Asymptotic Methods In The Theory Of Plates With Mixed Boundary Conditions

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Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions

Author : Igor Andrianov
Publisher : John Wiley & Sons
ISBN 13 : 111872514X
Total Pages : 288 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions by : Igor Andrianov

Download or read book Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions written by Igor Andrianov and published by John Wiley & Sons. This book was released on 2014-02-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Methods in the Theory of Plates with MixedBoundary Conditions comprehensively covers the theoreticalbackground of asymptotic approaches and their use in solvingmechanical engineering-oriented problems of structural members,primarily plates (statics and dynamics) with mixed boundary conditions. The first part of this book introduces the theory and applicationof asymptotic methods and includes a series of approaches that havebeen omitted or not rigorously treated in the existing literature.These lesser known approaches include the method of summation andconstruction of the asymptotically equivalent functions, methods ofsmall and large delta, and the homotopy perturbations method. The second part of the book contains original results devoted tothe solution of the mixed problems of the theory of plates,including statics, dynamics and stability of the studied objects.In addition, the applicability of the approaches presented to otherrelated linear or nonlinear problems is addressed. Key features: • Includes analytical solving of mixed boundary valueproblems • Introduces modern asymptotic and summationprocedures • Presents asymptotic approaches for nonlinear dynamics ofrods, beams and plates • Covers statics, dynamics and stability of plates withmixed boundary conditions • Explains links between the Adomian and homotopyperturbation approaches Asymptotic Methods in the Theory of Plates with MixedBoundary Conditions is a comprehensive reference forresearchers and practitioners working in the field of Mechanics ofSolids and Mechanical Engineering, and is also a valuable resourcefor graduate and postgraduate students from Civil and MechanicalEngineering.

Asymptotic Theory of Anisotropic Plates and Shells

Author : Lenser Aghalovyan
Publisher : World Scientific
ISBN 13 : 9814579041
Total Pages : 376 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Asymptotic Theory of Anisotropic Plates and Shells by : Lenser Aghalovyan

Download or read book Asymptotic Theory of Anisotropic Plates and Shells written by Lenser Aghalovyan and published by World Scientific. This book was released on 2015-03-03 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: A consistent theory for thin anisotropic layered structures is developed starting from asymptotic analysis of 3D equations in linear elasticity. The consideration is not restricted to the traditional boundary conditions along the faces of the structure expressed in terms of stresses, originating a new type of boundary value problems, which is not governed by the classical Kirchhoff-Love assumptions. More general boundary value problems, in particular related to elastic foundations are also studied. The general asymptotic approach is illustrated by a number of particular problems for elastic and thermoelastic beams and plates. For the latter, the validity of derived approximate theories is investigated by comparison with associated exact solution. The author also develops an asymptotic approach to dynamic analysis of layered media composed of thin layers motivated by modeling of engineering structures under seismic excitation. Contents:Plane Problem for a Rectangular Elastic StripThe Winkler-Fuss ModelDirect Asymptotic Integration of 3D Elasticity Equations for Orthotropic PlatesMatching of the Outer Solution and the Boundary Layer for an Orthotropic PlateElastic Plates of General AnisotropyNon-Classical Boundary Value Problems for Anisotropic PlatesTwo-Layer Anisotropic Plates. The Modulus of a Layered FoundationAsymptotic Analysis of the Outer Problem for an Orthotropic ShellBoundary Layer in Orthotropic ShellsNon-Classical Boundary Value Problems for Anisotropic ShellsSpatial Dynamic Problems for Anisotropic Plates Readership: Researchers and specialists in applied mathematics and mechanical engineering, undergraduates and graduate students. Keywords:Asymptotic Theories;Beams;Plates;Shells;Problems of Elasticity Theory;Layered Thermoelastic Thin Structures;Elastic Foundations;Non-Classical Boundary Problems for Anisotropic Beams, Plates and Shells;Singularly Perturbed Systems;Boundary LayerKey Features:The book exposits consistent theory for composite thin walled elastic structures. The obtained results are applied to justification and refinement of ad hoc engineering structural theoriesThe effective solutions of a variety of boundary value problems are obtainedThere is a clear potential for numerous advanced industrial applications

