Relevant bibliographies by topics / Plates (Engineering) – Vibration ; Structural dynamics – Mathematical models

Academic literature on the topic 'Plates (Engineering) – Vibration ; Structural dynamics – Mathematical models'

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Published: 10 December 2022
Last updated: 30 January 2023

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Journal articles on the topic "Plates (Engineering) – Vibration ; Structural dynamics – Mathematical models"

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Borkovic, Aleksandar, Dragan Milasinovic, Valentina Golubovic-Bugarski, Ognjen Mijatovic, and Manuel Desancic. "Experimental and numerical identification of structural modes for engineering education." Facta universitatis - series: Architecture and Civil Engineering 12, no. 2 (2014): 161–72. http://dx.doi.org/10.2298/fuace1402161b.

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Development of simple classroom demonstration device and software for visualization of structural normal modes is presented. Device is made of parts of old speaker, controlled with personal computer, where the harmonic motion of solenoid is used as an excitation for beam and plate models. Simple code for finite element free vibration analysis of plates is written in Wolfram Mathematica. Good agreement of results and attractive visual patterns of normal modes attracted attention of students. Results are confirmed using modern modal testing methods. Presented approach is complementary to standard teaching of structural dynamics.
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Tian, Ali, Renchuan Ye, Peng Ren, Pengming Jiang, Zengtao Chen, Xiaochun Yin, and Yuanshuai Zhao. "New Higher-Order Models for Sandwich Plates with a Flexible Core and their Accuracy Assessment." International Journal of Structural Stability and Dynamics 19, no. 03 (March 2019): 1950024. http://dx.doi.org/10.1142/s021945541950024x.

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Two higher-order analytical models based on a new higher-order theory for sandwich plates with flexible cores are developed considering the effect of the core material density and skin-to-core-stiffness-ratio (SCSR). The main difference between the two models is the role of the flexible core in the dynamic response of sandwich plates with cores of different stiffnesses. Firstly, the governing equations of a simply supported sandwich plate with a flexible core are derived based on the two models, and the analytical solutions are determined by using Navier’s approach. Then, the free vibration, static, dynamic bending and stress field characteristics of the sandwich plates with different SCSRs are investigated. The results obtained by the proposed method are compared with other published results. In particular, an accuracy assessment of the present dynamic models is conducted for different SCSRs. Finally, conclusions on the applicability of the proposed method and other theories on sandwich plates with different SCSRs are drawn.
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Zhang, Yichi, and Bingen Yang. "Medium-Frequency Vibration Analysis of Timoshenko Beam Structures." International Journal of Structural Stability and Dynamics 20, no. 13 (September 22, 2020): 2041009. http://dx.doi.org/10.1142/s0219455420410096.

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Medium-frequency (mid-frequency) vibration analysis of complex structures plays an important role in automotive, aerospace, mechanical, and civil engineering. Flexible beam structures modeled by the classical Euler–Bernoulli beam theory have been widely used in various engineering problems. A kinematic hypothesis made in the Euler–Bernoulli beam theory is that the plane sections of a beam normal to its neutral axis remain planes after the beam experiences bending deformation, which neglects shear deformation. However, previous investigations found out that the shear deformation of a beam (even with a large slenderness ratio) becomes noticeable in high-frequency vibrations. The Timoshenko beam theory, which describes both bending deformation and shear deformation, would naturally be more suitable for medium-frequency vibration analysis. Nevertheless, vibrations of Timoshenko beam structures in a medium frequency region have not been well studied in the literature. This paper presents a new method for mid-frequency vibration analysis of two-dimensional Timoshenko beam structures. The proposed method, which is called the augmented Distributed Transfer Function Method (DTFM), models a Timoshenko beam structure by a spatial state-space formulation in the [Formula: see text]-domain. The augmented DTFM determines the frequency response of a beam structure in an exact and analytical form, in any frequency region covering low, middle, or high frequencies. Meanwhile, the proposed method provides the local information of a beam structure, such as displacement, shear deformation, bending moment and shear force at any location, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated in numerical examples, where the efficiency and accuracy of the proposed method is demonstrated. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are examined through comparison of the Timoshenko beam and Euler–Bernoulli beam theories.
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Wu, D., and S. S. Law. "Crack Identification in Thin Plates With Anisotropic Damage Model and Vibration Measurements." Journal of Applied Mechanics 72, no. 6 (February 7, 2005): 852–61. http://dx.doi.org/10.1115/1.1985432.

