the bridge’s torsional behaviour was modelled to follow Saint-Venant’s torsional theory.</p><p>A first preliminary estimation of modal damping ratios was included. The results indicated that natural frequencies were in accordance between modelling and signal analysis results, especially concerning high energy modes. Estimated damping ratios for the first vibration modes far exceeded the lower limit value specified in bridge design codes and railway bridge dynamic analysis recommendations.</p>

Vibration generated from various sources (engine, road surface, tires, exhaust, etc.) should be considered in the design of a car body. These vibrations travel through transfer systems (drivetrain, suspension, body, etc.) to the steering wheel, seats and other areas where it is detected by the passengers of the vehicle. Transmission routes must be studied and efforts made to keep transfer systems from amplifying vibration and to absorb it instead. Since the superior vibration transfer system is the car body, finite element analysis and experimental vibration analysis are performed on car body-in-white. Body vibration analysis entails understanding and improving the body&rsquo / s dynamic characteristics that act as vibration transfer channels. In the previous study, a finite element model has been created for a car body-in-white available in Automotive Laboratory (Mechanical Engineering Department, Middle East Technical University, Ankara) and its natural frequencies and mode shapes have been determined using finite element analysis software. In this study, vibration tests have been performed on actual car body-in-white. Frequency response functions between 34 response locations and force application point have been measured. Using these frequency response functions, natural frequencies and mode shapes of the body-in-white have been determined. Finite element analysis and experimental results have been compared to evaluate the finite element model reliability.

Orientador: Prof. Dr. Reyolando M. L. R. F. Brasil / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Mecânica, 2017. / Neste trabalho realiza-se um estudo do efeito causado pela alteracao da rigidez geometrica, por meio de forcas axiais, na frequencia natural de bases de maquinas rotativas, na forma de viga e portico plano, todos metalicos, no intuito de tira-las na ressonancia ou proximo dessa regiao. Essa regiao proxima da ressonancia e chamada de regiao fora de seguranca e compreende o intervalo que comeca em 20% abaixo da frequencia da maquina ate 25% acima dela. Duas ferramentas foram utilizadas para realizar o estudo, Metodo de Rayleigh e Metodo dos Elementos Finitos (MEF). Na viga estuda-se um perfil estrutural de um tubo retangular em aco estrutural, utilizando o Metodo de Rayleigh e o MEF. Ja o portico e estudado somente pelo MEF, so que mais perfis foram analisados desse mesmo tubo. No caso da base como viga, sem carregamento algum, ela se mostrou dentro na zona perigosa, tanto por Rayleigh como por MEF. Uma intervencao com forcas axiais foi realizada para estabilizar as bases. No portico tanto portico, o perfil 60x60 nao ficou dentro da zona perigosa, ja os demais, 80x80 e perfil ¿§, ficaram dentro da regiao { 0,8¿¶, 1,25¿¶ }. O estudo mostrou que a rigidez geometrica / In this work a study of the effect caused by the alteration of the geometric stiffness, by means of axial forces, in the natural frequency of bases of rotating machines, in the form of beam and plan portico, all metallic, in order to take them out in the resonance or near this region. This region near the resonance is called unsafe region, and comprises the range starting at 20% below the frequency of the machine and to 25% above it. Two tools were used to carry out the study, Rayleigh Method and Finite Element Method (FEM). In the beam, a structural profile of a rectangular tube in structural steel is studied, using the Rayleigh Method and MEF. Already the portico is studied only by MEF, except that more profiles were analyze in this same tube. In the case of the base as beam, without any loading, it showed itself inside the dangerous zone, by both Rayleigh and MEF. An axial force intervention was performed to stabilize the bases. In the planar portal frame, the 60x60 profile was not inside the dangerous zone, while the others, 80x80 and profile É, were within the region {0.8Ù, 1.25Ù}. The study showed that the geometric stiffness has a close relation with the natural frequencies in solid structures.