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ABSTRACT Forced Vibration Testing and Analysis of Pre- and Post- Retrofit Buildings Erica Dawn Jacobsen The primary goal of the thesis was to detect the retrofit through vibration testing of both buildings. The secondary goal focused on correctly identifying the behavior of the building through FVT, comparing that behavior to computational model predictions, and determining the necessary level of detail to include in the computational modeling. Forced vibration testing (FVT) of two stiff-wall/flexible-diaphragm buildings yielded natural frequencies and mode shapes for the two buildings. The buildings were nearly identical with the exception that one had been retrofitted. Both buildings were comprised of concrete shearwalls and steel moment frames in the north/south direction and moment frames in the east/west direction. The retrofit strengthened the moment connections and added braces to the perimeter walls in the east/west direction. The natural frequencies were found through FVT by setting a 30-lb shaker on the roof of both buildings and sweeping through a range of frequencies in both the east/west and north/south directions. Accelerometers were placed on the building to detect the accelerations. The peaks on the Fast Fourier Transform (FFT) graphs indicated the frequencies at which the structure resonated. Mode shapes were tested for by placing the shaker in a position ideal for exciting the mode and setting the shaker to the natural frequency detected from the FFT graphs. The accelerometers were placed around the roof of the building to record the mode shape. After testing, computational models were created to determine if the models could accurately predict the frequencies and mode shapes of the buildings as well as the effect of the retrofit. A series of increasingly complex computational models, ranging from hand calculations to 3D models, were created to determine the level of detail necessary to predict the building behavior. Natural frequencies were the primary criteria used to determine whether the model accurately predicted the building behavior. The mid-diaphragm deflection and base shear from spectral analysis were the final criteria used to compare these select models. It was determined that in order to properly capture the modal behavior of the building, the sawtooth framing, major beams, and the lateral-force-resisting-system (LFRS) must be modeled. Though the mode shape of the building is dominated by the flexible diaphragm, the LFRS is necessary to model to accurately predict both the natural frequency of the building as well as the diaphragm deflection.

The Point Sur Lighthouse is an unreinforced stone masonry building completed in 1889 on the central coast of California. The lighthouse is listed on the National Register of Historic Places and is still an active aid to navigation. The original first-order Fresnel lens was removed from the lantern room and placed in safekeeping due to its high risk of damage in the event of a strong earthquake. The lens has been approved to return to its original setting but the seismic performance of the building must first be assessed in order to ensure the safety of the lens and lighthouse, specifically the out-of-plane behavior of the unreinforced masonry walls, the implementation of possible seismic retrofit schemes, and the effects of the lens’s added weight. This research focuses on the dynamic behavior of the lighthouse in its current state and the changes in the dynamic behavior each of the proposed seismic retrofit schemes might cause. For the purposes of this research, dynamic behavior is considered as natural frequencies, mode shapes, and related structural properties. The dynamic behavior of the lighthouse was assessed using two main methods: forced vibration testing and finite element computer modeling. Forced vibration testing is a nondestructive testing method that can be used to directly characterize dynamic behavior of a structure, and finite element computer modeling is useful for the design and simulation of dynamic behavior of both new and existing structures. The combination of these two methods on the Point Sur Lighthouse will work to develop and prove state-of-the-art seismic retrofitting techniques.

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An assessment of the validity of idealizing a concrete diaphragm as rigid was performed through the modal analysis of three existing buildings. Modal analysis was performed both by physical experimentation and computational analysis. Experimental determination of the mode shapes shows that two of the three buildings’ diaphragms exhibited flexible behavior. The experimental results were compared to computational analysis results and were shown to be similar, confirming that that the two building diaphragms are not rigid. As a standard, diaphragms with aspect ratios less than three are permitted to be idealized as rigid per ASCE 7-05. To determine the effect of the rigid diaphragm idealization, the design forces and roof deflections for each building were determined from the computational model through a spectral analysis for both a model with rigid diaphragms and a model with semi-rigid diaphragms. It was found that the design seismic demands for the two buildings with flexible diaphragms were higher when modeled with semi-rigid diaphragms than with rigid diaphragms. The conclusion is made that idealizing a concrete diaphragm as rigid solely based on its aspect ratio may result in an unconservative estimate of the seismic demands on a building.