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Many approaches on modeling of cracks in structural members have been reported in the literatures. However, most of them are explicitly developed for the purpose of studying the changes in static and dynamic responses of the structure due to the crack damage, which is a forward problem mathematically. Thereby the use of these models is inconvenient or even impossible for detecting damage in structures from vibration measurements, which is usually an inverse problem. An anisotropic damage model is proposed for a two-dimensional plate element with an edge-parallel crack. The cracked plate element is represented by a plate element with orthotropic anisotropic material expressed in terms of the virgin material stiffness and a tensor of damage variables. Instead of using the effective stress concept, strain equivalence, or strain energy equivalence principles, the vector of damage variables is identified based on the principle of equivalent static and dynamic behaviors. A nonmodel-based damage identification approach is developed incorporating the proposed anisotropic model and the estimated uniform load surface curvature (ULSC) from vibration measurements. The actual length of the crack is then predicted from the identified variables based on conservation law of potential energy for crack growth. The validity of the methodology is demonstrated by numerical examples and experiment results with comparison to results from existing strain energy equivalence theory.
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Xiao, Tian Yin, Jian Gang Han, and Hong Bo Gao. "Finite Element Model Updating of Space Grid Structures." Advanced Materials Research 243-249 (May 2011): 116–19. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.116.

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The aim of updating models is to generate improved numerical models which may be applied in order to predict actual dynamic behaviors of the structure. The approach of numerical predictions to the behavior of a physical system is limited by the assumptions used in the development of the mathematical model. Model updating is about correcting invalid assumptions by processing vibration test results. Updating by improving the physical meaning of the model requires the application of considerable physical insight in the choice of parameters to update and the arrangement of constraints, force inputs and response measurements in the vibration test. The choice of updating parameters is the most important and the numerical predictions should be sensitive to small changes in the parameters. So methods used in model updating places a demand that the mass, stiffness and damping terms should be based on physically meaningful parameters. Using the structure frequency and local modal shape acquired from structural time-history responses, a model updating method of space grid structures was established in this paper. A numerical example is provided to prove the accuracy of this method. The results show that the method can be effectively used to correct the finite element model of space grid structures.
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Hache, F., N. Challamel, and I. Elishakoff. "Nonlocal Approaches for the Vibration of Lattice Plates Including Both Shear and Bending Interactions." International Journal of Structural Stability and Dynamics 18, no. 07 (July 2018): 1850094. http://dx.doi.org/10.1142/s0219455418500943.

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The present study investigates the dynamical behavior of lattice plates, including both bending and shear interactions. The exact natural frequencies of this lattice plate are calculated for simply supported boundary conditions. These exact solutions are compared with some continuous nonlocal plate solutions that account for some scale effects due to the lattice spacing. Two continualized and one phenomenological nonlocal UflyandMindlin plate models that take into account both the rotary inertia and the shear effects are developed for capturing the small length scale effect of microstructured (or lattice) thick plates by associating the small length scale coefficient introduced in the nonlocal approach to some length scale coefficients given in a Taylor or a rational series expansion. The nonlocal phenomenological model constitutes the stress gradient Eringen’s model applied at the plate scale. The continualization process constructs continuous equation from the one of the discrete lattice models. The governing partial differential equations are solved in displacement for each nonlocal plate model. An exact analytical vibration solution is obtained for the natural frequencies of the simply supported rectangular nonlocal plate. As expected, it is found that the continualized models lead to a constant small length scale coefficient, whereas for the phenomenological nonlocal approaches, the coefficient, calibrated with respect to the element size of the microstructured plate, is structure-dependent. Moreover, comparing the natural frequencies of the continuous models with the exact discrete one, it is concluded that the continualized models provide much more accurate results than the nonlocal Uflyand–Mindlin plate models.
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Moon, Francis C., and Preston D. Stiefel. "Coexisting chaotic and periodic dynamics in clock escapements." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1846 (July 28, 2006): 2539–64. http://dx.doi.org/10.1098/rsta.2006.1839.

