The book examines vibration phenomena with an emphasis on fractional vibrations using the functional form of linear vibrations with frequency-dependent mass, damping, or stiffness, covering the theoretical analysis potentially applicable to structures and, in particular, ship hulls. Covering the six classes of fractional vibrators and seven classes of fractionally damped Euler-Bernoulli beams that play a major role in hull vibrations, this book presents analytical formulas of all results with concise expressions and elementary functions that set it apart from other recondite studies. The results show that equivalent mass or damping can be negative and depends on fractional orders. Other key highlights of the book include a concise mathematical explanation of the Rayleigh damping assumption, a novel description of the nonlinearity of fractional vibrations, and a new concept of fractional motion, offering exciting additions to the field of fractional vibrations. This title will be a must-read for students, mathematicians, physicists, and engineers interested in vibration phenomena and novel vibration performances, especially fractional vibrations.

Introduces a new convolution representation of a fractional derivative and the classification of fractional vibrations Proposes equivalent motion equations of six classes of fractional vibrators Establishes a mathematical explanation of the Rayleigh damping assumption Sets up a method for the record length requirement of ocean surface waves Proposes an optimal controller of irregular wave maker

The uncertainties or randomness of the material properties of structural components are of serious concern to engineers. Structural analysis is usually done by taking into account only deterministic or crisp parameters; however, building materials can have the aspects of uncertainty. The causes of this uncertainty or randomness are defects in atomic configurations, measurement errors, environmental conditions, and other factors. The influence of uncertainties is more profound for nanoscale and microstructures due to their small-scale effects. Several nanoscale experiments and molecular dynamics studies also support the claim of possible attachment of randomness for various parameters. With regard to these concerns, it is necessary to propose new models that specifically integrate and effectively overcome imprecisely defined parameters of the system. Structural Dynamics in Uncertain Environments presents the uncertainty modeling of nanobeams, microbeams, and Funtionally Graded (FG) beams using non-probabilistic approaches which include interval and fuzzy concepts. Vibration and stability analyses of the beams are conducted using different analytical, semi-analytical, and numerical methods for finding exact and/or approximate solutions of governing equations arising in uncertain environments. In this context, this book addresses structural uncertainties and investigates the dynamic behavior of micro-, nano-, and FG beams. Examines the concepts of fuzzy uncertain environments in structural dynamics Presents comprehensive analysis of propagation of uncertainty in vibration and buckling analyses Explains efficient mathematical methods to handle uncertainties in the governing equations

Nanomechanics of Structures and Materials highlights and compares the advantages and disadvantages of diverse modeling and analysis techniques across a wide spectrum of different nanostructures and nanomaterials. It focuses on the behavior of media with nanostructural features where the classic continuum theory ceases to hold and augmented continuum theories such as nonlocal theory, gradient theory of elasticity, and the surface elasticity model should be adopted. These generalized frameworks, tailored to address the intricate characteristics inherent at the nanoscale level, are discussed in depth, and their application to a variety of different materials and structures, including graphene, shells, arches, nanobeams, carbon nanotubes, porous materials, and more, is covered. Key Features Outlines the advantages and limitations of size-dependent continuum theories and modeling techniques when studying fundamental problems in the nanomechanics of structures and materials Discusses various analytical and numerical tools for identifying nanomechanical defects in structures Explores a diverse array of structures and materials, including graphene, shells, arches, nanobeams, carbon nanotubes, and porous materials

This book consists of select proceedings of the National Conference on Wave Mechanics and Vibrations (WMVC 2018). It covers recent developments and cutting-edge methods in wave mechanics and vibrations applied to a wide range of engineering problems. The book presents analytical and computational studies in structural mechanics, seismology and earthquake engineering, mechanical engineering, aeronautics, robotics and nuclear engineering among others. This book can be useful for students, researchers, and professionals interested in the wide-ranging applications of wave mechanics and vibrations.

Brings mathematics to bear on your real-world, scientific problems Mathematical Methods in Interdisciplinary Sciences provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics. The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include: Structural static and vibration problems Heat conduction and diffusion problems Fluid dynamics problems The book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.

This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author’s own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering.