Structural Health Monitoring (SHM) is the implementation of damage detection and characterization algorithms using in vitro sensing and actuation for rapidly determining faults in structural systems before the damage leads to catastrophic failure. SHM systems provide near real time information on the state of the integrity of civil, mechanical and aerospace structures. A roadblock in implementing SHM systems in practice is the possibility of false positives introduced by environmental changes. In particular, temperature changes can cause many SHM algorithms to indicate damage when no damage exists. While several experimentally based efforts have been attempted to alleviate temperature effects on SHM algorithms, fundamental research on the effects of temperature on SHM has not been investigated. The work presented in this dissertation composes of two main parts: the first part focuses on the experimental studies of different mechanical structures of aluminum beams, lug samples and railroad switch bolts. The experimental study of the aluminum lug samples and beams is done to propose and examine methods and models for in situ interrogation and detection of damage (in the form of a fatigue crack) in these specimen and to quantify the smallest detectable crack size in aluminum structures. This is done by applying the electrical impedance-based SHM method and using piezoceramic sensors and actuators. Moreover, in order to better extract the damage features from the measured electrical impedance, the ARX non-linear feature extraction is employed. This non-linear feature extraction, compared to the linear one, results in detection of damages in the micro-level size and improves the early detection of fatigue cracks in structures. Experimental results also show that the temperature variation is an important factor in the structural health monitoring applications and its effect on the impedance-based monitoring of the initiation and growth of fatigue cracks in the lug samples is experimentally investigated. The electrical impedance-based SHM technique is also applied in monitoring the loosening of bolted joints in a full-scale railroad switch and the sensitivity of this technique to different levels of loosening of the bolts is investigated. The second part of the work presented here focuses on the analytical study and better understanding of the effect of temperature on the vibration-based SHM. This is done by analytical modeling of the vibratory response of an Euler-Bernoulli beam with two different support conditions of simply supported and clamped-clamped and with a single, non-breathing fatigue crack at different locations along the length of the beam. The effect of temperature variations on the vibratory response of the beam structure is modeled by considering the two effects of temperature-dependent material properties and thermal stress formations inside the structure. The inclusion of thermal effects from both of these points of view (i.e. material properties variations and generation of thermal stresses) as independent factors is investigated and justified by studying the formulations of Helmholtz free energy and stresses inside a body. The effect of temperature variations on the vibratory response of the cracked beam are then studied by integrating these two temperature-related effects into the analytical modeling. The effect of a growing fatigue crack as well as temperature variations and thermal loadings is then numerically studied on the deflection of the beam and the output voltage of a surface-bonded piezoceramic sensor. / Ph. D.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第17985号 / 工博第3814号 / 新制||工||1584(附属図書館) / 80829 / 京都大学大学院工学研究科電子工学専攻 / (主査)教授 川上 養一, 教授 藤田 静雄, 准教授 浅野 卓 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Rotating Euler-Bernoulli beams and non-homogeneous Timoshenko beams are widely used to model important engineering structures. Hence the vibration analyses of these beams are an important problem from a structural dynamics point of view. The governing differential equations of both these type of beams do not yield any simple closed form solutions, hence we look for the inverse problem approach in determining the beam property variations given certain solutions. Firstly, we look for a rotating beam, with pinned-free boundary conditions, whose eigenpair (frequency and mode-shape) is same as that of a uniform non-rotating beam for a particular mode. It is seen that for any given mode, there exists a flexural stiffness function (FSF) for which the ith mode eigenpair of a rotating beam with uniform mass distribution, is identical to that of a corresponding non-rotating beam with same length and mass distribution. Inserting these derived FSF's in a finite element code for a rotating pinned-free beam, the frequencies and mode shapes of a non-rotating pinned-free beam are obtained. For the first mode, a physically realistic equivalent rotating beam is possible, but for higher modes, the FSF has internal singularities. Strategies for addressing these singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test functions for rotating beam codes and also for targeted destiffening of rotating beams. Secondly, we study the free vibration of rotating Euler-Bernoulli beams, under cantilever boundary condition. For certain polynomial variations of the mass per unit length and the flexural stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation. It is found that there are an infinite number of rotating beams, with various mass per unit length variations and flexural stiffness distributions, which share the same fundamental frequency and mode shape. The derived flexural stiffness polynomial functions are used as test functions for rotating beam numerical codes. They are also used to design rotating cantilever beams which may be required to vibrate with a particular frequency. Thirdly, we study the free vibration of non-homogeneous Timoshenko beams, under fixed-fixed and fixed-hinged boundary conditions. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, there exists a fundamental closed form solution to the coupled second order governing differential equations. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions, which share the same fundamental frequency and mode shape. They can be used to design non-homogeneous Timoshenko beams which may be required for certain engineering applications.

Rotating and non-rotating beams are widely used to model important engineering struc-tures. Hence, the vibration analyses of these beams are an important problem from a structural dynamics point of view. Depending on the beam dimensions, they are mod-eled using different beam theories. In most cases, the governing differential equations of these types of beams do not yield any simple closed-form solutions; hence we look for the inverse problem approach in determining the beam property variations given certain solutions. The long and slender beams are generally modeled using the Euler-Bernoulli beam theory. Under the premise of this theory, we study (i) the second mode tailoring of non-rotating beams having six different boundary conditions, (ii) closed-form solutions for free vibration analysis of free-free beams, (iii) closed-form solutions for free vibration analysis for gravity-loaded cantilever beams, (iv) closed-form solutions for free vibration analysis of rotating cantilever and pinned-free beams and (v) beams with shared eigen-pair. Short and thick beams are generally modeled using the Timoshenko beam theory. Here, we provide analytical closed-form solutions for the free vibration analysis of ro-tating non-homogeneous Timoshenko beams. The Rayleigh beam provides a marginal improvement over the Euler-Bernoulli beam theory without venturing into the math-ematical complexities of the Timoshenko beam theory. Under this theory, we provide closed-form solutions for the free vibration analysis of cantilever Rayleigh beams under three different axial loading conditions - uniform loading, gravity-loading and centrifu-gally loaded. We assume simple polynomial mode shapes which satisfy the different boundary conditions of a particular beam, and derive the corresponding beam property variations. In case of the shared eigenpair, we use the mode shape of a uniform beam which has a closed-form solution and use it to derive the stiffness distribution of a corresponding axially loaded beam having same length, mass variation and boundary condition. For the Timoshenko beam, we assume polynomial functions for the bending displacement and the rotation due to bending. The derived properties are demonstrated as benchmark analytical solutions for approximate and numerical methods used for the free vibration analysis of beams. They can also aid in designing actual beams for a pre-specified frequency or nodal locations in some cases. The effect of different parameters in the derived property variations and the bounds on the pre-specified frequencies and nodal locations are also studied for certain cases. The derived analytical solutions can also serve as a benchmark solution for different statistical simulation tools to find the probabilistic nature of the derived stiffness distri-bution for known probability distributions of the pre-specified frequencies. In presence of uncertainty, this flexural stiffness is treated as a spatial random field. For known probability distributions of the natural frequencies, the corresponding distribution of this field is determined analytically for the rotating cantilever Euler-Bernoulli beams. The derived analytical solutions are also used to derive the coefficient of variation of the stiffness distribution, which is further used to optimize the beam profile to maximize the allowable tolerances during manufacturing.