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This paper addresses the nature of noise in machines. As a concrete example, we examine the dynamics of clock escapements from experimental, historical and analytical points of view. Experiments on two escapement mechanisms from the Reuleaux kinematic collection at Cornell University are used to illustrate chaotic-like noise in clocks. These vibrations coexist with the periodic dynamics of the balance wheel or pendulum. A mathematical model is presented that shows how self-generated chaos in clocks can break the dry friction in the gear train. This model is shown to exhibit a strange attractor in the structural vibration of the clock. The internal feedback between the oscillator and the escapement structure is similar to anti-control of chaos models.
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Gozum, Mehmet Murat, Amirreza Aghakhani, Gokhan Serhat, and Ipek Basdogan. "Electroelastic modeling of thin-laminated composite plates with surface-bonded piezo-patches using Rayleigh–Ritz method." Journal of Intelligent Material Systems and Structures 29, no. 10 (March 1, 2018): 2192–205. http://dx.doi.org/10.1177/1045389x18758189.

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Laminated composite panels are extensively used in various engineering applications. Piezoelectric transducers can be integrated into such composite structures for a variety of vibration control and energy harvesting applications. Analyzing the structural dynamics of such electromechanical systems requires precise modeling tools which properly consider the coupling between the piezoelectric elements and the laminates. Although previous analytical models in the literature cover vibration analysis of laminated composite plates with fully covered piezoelectric layers, they do not provide a formulation for modeling the piezoelectric patches that partially cover the plate surface. In this study, a methodology for vibration analysis of laminated composite plates with surface-bonded piezo-patches is developed. Rayleigh–Ritz method is used for solving the modal analysis and obtaining the frequency response functions. The developed model includes mass and stiffness contribution of the piezo-patches as well as the two-way electromechanical coupling effect. Moreover, an accelerated method is developed for reducing the computation time of the modal analysis solution. For validations, system-level finite element simulations are performed in ANSYS software. The results show that the developed analytical model can be utilized for accurate and efficient analysis and design of laminated composite plates with surface-bonded piezo-patches.
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Yao, Qiang, Xingguo Yang, and Hongtao Li. "A Fuzzy AHP-Based Method for Comprehensive Blasting Vibration Comfort Evaluation Forecast." Advances in Civil Engineering 2020 (February 8, 2020): 1–11. http://dx.doi.org/10.1155/2020/8919314.

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Blasting vibration comfort evaluation (BVCE) is an emerging interdisciplinary multilayer and multifactor issue that involves explosion mechanics, structural dynamics, biodynamics, statistics, psychology, and many other disciplines. The evaluation index system of blasting vibration comfort is divided into three levels: target level, criterion level, and index level. The absorption blasting vibration energy (ABVE) value is calculated based on triangular membership function, while the value of residual subjective evaluation index is obtained based on evaluation standard. The weight of each index is determined using the analytic hierarchy process. By developing the mathematical models, defining and quantifying the BVCE indices, and analyzing the factors that influence blasting vibration comfort in a hierarchical manner, this study proposes an exploratory fuzzy AHP-based method for comprehensive BVCE. The feasibility\reliability of this method is verified on the basis of 166 groups of comfort survey data. It is found that more than 85% and 62% of forecast results had an error of less than 1.0 and 0.5, respectively. The aim of combining qualitative and quantitative approaches to evaluate and forecast blasting vibration comfort can be initially realized. Further sensitivity analyses show that the absorbed blasting vibration energy (ABVE) index had the most significant influence, followed by environmental vibration, environmental noise, blasting noise, and lastly other factors on blasting vibration comfort. The presented results can provide a reference and guidance for actively creating the favorable conditions in blasting construction practice to improve the resident comfort and to realize the goal of “undisturbing, safe, and harmonious blasting construction.”
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Liu, Qi, Yong Xu, Jürgen Kurths, and Xiaochuan Liu. "Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (June 2022): 062101. http://dx.doi.org/10.1063/5.0093478.

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During the past few decades, several significant progresses have been made in exploring complex nonlinear dynamics and vibration suppression of conceptual aeroelastic airfoil models. Additionally, some new challenges have arisen. To the best of the author’s knowledge, most studies are concerned with the deterministic case; however, the effects of stochasticity encountered in practical flight environments on the nonlinear dynamical behaviors of the airfoil systems are neglected. Crucially, coupling interaction of the structure nonlinearities and uncertainty fluctuations can lead to some difficulties on the airfoil models, including accurate modeling, response solving, and vibration suppression. At the same time, most of the existing studies depend mainly on a mathematical model established by physical mechanisms. Unfortunately, it is challenging and even impossible to obtain an accurate physical model of the complex wing structure in engineering practice. The emergence of data science and machine learning provides new opportunities for understanding the aeroelastic airfoil systems from the data-driven point of view, such as data-driven modeling, prediction, and control from the recorded data. Nevertheless, relevant data-driven problems of the aeroelastic airfoil systems are not addressed well up to now. This survey contributes to conducting a comprehensive overview of recent developments toward understanding complex dynamical behaviors and vibration suppression, especially for stochastic dynamics, early warning, and data-driven problems, of the conceptual two-dimensional airfoil models with different structural nonlinearities. The results on the airfoil models are summarized and discussed. Besides, several potential development directions that are worth further exploration are also highlighted.
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Dissertations / Theses on the topic "Plates (Engineering) – Vibration ; Structural dynamics – Mathematical models"