Asymptotic Theories for Plates and Shells

Author : Klaus Hackl
Publisher : CRC Press
ISBN 13 : 9780582248755
Total Pages : 148 pages
Book Rating : 4.2/5 (487 download)

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Book Synopsis Asymptotic Theories for Plates and Shells by : Klaus Hackl

Download or read book Asymptotic Theories for Plates and Shells written by Klaus Hackl and published by CRC Press. This book was released on 1995-03-06 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note contains papers presented at the SIAM 40th anniversary meeting organised by the editors and held in Los Angeles in 1992. The papers focus on new fundamental results in the theory of plates and shells, with particular emphasis on the treatment of different materials and the nonlinearities involved. Asymptotic methods, such as formal expansions, homogenization, and two-scale convergence, are analytical tools that pervade much of the research. Some of the papers are also concerned with existence results, especially for nonlinear problems, using various functional analytic methods.

Asymptotic Methods for Engineers

Author : Igor V. Andrianov
Publisher : CRC Press
ISBN 13 : 104003277X
Total Pages : 409 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Asymptotic Methods for Engineers by : Igor V. Andrianov

Download or read book Asymptotic Methods for Engineers written by Igor V. Andrianov and published by CRC Press. This book was released on 2024-05-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Methods for Engineers is based on the authors’ many years of practical experience in the application of asymptotic methods to solve engineering problems. This book is devoted to modern asymptotic methods (AM), which is widely used in engineering, applied sciences, physics, and applied mathematics. Avoiding complex formal calculations and justifications, the book’s main goal is to describe the main ideas and algorithms. Moreover, not only is there a presentation of the main AM, but there is also a focus on demonstrating their unity and inseparable connection with the methods of summation and asymptotic interpolation. The book will be useful for students and researchers from applied mathematics and physics and of interest to doctoral and graduate students, university and industry professors from various branches of engineering (mechanical, civil, electro-mechanical, etc.).

Nonlinear Wave Dynamics of Materials and Structures

Author : Holm Altenbach
Publisher : Springer Nature
ISBN 13 : 3030387089
Total Pages : 473 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Nonlinear Wave Dynamics of Materials and Structures by : Holm Altenbach

Download or read book Nonlinear Wave Dynamics of Materials and Structures written by Holm Altenbach and published by Springer Nature. This book was released on 2020-04-22 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.

Computational Analysis of Structured Media

Author : Simon Gluzman
Publisher : Academic Press
ISBN 13 : 0128110473
Total Pages : 328 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Computational Analysis of Structured Media by : Simon Gluzman

Download or read book Computational Analysis of Structured Media written by Simon Gluzman and published by Academic Press. This book was released on 2017-09-20 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Analysis of Structured Media presents a systematical approach to analytical formulae for the effective properties of deterministic and random composites. Schwarz’s method and functional equations yield for use in symbolic-numeric computations relevant to the effective properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis, and their applications to composites. Symbolic-numerical computations are widely used to deduce new formulae interesting for applied mathematicians and engineers. The main line of presentation is the investigation of two-phase 2D composites with non-overlapping inclusions randomly embedded in matrices. Computational methodology for main classes of problems in structured media Theory of Representative Volume Element Combines exact results, Monte-Carlo simulations and Resummation techniques under one umbrella Contains new analytical formulae obtained in the last ten years and it combines different asymptotic methods with the corresponding computer implementations

Modern Trends in Structural and Solid Mechanics 2

Author : Noel Challamel
Publisher : John Wiley & Sons
ISBN 13 : 1119831849
Total Pages : 306 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Modern Trends in Structural and Solid Mechanics 2 by : Noel Challamel

Download or read book Modern Trends in Structural and Solid Mechanics 2 written by Noel Challamel and published by John Wiley & Sons. This book was released on 2021-06-08 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprised of three separate volumes presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This second volume is devoted to the vibrations of solid and structural members. Modern Trends in Structural and Solid Mechanics 2 has broad scope, covering topics such as: exact and approximate vibration solutions of rods, beams, membranes, plates and three-dimensional elasticity problems, Bolotins dynamic edge effect, the principles of plate theories in dynamics, nano- and microbeams, nonlinear dynamics of shear extensible beams, the vibration and aeroelastic stability behavior of cellular beams, the dynamic response of elastoplastic softening oscillators, the complex dynamics of hysteretic oscillators, bridging waves, and the three-dimensional propagation of waves. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.