A clássica teoria de Euler-Bernoulli para vibrações transversais de vigas elásticas é sabido não ser adequada para vibrações de altas freqüências, como é o caso de vibração de vigas curtas. Esta teoria assume que a deflexão deve-se somente ao momento fletor, uma vez que os efeitos da inércia de rotação e da força cortante são negligenciados. Lord Rayleigh complementou a teoria clássica demonstrando a contribuição da inércia de rotação e Timoshenko estendeu a teoria ao incluir os efeitos da força cortante. A equação resultante é conhecida como sendo a que caracteriza a chamada teoria de viga de Timoshenko. Usando-se a matriz de rigidez dinâmica, as freqüências naturais e a resposta dinâmica de estruturas de barras são determinadas e comparadas de acordo com resultados de quatro modelos de vibração. São estudados o problema de vibração flexional de vigas, pórticos e grelhas, bem como o problema de fundação elástica segundo o modelo de Winkler e também a versão mais avançada que é o modelo de Pasternak. / Classical Euler-Bernoulli theory for transverse vibrations of elastic beams is known to be inadequate to consider high frequency modes which occur for short beams, for example. This theory is derived under the assumption that the deflection is only due to bending. The effects of rotary inertia and shear deformation are ignored. Lord Rayleigh improved the classical theory by considering the effect of rotary inertia. Timoshenko extended the theory to include the effects of shear deformation. The resulting equation is known as Timoshenko beam theory. The natural frequencies and dynamic reponse of framed structures are determined by using the dynamic stiffness matrix and compered according to these theories. The flexional vibration problems of beams, plane frames and grids are analysed, as well problems of elastic foundation according the well known Winkler model and also the more general Pasternak model.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-03-29T15:39:07Z No. of bitstreams: 2 Dissertação - Henrique Araujo Rodrigues Sattler - 2015.pdf: 3327262 bytes, checksum: 1c260793f2aa5b49f25d29e6835ab326 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-03-29T15:41:36Z (GMT) No. of bitstreams: 2 Dissertação - Henrique Araujo Rodrigues Sattler - 2015.pdf: 3327262 bytes, checksum: 1c260793f2aa5b49f25d29e6835ab326 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-03-29T15:41:37Z (GMT). No. of bitstreams: 2 Dissertação - Henrique Araujo Rodrigues Sattler - 2015.pdf: 3327262 bytes, checksum: 1c260793f2aa5b49f25d29e6835ab326 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-08-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work is a study of linear and nonlinear free vibration of a cylindrical panel simply supported subjected to a dependent loading time. From the full potential and kinetic energy functional of a cylindrical panel to determine the system's equations of motion, whereas the field of deformations of the cylindrical panel follows the non-linear theory for Donnell shallow shell. For discretization of the cylindrical panel moving system of equations is performed a test procedure able to obtain the fields axial and circumferential displacements from a modal expansion radial displacement field, creating a low-dimensional discretized model. Determine the radial displacement field from perturbation techniques that provides the nonlinear modes which couple to the linear vibration mode of the system from the quadratic and cubic non-linearities present in the cylindrical panel equilibrium equations. With this system of equations is reduced to a partial differential equation as a function of the expansion of the modal amplitudes for the radial displacement being discretized then the Galerkin method. They present the results of various free, linear and non-linear vibrations, and forced into a cylindrical simply supported panel, showing the remarkable influence of the modal coupling in modal solution to this radial displacement and the panel geometry. / Neste trabalho, realiza-se um estudo das vibrações livres, lineares e não lineares, e forçadas de um painel cilíndrico simplesmente apoiado submetido a um carregamento dependente do tempo. A partir dos funcionais de energia potencial total e cinética de um painel cilíndrico, determinam-se as equações de movimento do sistema, considerando que o campo de deformações do painel cilíndrico segue a teoria não linear de Donnell para cascas abatidas. Para obter a discretização do sistema de equações de movimento do painel cilíndrico, realiza-se um procedimento analítico capaz de obter os campos de deslocamentos axial e circunferencial a partir de uma expansão modal para campo de deslocamento radial, criando um modelo discretizado de baixa dimensão. Determina-se o campo de deslocamentos radiais a partir de técnicas de perturbação que fornece os modos não lineares que se acoplam ao modo linear de vibração do sistema a partir das não linearidades quadráticas e cúbicas presentes nas equações de equilíbrio do painel cilíndrico. Com isto o sistema de equações é reduzido para uma equação diferencial parcial em função das amplitudes modais da expansão para o deslocamento radial, sendo discretizada, em seguida, pelo método de Galerkin. Apresentam-se diversos resultados das vibrações livres, lineares e não-lineares, e forçadas para um painel cilíndrico simplesmente apoiado, mostrando a marcante influência do acoplamento modal presente na solução modal para os deslocamentos radiais e da geometria do painel.

A clássica teoria de Euler-Bernoulli para vibrações transversais de vigas elásticas é sabido não ser adequada para vibrações de altas freqüências, como é o caso de vibração de vigas curtas. Esta teoria assume que a deflexão deve-se somente ao momento fletor, uma vez que os efeitos da inércia de rotação e da força cortante são negligenciados. Lord Rayleigh complementou a teoria clássica demonstrando a contribuição da inércia de rotação e Timoshenko estendeu a teoria ao incluir os efeitos da força cortante. A equação resultante é conhecida como sendo a que caracteriza a chamada teoria de viga de Timoshenko. Usando-se a matriz de rigidez dinâmica, as freqüências naturais e a resposta dinâmica de estruturas de barras são determinadas e comparadas de acordo com resultados de quatro modelos de vibração. São estudados o problema de vibração flexional de vigas, pórticos e grelhas, bem como o problema de fundação elástica segundo o modelo de Winkler e também a versão mais avançada que é o modelo de Pasternak. / Classical Euler-Bernoulli theory for transverse vibrations of elastic beams is known to be inadequate to consider high frequency modes which occur for short beams, for example. This theory is derived under the assumption that the deflection is only due to bending. The effects of rotary inertia and shear deformation are ignored. Lord Rayleigh improved the classical theory by considering the effect of rotary inertia. Timoshenko extended the theory to include the effects of shear deformation. The resulting equation is known as Timoshenko beam theory. The natural frequencies and dynamic reponse of framed structures are determined by using the dynamic stiffness matrix and compered according to these theories. The flexional vibration problems of beams, plane frames and grids are analysed, as well problems of elastic foundation according the well known Winkler model and also the more general Pasternak model.

This diploma thesis deals with dynamic analysis of the steam turbine blade. This blade is part of the last row of low pressure level of steam turbine. Computational analysis has been performed in first part using FEM and software ANSYS. A Transient analysis has been used to solve forced vibrations. Main goal is to obtain a behavior of main stresses and its directions as a function of loading of the blade in the crack initiation area. Second part deals contain a an experiment. Experiment has been set up to perform a modal analysis which is necessary to obtain a fundamental numbers. Then the vibration of the blade has been performed. To perform this experiment same edge conditions as which has been used during the computational analysis. Goal is the same as in the first part – obtain a behavior of main stresses and its directions as a function of loading of the blade in the crack initiation area. The comparison of results obtained during experimental analysis and computational analysis has been performed in the last part of the thesis. Also the question if any geometrical nonlinearities appeared during analyses is answered.

The Bridge House is a steel building structure located in Poly Canyon, a rural area inside the campus of California Polytechnic State University, San Luis Obispo. The Bridge House is a one story steel structure supported on 4 concrete piers with a lateral force resisting system (LFRS) composed of ordinary moment frames in the N-S direction and braced frames in the E-W direction and vertically supported by a pair of trusses. The dynamic response of the Bridge House was investigated by means of system identification through ambient and forced vibration testing. Interesting findings such as diaphragm flexibility, foundation flexibility and frequency shifts due to thermal effects were all found throughout the mode shape mapping process. Nine apparent mode shapes were experimentally identified, N-S and E-W translational, rotational and 6 vertical modes. A computational model was also created and refined through correlation with the modal parameters obtained through FVTs. When compared to the experimental results, the computational model estimated the experimentally determined building period within 8% and 10% for both N-S and E-W translational modes and within 10% for 4 of the vertical modes.