Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems.
There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between theory and practice, fundamentals and advanced subjects, and generality and specialization.
None of the books in this area have completely studied and analyzed nonlinear equation in dynamical and vibratory systems using the latest analytical and numerical methods, so that the user can solve the problems without the need of studying too many different references. Thereby in this book, by the use of the latest analytic, numeric laboratorial methods and using more than 300 references like books, papers and the researches done by the authors and by considering almost all possible processes and situation, new theories has been proposed to encounter applied problems in engineering and applied sciences. In this way, the user (bachelor’s, master’s and PhD students, university teachers and even in research centers in different fields of mechanical, civil, aerospace, electrical, chemical, applied mathematics, physics, and etc.) can encounter such systems confidently. In the different chapters of the book, not only are the linear and especially nonlinear problems with oscillatory form broadly discussed, but also applied examples are practically solved by the proposed methodology.
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Studies in Applied Mechanics, 4: Variational, Incremental, and Energy Methods in Solid Mechanics and Shell Theory covers the subject of variational, incremental, and energy methods in Solid Mechanics and Shell Theory from a general standpoint, employing general coordinates and tensor notations. The publication first ponders on mathematical preliminaries, kinematics and stress in three-dimensional solid continua, and the first and second laws of thermodynamics. Discussions focus on the principles of virtual displacements and virtual forces, kinematics of rigid body motions, incremental stresses, kinematics of incremental deformation, description of motion, coordinates, reference and deformed states, tensor formulas for surfaces, and differentials and derivatives of operators. The text then elaborates on constitutive material laws, deformation and stress in shells, first law of thermodynamics applied to shells, and constitutive relations and material laws for shells. Concerns cover hyperelastic incremental material relations, material laws for thin elastic shells, incremental theory and stability, reduced and local forms of the first law of thermodynamics, and description of deformation and motion in shells. The book examines elastic stability, finite element models, variational and incremental principles, variational principles of elasticity and shell theory, and constitutive relations and material laws for shells. The publication is a valuable reference for researchers interested in the variational, incremental, and energy methods in solid mechanics and shell theory.
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Structural Mechanics Fundamentals gives you a complete and uniform treatment of the most fundamental and essential topics in structural mechanics. Presenting a traditional subject in an updated and modernized way, it merges classical topics with ones that have taken shape in more recent times, such as duality. This book is extensively based on the introductory chapters to the author’s Structural Mechanics: A Unified Approach.
Coverage includes:
The basic topics of geometry of areas and of kinematics and statics of rigid body systems
The mechanics of linear elastic solids―beams, plates, and three-dimensional solids―examined using a matrix approach
The analysis of strain and stress around a material point
The linear elastic constitutive law, with related Clapeyron’s and Betti’s theorems
Kinematic, static, and constitutive equations
The implication of the principle of virtual work
The Saint Venant problem
The theory of beam systems―statically determinate or indeterminate
Methods of forces and energy for the examination of indeterminate beam systems
The book draws on the author’s many years of teaching experience and features a wealth of illustrations and worked examples to help explain the topics clearly yet rigorously. The book can be used as a text for senior undergraduate or graduate students in structural engineering or architecture and as a valuable reference for researchers and practicing engineers.
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Author(s)/Editor(s): Ján Balaš, Ján Sládek and Vladimír Sládek (Eds.) | Size: 9 MB | Format:PDF | Quality:Unspecified | Publisher: Academic Press, Elsevier | Year: 1989 | pages: 695 | ISBN: 9780444988300
The boundary element method is an extremely versatile and powerful tool of computational mechanics which has already become a popular alternative to the well established finite element method. This book presents a comprehensive and up-to-date treatise on the boundary element method (BEM) in its applications to various fields of continuum mechanics such as: elastostatics, elastodynamics, thermoelasticity, micropolar elasticity, elastoplasticity, viscoelasticity, theory of plates and stress analysis by hybrid methods. The fundamental solution of governing differential equations, integral representations of the displacement and temperature fields, regularized integral representations of the stress field and heat flux, boundary integral equations and boundary integro-differential equations are derived. Besides the mathematical foundations of the boundary integral method, the book deals with practical applications of this method. Most of the applications concentrate mainly on the computational problems of fracture mechanics. The method has been found to be very efficient in stress-intensity factor computations.
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Author(s)/Editor(s): Alan P Jeary | Size: 7,2 MB | Format:PDF | Quality:Unspecified | Publisher: University College London | Year: 1981 | pages: 208
A study of the measurement, prediction and characterisation of
the dynamic behaviour of tall buildings is presented. Initially
a review of the history of tall buildings and the study of their
dynamic behaviour is presented. The characterisation of tall
buildings by conventional means and by the use of spectral
functions is considered.
The results of tests on twelve tall buildings and one quarter-scale
model are presented. The response of twelve of these structures
to wind excitation has been monitored, and, for the purpose of
calibration, all but one of the buildings has been excited
artificially by the use of eccentric mass vibrators. The handling
of deterministic and random data is considered and some new
techniques for their reduction are presented.
The introduction of a new vibrator system has allowed the study of
the dynamic characteristics of tall buildings with a greater
precision than has previously been possible. The new precision
has suggested reasons for the confusion which previously existed
in the assessment of dynamic characteristics of tall buildings,
and a new rationale for the prediction of natural frequencies and
damping ratios is presented.
Finally, currently popular methods for the prediction of the
response of tall buildings to wind excitation are considered and
comparisons have suggested several areas where research is
urgently needed.