Shell Structures: Theory and Applications Volume 4

Author : Wojciech Pietraszkiewicz
Publisher : CRC Press
ISBN 13 : 135168048X
Total Pages : 574 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Shell Structures: Theory and Applications Volume 4 by : Wojciech Pietraszkiewicz

Download or read book Shell Structures: Theory and Applications Volume 4 written by Wojciech Pietraszkiewicz and published by CRC Press. This book was released on 2017-10-30 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shells are basic structural elements of modern technology and everyday life. Examples of shell structures in technology include automobile bodies, water and oil tanks, pipelines, silos, wind turbine towers, and nanotubes. Nature is full of living shells such as leaves of trees, blooming flowers, seashells, cell membranes or wings of insects. In the human body arteries, the eye shell, the diaphragm, the skin and the pericardium are all shells as well. Shell Structures: Theory and Applications, Volume 4 contains 132 contributions presented at the 11th Conference on Shell Structures: Theory and Applications (Gdansk, Poland, 11-13 October 2017). The papers reflect a wide spectrum of scientific and engineering problems from theoretical modelling through strength, stability and dynamic behaviour, numerical analyses, biomechanic applications up to engineering design of shell structures. Shell Structures: Theory and Applications, Volume 4 will be of interest to academics, researchers, designers and engineers dealing with modelling and analyses of shell structures. It may also provide supplementary reading to graduate students in Civil, Mechanical, Naval and Aerospace Engineering.

Asymptotical Mechanics of Thin-Walled Structures

Author : Igor V. Andrianov
Publisher : Springer Science & Business Media
ISBN 13 : 354045246X
Total Pages : 527 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Asymptotical Mechanics of Thin-Walled Structures by : Igor V. Andrianov

Download or read book Asymptotical Mechanics of Thin-Walled Structures written by Igor V. Andrianov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book a detailed and systematic treatment of asymptotic methods in the theory of plates and shells is presented. The main features of the book are the basic principles of asymptotics and their applications, traditional approaches such as regular and singular perturbations, as well as new approaches such as the composite equations approach. The book introduces the reader to the field of asymptotic simplification of the problems of the theory of plates and shells and will be useful as a handbook of methods of asymptotic integration. Providing a state-of-the-art review of asymptotic applications, this book will be useful as an introduction to the field for novices as well as a reference book for specialists.

Approximate Models of Mechanics of Composites

Author : Igor V. Andrianov
Publisher : CRC Press
ISBN 13 : 1000890201
Total Pages : 368 pages
Book Rating : 4.0/5 (8 download)

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Book Synopsis Approximate Models of Mechanics of Composites by : Igor V. Andrianov

Download or read book Approximate Models of Mechanics of Composites written by Igor V. Andrianov and published by CRC Press. This book was released on 2023-06-20 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1) Provides analytical solutions based on a three-phase model for composites of various structures 2) Identifies computational models to solve problems within all applications of composite materials 3) Constructs higher approximations of the Maxwell formula 4) Proposes efficient analytical algorithms ensuring reliable computational analysis

Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains

Author : Dmitrii Korikov
Publisher : Springer Nature
ISBN 13 : 3030653722
Total Pages : 404 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains by : Dmitrii Korikov

Download or read book Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains written by Dmitrii Korikov and published by Springer Nature. This book was released on 2021-04-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.

Asymptotical Mechanics of Composites

Author : Igor V. Andrianov
Publisher : Springer
ISBN 13 : 3319657860
Total Pages : 329 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Asymptotical Mechanics of Composites by : Igor V. Andrianov

Download or read book Asymptotical Mechanics of Composites written by Igor V. Andrianov and published by Springer. This book was released on 2017-11-09 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors show that it is possible to construct efficient computationally oriented models of multi-parameter complex systems by using asymptotic methods, which can, owing to their simplicity, be directly used for controlling processes arising in connection with composite material systems. The book focuses on this asymptotic-modeling-based approach because it allows us to define the most important out of numerous parameters describing the system, or, in other words, the asymptotic methods allow us to estimate the sensitivity of the system parameters. Further, the book addresses the construction of nonlocal and higher-order homogenized models. Local fields on the micro-level and the influence of so-called non-ideal contact between the matrix and inclusions are modeled and investigated. The book then studies composites with non-regular structure and cluster type composite conductivity, and analyzes edge effects in fiber composite materials. Transition of load from a fiber to a matrix for elastic and viscoelastic composites, various types of fiber composite fractures, and buckling of fibers in fiber-reinforced composites is also investigated. Last but not least, the book includes studies on perforated membranes, plates, and shells, as well as the asymptotic modeling of imperfect nonlinear interfaces.

Shell-like Structures

Author : Holm Altenbach
Publisher : Springer Science & Business Media
ISBN 13 : 3642218555
Total Pages : 750 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Shell-like Structures by : Holm Altenbach

Download or read book Shell-like Structures written by Holm Altenbach and published by Springer Science & Business Media. This book was released on 2011-07-03 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume scientists and researchers from industry discuss the new trends in simulation and computing shell-like structures. The focus is put on the following problems: new theories (based on two-dimensional field equations but describing non-classical effects), new constitutive equations (for materials like sandwiches, foams, etc. and which can be combined with the two-dimensional shell equations), complex structures (folded, branching and/or self intersecting shell structures, etc.) and shell-like structures on different scales (for example: nano-tubes) or very thin structures (similar to membranes, but having a compression stiffness). In addition, phase transitions in shells and refined shell thermodynamics are discussed. The chapters of this book are the most exciting contributions presented at the EUROMECH 527 Colloquium “Shell-like structures: Non-classical Theories and Applications” held in Wittenberg, Germany.

Asymptotic Approaches in Nonlinear Dynamics

Author : Jan Awrejcewicz
Publisher : Springer Science & Business Media
ISBN 13 : 364272079X
Total Pages : 321 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Asymptotic Approaches in Nonlinear Dynamics by : Jan Awrejcewicz

Download or read book Asymptotic Approaches in Nonlinear Dynamics written by Jan Awrejcewicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers developments in the theory of oscillations from diverse viewpoints, reflecting the fields multidisciplinary nature. It introduces the state-of-the-art in the theory and various applications of nonlinear dynamics. It also offers the first treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with Pad approximations. With its wealth of interesting examples, this book will prove useful as an introduction to the field for novices and as a reference for specialists.

Dynamical Systems in Theoretical Perspective

Author : Jan Awrejcewicz
Publisher : Springer
ISBN 13 : 3319965980
Total Pages : 413 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Dynamical Systems in Theoretical Perspective by : Jan Awrejcewicz

Download or read book Dynamical Systems in Theoretical Perspective written by Jan Awrejcewicz and published by Springer. This book was released on 2018-09-01 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on theoretical aspects of dynamical systems in the broadest sense. It highlights novel and relevant results on mathematical and numerical problems that can be found in the fields of applied mathematics, physics, mechanics, engineering and the life sciences. The book consists of contributed research chapters addressing a diverse range of problems. The issues discussed include (among others): numerical-analytical algorithms for nonlinear optimal control problems on a large time interval; gravity waves in a reservoir with an uneven bottom; value distribution and growth of solutions for certain Painlevé equations; optimal control of hybrid systems with sliding modes; a mathematical model of the two types of atrioventricular nodal reentrant tachycardia; non-conservative instability of cantilevered nanotubes using the Cell Discretization Method; dynamic analysis of a compliant tensegrity structure for use in a gripper application; and Jeffcott rotor bifurcation behavior using various models of hydrodynamic bearings.

Recent Advances in Mechanics

Author : E.E. Gdoutos
Publisher : Springer Science & Business Media
ISBN 13 : 9400705573
Total Pages : 459 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Recent Advances in Mechanics by : E.E. Gdoutos

Download or read book Recent Advances in Mechanics written by E.E. Gdoutos and published by Springer Science & Business Media. This book was released on 2011-01-19 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 24 papers presented at the symposium on “Recent Advances in Mechanics” dedicated to the late Professor – Academician Pericles S. Theocaris in commemoration of the tenth anniversary of his death. The papers are written by world renowned and recognized experts in their fields and serve as a reference and guide for future research. The topics covered in the book can be divided into three major themes: Mathematical methods in applied mechanics (nine papers), experimental mechanics (nine papers) and fracture mechanics (six papers). Topics covered include: Application of reciprocity relations to laser-based ultrasonics, boundary value problems of the theory of elasticity, optimal design in contact mechanics, scaling of strength and lifetime distributions of quasibrittle structures, directional distortional hardening in plasticity, vibration of systems, instability phenomena in damped systems, variational methods for static and dynamic elasticity problems, an accelerated Newmark scheme for solving the equations of motion in the time domain, photoelastic tomography, electronic speckle pattern interferometry, composites exposed to fire, sampling moiré, microelecromechanical systems, experimental mechanics in nano-scale, advanced cement based nanocomposites, piezonuclear transmutations in brittle rocks under mechanical loading, stress triaxiality at crack tips studied by caustics, reinforcement of a cracked elastic plate with defects, some actual problems of fracture mechanics, cyclic plasticity with applications to extremely low cycle fatigue of structural steel, and fracture of a highly filled polymer composite.

Deterministic Chaos in One-Dimensional Continuous Systems

Author : Jan Awrejcewicz
Publisher : World Scientific
ISBN 13 : 9814719714
Total Pages : 576 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Deterministic Chaos in One-Dimensional Continuous Systems by : Jan Awrejcewicz

Download or read book Deterministic Chaos in One-Dimensional Continuous Systems written by Jan Awrejcewicz and published by World Scientific. This book was released on 2016-03-14 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler–Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic–plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels. The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering. Contents:Bifurcational and Chaotic Dynamics of Simple Structural Members:BeamsPlatesPanelsShellsIntroduction to Fractal Dynamics:Cantor Set and Cantor DustKoch Snowflake1D MapsSharkovsky's TheoremJulia SetMandelbrot's SetIntroduction to Chaos and Wavelets:Routes to ChaosQuantifying Chaotic DynamicsSimple Chaotic Models:IntroductionAutonomous SystemsNon-Autonomous SystemsDiscrete and Continuous Dissipative Systems:IntroductionLinear FrictionNonlinear FrictionHysteretic FrictionImpact DampingDamping in Continuous 1D SystemsEuler-Bernoulli Beams:IntroductionPlanar BeamsLinear Planar Beams and Stationary Temperature FieldsCurvilinear Planar Beams and Stationary Temperature and Electrical FieldsBeams with Elasto-Plastic DeformationsMulti-Layer BeamsTimoshenko and Sheremetev-Pelekh Beams:The Timoshenko BeamsThe Sheremetev-Pelekh BeamsConcluding RemarksPanels:Infinite Length PanelsCylindrical Panels of Infinite LengthPlates and Shells:Plates with Initial ImperfectionsFlexible Axially-Symmetric Shells Readership: Post-graduate and doctoral students, applied mathematicians, physicists, mechanical and civil engineers. Key Features:Includes fascinating and rich dynamics exhibited by simple structural members and by the solution properties of the governing 1D non-linear PDEs, suitable for applied mathematicians and physicistsCovers a wide variety of the studied PDEs, their validated reduction to ODEs, classical and non-classical methods of analysis, influence of various boundary conditions and control parameters, as well as the illustrative presentation of the obtained results in the form of colour 2D and 3D figures and vibration type charts and scalesContains originally discovered, illustrated and discussed novel and/or modified classical scenarios of transition from regular to chaotic dynamics exhibited by 1D structural members, showing a way to control chaotic and bifurcational dynamics, with directions to study other dynamical systems modeled by chains of nonlinear oscillators