Mircea D. Grigoriu

This book constructs input finite dimensional (FD) models that are amendable for numerical calculations and provides accurate representations for responses of dynamical systems to these inputs, i.e., numerical solutions of stochastic equations. It establishes conditions under which numerical solutions of these equations deliver accurate estimates of extreme responses of dynamical systems that are needed to, for example, predict extreme weather events and design reliable aircrafts. It is intended to serve a broad audience including graduate students, researchers, engineers, scientists and applied mathematicians interested in the formulation and solutions of complex stochastic problems.

This book constructs input finite dimensional (FD) models that are amendable for numerical calculations and provides accurate representations for responses of dynamical systems to these inputs, i.e., numerical solutions of stochastic equations. It establishes conditions under which numerical solutions of these equations deliver accurate estimates of extreme responses of dynamical systems that are needed to, for example, predict extreme weather events and design reliable aircrafts. It is intended to serve a broad audience including graduate students, researchers, engineers, scientists and applied mathematicians interested in the formulation and solutions of complex stochastic problems.

This textbook provides a concise, clear, and rigorous presentation of the dynamics of linear systems that delivers the necessary tools for the analysis and design of mechanical/ structural systems, regardless of their complexity. The book is written for senior undergraduate and first year graduate students as well as engineers working on the design of mechanical/structural systems subjected to dynamic actions, such as wind/earthquake engineers and mechanical engineers working on wind turbines. Professor Grigoriu's lucid presentation maximizes student understanding of the formulation and the solution of linear systems subjected to dynamic actions, and provides a clear distinction between problems of practical interest and their special cases. Based on the author's lecture notes from courses taught at Cornell University, the material is class-tested over many years and ideal as a core text for a range of classes in mechanical, civil, and geotechnical engineering, as well as for self-directed learning by practitioners in the field.

This textbook provides a concise, clear, and rigorous presentation of the dynamics of linear systems that delivers the necessary tools for the analysis and design of mechanical/ structural systems, regardless of their complexity. The book is written for senior undergraduate and first year graduate students as well as engineers working on the design of mechanical/structural systems subjected to dynamic actions, such as wind/earthquake engineers and mechanical engineers working on wind turbines. Professor Grigoriu's lucid presentation maximizes student understanding of the formulation and the solution of linear systems subjected to dynamic actions, and provides a clear distinction between problems of practical interest and their special cases. Based on the author's lecture notes from courses taught at Cornell University, the material is class-tested over many years and ideal as a core text for a range of classes in mechanical, civil, and geotechnical engineering, as well as for self-directed learning by practitioners in the field.

Random Vibration of Complex Systems provides a new framework for assessing the performance of complex dynamic systems subject to random input. While most current books on random vibration treat the four different scenarios defined by the type of input and dynamic system independently and provide different methods for the analysis of each, Field and Grigoriu provide a unified approach for the analysis of linear and/or nonlinear dynamic systems subject to Gaussian and/or non-Gaussian input. Using numerous real-world engineering problems to illustrate the application of this new approach, Random Vibration of Complex Systems presents methods and techniques in a practical way to make them easily transferable to your vibration problems. Intended as a reference resource for applied scientists and engineers interested in analytical and numerical methods for solving random vibration problems, the book will be of particular interest to those working in the aerospace, automotive, civil engineering industries. Provides the first reference resource to guide you through the analysis of randomness and complexity in a unified way. Offers a new framework for analyzing complex dynamic systems with different input scenarios, unlike most other books that provide different methods for each scenario or consider only one or two academic situations. Demonstrates methods and techniques through the use of real-world engineering case studies with the aim of making the approach easily transferable to your vibration problems.