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張啓軍 and Qijun Zhang. "The Galerkin Element Method and power flow in acoustic-structural problems with damped sandwich plates." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31239742.

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Tso, Y. (Yan). "A study of the transmission of vibration in structures characteristic of naval ships / Yan Tso." 1996. http://hdl.handle.net/2440/18755.

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Bibliography: leaves 159-169.
xii, 170 leaves : ill. (some col.) ; 30 cm.
Title page, contents and abstract only. The complete thesis in print form is available from the University Library.
This thesis is concerned with the transmission and distribution of vibratory power in built-up structures, and in particular, structures characteristic of naval ships. The study consists of a detailed investigation of the wave transmission properties of structural junctions, followed by an analysis of the wave propagation through plates with periodic stiffeners. The results are used to develop Statistical Energy Analysis (SEA) models for the prediction of vibration levels in structures characteristic of naval ships.
Thesis (Ph.D.)--University of Adelaide, Dept. of Mechanical Engineering, 1996
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Tso, Y. (Yan). "A study of the transmission of vibration in structures characteristic of naval ships / Yan Tso." Thesis, 1996. http://hdl.handle.net/2440/18755.

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Bibliography: leaves 159-169.
xii, 170 leaves : ill. (some col.) ; 30 cm.
This thesis is concerned with the transmission and distribution of vibratory power in built-up structures, and in particular, structures characteristic of naval ships. The study consists of a detailed investigation of the wave transmission properties of structural junctions, followed by an analysis of the wave propagation through plates with periodic stiffeners. The results are used to develop Statistical Energy Analysis (SEA) models for the prediction of vibration levels in structures characteristic of naval ships.
Thesis (Ph.D.)--University of Adelaide, Dept. of Mechanical Engineering, 1996
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Kruchoski, Brian L. (Brian Louis). "Identification of structural parameters and hydrodynamic effects for forced and free vibration." Thesis, 1992. http://hdl.handle.net/1957/36152.

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Statistically-based estimation techniques are presented in this study. These techniques incorporate structural test data to improve finite element models used for dynamic analysis. Methods are developed to identify optimum values of the parameters of finite element models describing structures. The parameters which may be identified are : element area, mass density, and moment of inertia; lumped mass and stiffness; and the Rayleigh damping coefficients. A technique is described for incorporating hydrodynamic effects on small bodies by identifying equivalent structure mass, stiffness, and damping properties. Procedures are presented for both the free vibration problem and for forced response in the time domain. The equations for parameter identification are formulated in terms of measured response, calculated response, the prior estimate of the parameters, and a weighting matrix. The form of the weighting matrix is presented for three identification schemes : Least Squares, Weighted Least Squares, and Bayesian. The weighting matrix is shown to be a function of a sensitivity matrix relating structural response to the parameters of the finite element model. Sensitivities for the forced vibration problem are derived from the Wilson Theta equations, and are presented for the free vibration problem. The algorithm used for parameter identification is presented, and its implementation in a computer program is described. Numerical examples are included to demonstrate the solution technique and the validity and capability of the identification method. All three estimation schemes are found to provide efficient and reliable parameter identification for many modeling situations.
Graduation date: 1993
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Books on the topic "Plates (Engineering) – Vibration ; Structural dynamics – Mathematical models"

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Mukhopadhyay, Madhujit. Vibrations, dynamics and structural systems. 2nd ed. Rotterdam: A. A. Balkema, 2000.

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Göran, Sandberg, and Ohayon R, eds. Computational aspects of structural acoustics and vibration. Wien: Springer, 2008.

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M, Ayyub Bilal, Guran A, and Haldar Achintya, eds. Uncertainty modeling in vibration, control and fuzzy analysis of structural systems. Singapore: World Scientific, 1997.

