Mechanical vibrations : theory and application to structural dynamics / / Michel Geradin, Daniel J. Rixen

• Record Nr.: UNINA9910459854803321
• Autore: Géradin Michel <1945->
• Pubbl/distr/stampa: Hoboken, New Jersey : , : Wiley, , 2015; ©1997
• ISBN: 1-118-90019-7; 1-118-90018-9
• Edizione: [Third edition.]
• Descrizione fisica: 1 online resource (617 p.)
• Classificazione: SCI041000
• Disciplina: 624.1/76
• Soggetti: Structural dynamics; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; TItle Page; Copyright; Contents; Foreword; Preface; Introduction; Suggested Bibliography; List of main symbols and definitions; Chapter 1 Analytical Dynamics of Discrete Systems; Definitions; 1.1 Principle of virtual work for a particle; 1.1.1 Nonconstrained particle; 1.1.2 Constrained particle; 1.2 Extension to a system of particles; 1.2.1 Virtual work principle for N particles; 1.2.2 The kinematic constraints; 1.2.3 Concept of generalized displacements; 1.3 Hamilton's principle for conservative systems and Lagrange equations; 1.3.1 Structure of kinetic energy and classification of inertia forces1.3.2 Energy conservation in a system with scleronomic constraints; 1.3.3 Classification of generalized forces; 1.4 Lagrange equations in the general case; 1.5 Lagrange equations for impulsive loading; 1.5.1 Impulsive loading of a mass particle; 1.5.2 Impulsive loading for a system of particles; 1.6 Dynamics of constrained systems; 1.7 Exercises; 1.7.1 Solved exercises; 1.7.2 Selected exercises; References; Chapter 2 Undamped Vibrations of n-Degree-of-Freedom Systems; Definitions; 2.1 Linear vibrations about an equilibrium configuration2.1.1 Vibrations about a stable equilibrium position; 2.1.2 Free vibrations about an equilibrium configuration corresponding to steady motion; 2.1.3 Vibrations about a neutrally stable equilibrium position; 2.2 ; Normal modes of vibration; 2.2.1 Systems with a stable equilibrium configuration; 2.2.2 Systems with a neutrally stable equilibrium position; 2.3 Orthogonality of vibration eigenmodes; 2.3.1 Orthogonality of elastic modes with distinct frequencies; 2.3.2 Degeneracy theorem and generalized orthogonality relationships; 2.3.3 Orthogonality relationships including rigid-body modes2.4 Vector and matrix spectral expansions using eigenmodes; 2.5 Free vibrations induced by nonzero initial conditions; 2.5.1 Systems with a stable equilibrium position; 2.5.2 Systems with neutrally stable equilibrium position; 2.6 Response to applied forces: forced harmonic response; 2.6.1 Harmonic response, impedance and admittance matrices; 2.6.2 Mode superposition and spectral expansion of the admittance matrix; 2.6.3 Statically exact expansion of the admittance matrix; 2.6.4 Pseudo-resonance and resonance; 2.6.5 Normal excitation modes2.7 Response to applied forces: response in the time domain; 2.7.1 Mode superposition and normal equations; 2.7.2 Impulse response and time integration of the normal equations; 2.7.3 Step response and time integration of the normal equations; 2.7.4 Direct integration of the transient response; 2.8 Modal approximations of dynamic responses; 2.8.1 Response truncation and mode displacement method; 2.8.2 Mode acceleration method; 2.8.3 Mode acceleration and model reduction on selected coordinates; 2.9 Response to support motion; 2.9.1 Motion imposed to a subset of degrees of freedom
• Sommario/riassunto: "Mechanical Vibrations: Theory and Application to Structural Dynamics, Third Edition is a comprehensively updated and reorganized new edition of the popular textbook. It presents the theory of vibrations in the context of structural analysis and covers applications in mechanical and aerospace engineering, This new edition now includes the fundamentals of signal processing and identification technique, and develops the concepts of dynamic reduction and substructuring.A more detailed discussion of the concept of eigensolution sensitivity to physical parameters is included and the fundamental cases of wave propagation in solids are considered. It also includes a chapter on the finite element method for one-dimensional structures.This new edition contains coherent and uniform notation and now includes solved exercises at the end of each chapter"--

More Calculus of a Single Variable / / by Peter R. Mercer

• Record Nr.: UNINA9910299980103321
• Autore: Mercer Peter R
• Pubbl/distr/stampa: New York, NY : , : Springer New York : , : Imprint : Springer, , 2014
• ISBN: 1-4939-1926-1
• Edizione: [1st ed. 2014.]
• Descrizione fisica: 1 online resource (XVI, 411 p. 60 illus.)
• Collana: Undergraduate Texts in Mathematics, , 0172-6056
• Disciplina: 510
• Soggetti: Mathematical analysis; Analysis (Mathematics); Analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: Preface -- 1 The Real Numbers -- 2 Famous Inequalities -- 3 Continuous Functions -- 4 Differentiable Functions -- 5 The Mean Value Theorem -- 6 The Exponential Function -- 7 Other Mean Value Theorems -- 8 Convex Functions and Taylor's Theorem -- 9 Integration of Continuous Functions -- 10 The Fundamental Theorem of Calculus -- 11 Techniques of Integration -- 12 Classic Examples -- 13 Simple Quadrature Rules -- 14 Error Terms -- A The Proof of Theorem 9.1 -- Index.
• Sommario/riassunto: This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus — such as the real numbers, differentiation and integration, mean value theorems, the exponential function — are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for π. Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the many threads of calculus, the coherence of the subject is preserved throughout by an emphasis on patterns of development, of proof and argumentation, and of generalization. More Calculus of a Single Variable is suitable as a text for a course in advanced calculus, as a supplementary text for courses in analysis, and for self-study by students, instructors, and, ; indeed, all connoisseurs of ingenious calculations.