KEYWORDS: Structural health monitoring, Matrices, Inverse problems, Data modeling, Systems modeling, Mechanical engineering, Modal analysis, Error analysis, Algorithm development, Chemical elements
The spectral data i.e. eigenvalues (natural-frequencies) and eigenvectors (mode-shapes), characterizes the dynamics of
the system. The dynamic analysis of physical systems leads to certain direct and inverse eigenvalue problems. The direct
eigenvalue problem deals in evaluating the spectral behavior of structures for given distributions of physical parameters
such as mass, area, stiffness etc. whereas, the estimation of these physical parameters form the spectral data is known as
inverse eigenvalue problem. The detection of minuscule (small) changes in the stiffness and mass of the structure, by
solving certain inverse eigenvalue problems, is addressed here by considering a grooved axially vibrating rod. In solving
direct problems, we have considered two types of eigenvalue problem: (i) traditional algebraic eigenvalue problems and
(ii) transcendental eigenvalue problems associated with the continuous system. In conclusion, we have (a) obtained the
eigenvalues of damaged rod, (b) analyzed the behavior of the spectral data due to minuscule change in the physical
parameters, and (c) determined the different type of spectral data that are required for detecting damage parameters.
Several numerical examples are solved here demonstrating the feasibility and accuracy of the identification technique by
solving Transcendental Inverse Eigenvalue Problems.
Thermal protection system is a critical component of a space vehicle and is essential for safe re-entry into the atmosphere. The loss of stiffness in tile-based thermal protection system is an essential mode of damage and has lead to loss of a space vehicle due to excessive aero-dynamic heating during re-entry. The inherent nonlinear nature of the coupling of these tiles with the space vehicle body is well-known. This paper explores this nonlinear
coupling and proposes a method based on continuation analysis of the nonlinear model to detect and track this damage. The model used was first proposed by Luo and Hanagud.1 White, Adams and Jata (2005)2 used modal analysis to conduct system identification and damage identification on a similar system using method of virtual forces. The present research presents another approach by utilizing periodic excitations to estimate the presence and degree of damage. Parametric studies are also conducted to study the effect of variations in mass on the detection of change in stiffness using the proposed method.
When processing a signal or an image using the Discrete Cosine Transform (DCT) or Discrete Sine Transform (DST), a typical approach is to extract a portion of the signal by windowing and then form the DCT or DST of the window contents. By shifting the window point by point over the signal, the entire signal may be processed. DCTs and DSTs are defined where the denominator in the transform kernel is either an odd or an even integer, resulting in transforms known as the even DCT (EDCT), even DST (EDST), odd DCT (ODCT) and odd DST (ODST). Each is available in types I to IV, for a total of 16 different transforms. The widely used transform commonly called the "DCT" is actually the EDCT-II. In this paper we extend our previous work using the EDCT-II and EDST-II, and show that a similar approach yields algorithms for the ODCT-II and ODST-II. We develop algorithms to "update" the ODCT-II and ODST-II simultaneously to reflect the modified window contents using less computation than directly evaluating the modified transform via standard Fast Transform algorithms. These algorithms are able to handle arbitrary step sizes up to the length of the transform, i.e. the algorithm simultaneously updates the ODCT-II and ODST-II to reflect inclusion of r, where 1 ≤ r ≤ N-1, additional data points and removal of r old points from the signal. Examples of applications where this algorithm would be useful include target recognition where time constraints may not permit the immediate processing of every incoming data point, adaptive system identification, etc.
Prognosis integrates physics based models of damage, noninvasive real time interrogation techniques and data/signature analysis to predict future performance. One of the significant capabilities essential for the prognosis methodology to work is to develop analysis methods for multiple and interacting damage and failure mechanisms. In this paper the proposed methodology has been demonstrated with the help of a nonlinear multi-degree-of-freedom system which exhibits multiple phenomenological damage phenomenon. It is shown that the participation factors for the bifurcating damage modes can be used to characterize the damage mechanism.