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Abstract: The objective of this study is to assess the seismic behavior of reinforced concrete bridges with skew-angled seat-type abutments through a performance-based methodology. Special attention is given to the exploration of variations in the seismic behavior of such bridges with respect to the angle of skew. Post-earthquake reconnaissance studies have reported that larger values of skew angle adversely affect performance. The idiosyncratic, "multi-phasic," behavior of skew bridges--observed during initial simulations of the present study--led to the development of a novel assessment methodology. This methodology is applied to a comprehensive database of bridges, which comprise combinations of a variety of geometric properties including: (1) number of spans, (2) number of columns per bent, (3) column-bent height, (4) span arrangement, and (5) abutment skew angle. An extensive set of nonlinear response history analyses were conducted using distinct suites of ground motions representing records for rock and soil sites, and another set that contained pronounced velocity pulses. The findings indicate that demand parameters for skew-abutment bridges--e.g., deck rotation, abutment unseating, and column drift ratio--are generally higher than those for straight bridges. Through detailed investigations of the sensitivity of various response parameters to variations in bridge geometry and ground motion characteristics, we observed that bridges with larger abutment skew angles bear a higher probability of collapse due to excessive rotations. We also found that shear keys can play a major role in abating deck rotations and thus the probability of collapse. It was further observed that the resultant peak ground velocity (PGVres) is the most efficient ground motion intensity measure (IM) for assessing skewed bridges' seismic response.
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Seismic earth pressures on retaining structures in cohesionless soils
Author(s): Mikola, Roozbeh Geraili; Sitar, Nicholas
Published By:University of California
Published Year:2013
Size: 4,2 MB
Quality:Unspecified
Abstract: Observations of the performance of basement walls and retaining structures in recent
earthquakes show that failures of basement or deep excavation walls in earthquakes are rare even
if the structures were not designed for the actual intensity of the earthquake loading. Failures of
retaining structures are most commonly confined to waterfront structures retaining saturated
backfill with liquefaction being the critical factor in the failures. Failures of other types of
retaining structures are relatively rare and usually involve a more complex set of conditions, such
as sloping ground either above or below the retaining structure, or both. While some failures
have been observed, there is no evidence of a systemic problem with traditional static retaining
wall design even under quite severe loading conditions. No significant damage or failures of
retaining structures occurred in the recent earthquakes such as Wenchuan earthquake in China
(2008) and, or the large subduction zone earthquakes in Chile (2010) and Japan (2011).
Therefore, this experimental and analytical study was undertaken to develop a better
understanding of the distribution and magnitude of seismic earth pressures on cantilever
retaining structures.
The experimental component of the study consists of two sets of dynamic centrifuge
model experiments. In the first experiment two model structures representing basement type
setting were used, while in the second test a U-shaped channel with cantilever sides and a simple
cantilever wall were studied. All of these structures were chosen to be representative of typical
designs. Dry medium-dense sand with relative density on the order of from 75% to 80% was
used as backfill. Results obtained from the centrifuge experiments were subsequently used to
develop and calibrate a two-dimensional, nonlinear, finite difference model built on the FLAC
platform.
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Seismic earth pressures on retaining structures with cohesive backfills
Author(s): Candia Agusti, Gabriel; Sitar, Nicholas
Published By:The Earthquake Engineering Online Archive
Published Year:2013
Size: 8 MB
Quality:Unspecified
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Abstract: Report presents the results of centrifuge model experiments and numerical analyses of seismic response of retaining structures with cohesive backfill. The experimental results show that the static and seismic earth pressures increase linearly with depth and that the resultant acts at 0.35H-0.4H, as opposed to 0.5-0.6H assumed in current engineering practice. Overall, the results also show that typical retaining walls designed with a static factor of safety of 1.5 have enough strength capacity to resist ground accelerations up to 0.4g.
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UCB/GT-2013-02, University of California, Berkeley, Geotechnical Engineering
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Author(s)/Editor(s): I. Elishakoff, J. Arbocz, C.D. Babcock and A. Libai (Eds.) | Size: 16 MB | Format:PDF | Quality:Unspecified | Publisher: Academic Press, Elsevier | Year: 1988 | pages: 458 | ISBN: 9780444704740
This collection of papers, written by friends and colleagues of Josef Singer, presents a comprehensive and timely review of the theoretical mechanics of thin shell-structures. Topics of great current interest such as the buckling of composite plates and shells, the plastic buckling of thin-walled structures and the optimum design of buckling sensitive curved composite panels are examined by experts, using a great diversity of approaches, whereby theoretical predictions are compared with experimental results whenever possible. Other topics reviewed include the buckling and post-buckling behaviour of imperfect shells under different external static or dynamic loads and a variety of boundary conditions. Papers dealing with the vibration and the dynamic response of thin elastic bodies are also presented. A strong emphasis is made on the practical applications aspect in the theories presented. Thus engineers, research workers and students who are involved with the design and analysis of shell structures made of different materials, and subjected to various static and dynamic loads will find this volume an invaluable source of reference.
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Author(s)/Editor(s): George Z. Voyiadjis and Dimitrios Karamanlidis (Eds.) | Size: 9 MB | Format:PDF | Quality:Unspecified | Publisher: Academic Press, Elsevier | Year: 1990 | pages: 313 | ISBN: 9780444883667
Plates and shells play an important role in structural, mechanical, aerospace and manufacturing applications. The theory of plates and shells have advanced in the past two decades to handle more complicated problems that were previously beyond reach. In this book, the most recent advances in this area of research are documented. These include topics such as thick plate and shell analyses, finite rotations of shell structures, anisotropic thick plates, dynamic analysis, and laminated composite panels. The book is divided into two parts. In Part I, emphasis is placed on the theoretical aspects of the analysis of plates and shells, while Part II deals with modern applications. Numerous eminent researchers in the various areas of plate and shell analyses have contributed to this work which pays special attention to aspects of research such as theory, dynamic analysis, and composite plates and shells.
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