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Conference on Mechanical Vibration and Noise (11th 1987 Boston, Mass.). Modal testing and analysis: Presented at the 1987 ASME Design Technology Conferences--11th Biennial Conference on Mechanical Vibration and Noise, Boston, Massachusetts, September 27-30, 1987. New York, N.Y. (345 E. 47th St., New York 10017): American Society of Mechanical Engineers, 1987.

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S, Tzou H., and Bergman Lawrence A, eds. Dynamics and control of distributed systems. Cambridge, [Eng.]: Cambridge University Press, 1998.

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P, Norton M. The prediction of dynamic stress in structures due to air- and structure-borne sound and vibration. East Perth, WA: The Institute, 1996.

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Dynamics of pavement structures. London: E & FN Spon, 1994.

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Modal testing: Theory, practice, and application. 2nd ed. Baldock, Hertfordshire, England: Research Studies Press, 2000.

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International Seminar on Modal Analysis (19th 1994 Katholieke Universiteit te Leuven). Proceedings ISMA 19, tools for noise and vibration analysis: Conference, September 12-14, 1994. Edited by Sas Paul and Katholieke Universiteit te Leuven (1970- ). Afdeling Mechanische Konstruktie en Produktie. Heverlee, Belgium: Katholieke Universiteit Leuven, Faculty of Engineering, Dept. of Mechanical Engineering, Division of Production Engineering, Machine Design & Automation, 1994.

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1969-, Kim Hongjin, ed. Wavelet-based vibration control of smart buildings and bridges. Boca Raton: Taylor & Francis, 2009.

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Conference papers on the topic "Plates (Engineering) – Vibration ; Structural dynamics – Mathematical models"

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Asadi, Saeed, Viktor Berbyuk, and Håkan Johansson. "Vibration Dynamics of a Wind Turbine Drive Train High Speed Subsystem: Modelling and Validation." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46016.

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Modern wind turbines are enormous large-scale electromechanical systems. They operate in complex conditions, determined by a turbulent wind field, by possible disturbances in the electricity grid and by the behavior of sea waves for offshore turbines. Guaranteeing the structural integrity of these machines during a lifetime of 20 years is an enormous challenge. In this paper the dynamics of a wind turbine drive train high speed subsystem is studied both by modeling and experiments with focus on system torsional and flexural vibrations and transient events which can reduce fatigue life of functional components (gearbox, bearings, shafts, couplings, others). A scaled down drive train high speed shaft test rig has been developed. Main components of the test rig are six-pole motor with variable frequency drive controller (up to 1000 rpm), shafts’ disk coupling and flexible mounting structure representing gearbox housing with output high speed bearing. The test rig is equipped with measurement system comprising a set of accelerometers and displacement sensors, data acquisition hardware and software (SKF WindCon3.0). Mathematical and computational models of the test rig have been developed and went through validation tests. The system kinematic and dynamic responses are studied for different operational scenarios and structural parameters (ratio of shaft bending stiffness and stiffness of mounting structures, unevenly inertia load distribution, others). The ultimate goal of the test rig is to get insight into interaction between internal dynamics of drive train functional components to be used the results obtained in developing novel methods to detect, predict and prevent faults and failures in wind turbine drive trains arising due to misalignments and transient external loads.
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Fritzen, C. P., D. Jennewein, and Th Kiefer. "Damage Detection Based on Vibration Measurements and Inaccurate Models." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4156.

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Abstract The paper presents a model-based approach for the detection of structural damage with respect to location and extent from measured vibration test data. The method which is tolerant to small modeling errors is based upon an analytically redundant mathematical model approximately representing the undamaged structure. The motivation was that in many practical cases it is not possible to obtain perfect correlation between the undamaged system and the original model due to modeling uncertainties or excessive modeling cost. On the other hand, in the early phase of damage evolution the changes of the dynamical characteristics are very small. If the changes due to the damage are superimposed by the effects of mismodeling it is nearly impossible to get reliable diagnostic results. Therefore, an approach is presented here for the case that a perfect model cannot be obtained. The resulting inverse problem usually is ill-posed, so that special attention must be paid to its accurate numerical solution. The application to damage detection problems requires the reduction of a large set of damage parameter candidates to a small subset of one or two parameters really describing the local change of the system. An orthogonalization strategy is given to reduce the parameter set and Akaike’s information criterion is used to confirm the correct size of the parametrization. The method is applied to two laboratory structures: a multi-story frame and a damaged plate. The results show that the algorithm is able to localize and quantify the damage also in the presence of modeling errors.
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Baz, A., and S. Poh. "Active Constrained Layer Damping of Seismic Excitations." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0632.