Damage prognosis of structures and systems can be significantly improved by developing intelligent sensors with adaptive sensitivity to the ambient signals via self-tuned criticality. Active amplification of weak signals using an inherent dynamical sensory mechanism which is maintained at the threshold of an oscillatory instability is proposed in this paper as a general framework for designing and developing sensors for damage detection and prognosis for civil and mechanical systems. This idea is inspired by the sensing mechanism of mammalian cochlea to develop a new sensing system paradigm. A numerical feasibility study of such a sensor system is conducted and presented as a building block for more general design and future implementation.
A neonatal transport cart is used by hospitals to transport critical infants. The ride during ground transportation generates severe vibrations which have been found to adversely affect the infant's physiological symptoms. This work is the first attempt to design a vibration isolation system using magneto-rheological fluid damper-based suspension system for the neonatal transport cart. In this paper the effect of various system and control parameters on the two-degree-of-freedom model are numerically studied for parametric bifurcation stability behavior. It is shown that system can undergo loss of stability via Hopf bifurcation and exhibit limit cycle oscillations which is counter to the goal of the proposed suspension design.
Design and development of electro-active polymeric devices for sensing and actuation requires accurate characterization of its nonlinear dynamic behavior and performance characteristics. Thin film cantilevers are being applied for numerous sensor and actuator applications. A nonlinear model of a piezoelectric thin plate cantilever is developed in this work using a two-mode approximation developed by Galerkin's method. This reduced order model is then studied using perturbation method for the nonlinear dynamic response due to a harmonic excitation. The results obtained demonstrate the nonlinear nature of the dynamic behavior of thin plates made of polymer polyvinylidene fluoride. The exhibited nonlinear behavior includes parameter dependent amplitude modulation, nonlinear jump and nonlinear dependence on excitation frequency and excitation amplitude. This study is a step forward in understanding the associated dynamics so as to utilize these geometries in various transducer applications.
Damage detection and prediction is essential for structural health monitoring. Vibration based methods have been used in health monitoring. In this work damage is proposed to be a nonlinear dynamical phenomenon and can be analyzed by utilizing the bifurcation theory. A methodology for predicting failure is proposed which utilizes the concepts of distance to stability boundary as estimated by bifurcation analysis. The proposed methodology is illustrated by developing bifurcation boundary for a two degree of freedom nonlinear mass-spring-damper system. Two damage models are investigated to illustrate the utility the proposed methodology in capturing and estimating the evolution of damage phenomenon.
The dynamic bending piezoelectric properties of polyvinylidene fluoride cantilevers in the millimeter size range is reported. These devices are being investigated with the intention of developing a piezoelectric device based inner ear cochlear implant. The size restrictions and fluid environment of the inner ear place special requirements on a piezoelectric device, and it is essential to perform basic studies on sensor materials, deformation modes and device configurations to develop a successful implant. Results from both basic vibration tests and underwater acoustic measurements are presented. Experimental modal analysis reveals that millimeter length cantilevers exhibit three bending resonances under 1 kHz. The modal frequencies are sensitive functions of the length and thickness of the film, and are also affected substantially by the width of the cantilever and the nature of the electrode material. Further, all bending piezoelectric modes display high piezoelectric coupling
coefficients in the range 0.2 - 0.35, and damping of < 2%.
Experimental results are compared with a theoretical model of unimorph piezoelectric cantilever beams. Underwater acoustic measurements also reveal that single-cantilever devices in the millimeter length display acoustic sensitivities in the -195 to -210 dB range, in the 2 - 10 kHz regime. These sensitivities are comparable to commercial devices of larger size and more complex
design. The viability of use of the conducting polymer polypyrrole
as the electrode material in polymer piezoelectric sensors is also
investigated. Results show that devices with polypyrrole electrodes are at least as sensitive as devices with metal electrodes, and these type all-polymer devices thus have great promise. The results presented in this paper can be used to design an appropriate sensory implant, as well as in other audio frequency applications.
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