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Abstract This paper aims at demonstrating the feasibility of Active Constrained Layer Dampers (ACLD) as an effective means for damping out seismic-induced vibrations of structures. The ACLD concept is motivated by the destructive effects that seismic excitations have on most of the uncontrolled structures. The effectiveness of the ACLD in enhancing the damping characteristics of conventional visco-elastic dampers is demonstrated experimentally for structures subjected to base excitations. Classical identification methods are used to identify a mathematical model that describes the interaction between the vibrating structures, the ACLD system and the seismic excitation. The model is integrated with a robust Continuous Sliding Mode (CSM) controller to reject the effect of the seismic excitations acting on vibrating structures with uncertain dynamic parameters. In this manner, the ACLD and the CSM algorithm present a simple but yet powerful alternative to classical control methods for rejecting seismic excitations and accommodating wide range of parameter uncertainty. The emphasis, in this paper, is placed on multi-story two-dimensional scaled structures which are provided with diagonal braces of the ACLD. However, the techniques developed can be readily extended to three-dimensional and larger structures.
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Armin, Milad, and Narakorn Srinil. "Wake-Induced Transverse Vibration of Two Interfering Cylinders in Tandem Arrangement: Modelling and Analysis." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10896.

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A considerable number of numerical and experimental studies have been performed on the problem of vortex induced vibration (VIV) of an isolated circular cylinder. A very few studies have considered a practical situation where cylinders are deployed in clusters. This study presents a mathematical fluid-structure interaction modelling and analysis of two flexibly-mounted circular cylinders arranged in tandem and subject to fluid cross flows. The hydrodynamic lift forces and their time variations are approximated by two different semi-empirical wake oscillator models based on the van der Pol and Rayleigh equations. These nonlinear wake oscillators are coupled with linear structural oscillators through the acceleration and velocity coupling terms, respectively. A direct numerical time integration approach is used to predict the response amplitude behaviors and parametrically investigate the vortex- and wake-induced vibration transverse response of the two interfering upstream and downstream cylinders. Some empirical coefficients are calibrated against available, although very limited, computational fluid dynamics results. Preliminary parametric studies are conducted with the case of varying reduced flow velocity, and some insightful aspects on the effect of mass and damping ratio are highlighted. Depending on system parameters, numerical prediction results based on the van der Pol and Rayleigh equations are compared, and a combination of the two wake oscillators is suggested as a new model for predicting the vortex and wake-induced of the two interfering cylinders.
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Changizi, M. Amin, and Ion Stiharu. "A Complete Parametric Study of Pull-In Voltage by Nonlinear Differential Equation." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37744.

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Micro-cantilever beams are interested structures in MEMS because of their fabrication is very easy and its versatility. The importance of micro-cantilevers beam in MEMS has driven various investigations like static and dynamic performances under different loading such as potential fields. In this research the non-linear differential equation which models dynamics of a micro-cantilever beams vibration subjected to electrostatic field has been studied. The model which has one degree of freedom is used to calculate the pull-in voltage. This model adopted based on different method of calculating stiffness of micro-cantilever beam. The nonlinear ordinary differential equation which used to model the dynamics of the cantilever subjected to electric field close to snap on is highly stiff. Investigation on solving of nonlinear stiff ordinary equation showed that only Lsode algorithm yield to correct solution to the problem. Lsode is equipped with a robust adaptive time step selection mechanism that enables solutions to very stiff problems, as the one under discussion. The best match in the resonant frequency for equivalent stiffness based on four different models was considered. The stiffness model suitable for the best match in deflection is proved to be different from the model that yields. Pull-in voltage under electric field was studied. Pull-in voltage has been investigated from the analytical and numerical perspective. A complete parametric study of structural damping effect on large deflection of micro-cantilever beam was studied was done numerically in this work. Different kind of impulse voltages were considered and effect of them on pulling voltage numerically was studied. A cumbersome mathematical method, Lie symmetry, was used to drive a closed from of time response to step voltage for undamped system and pull in voltage of such system was calculated. Finally, a closed form driven from the nonlinear ODE for calculating pulling voltage was presented.
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