Applied structural and mechanical vibrations : theory and methods / Paulo L. Gatti.

Review of some fundamentalsIntroductionThe role of modelling (linear and nonlinear, discrete and continuous systems, deterministic and random data)Some definitions and methodsSprings, dampers and massesSummary and commentsMathematical preliminariesIntroductionFourier series and Fourier transformLaplace transformDirac delta and related topicsThe notion of Hilbert spaceAnalytical mechanics: An overviewIntroductionSystems of material particlesThe principle of virtual work and d'Alembert's principle: Lagrange's and Hamilton's equationsLagrange's equations: Fundamental properties, some generalisations and complementsHamilton's principleSmall-amplitude oscillationsSingle degree of freedom systemsIntroductionHarmonic oscillator I: Free vibrationHarmonic oscillator II: Forced vibrationDamping in real systems, equivalent viscous dampingSummary and commentsMore SDOF systems: Shock response, transient response and some approximate methodsIntroductionTime domain: Impulse response function and Duhamel integralFrequency and Laplace domains: Frequency response function and transfer functionGeneralised SDOF systemsRayleigh (energy) method and improved Rayleigh methodSummary and commentsMultiple degrees of freedom (MDOF) systemsIntroductionA simple undamped -DOF system: Free vibrationUndamped n-DOF systems: Free vibrationEigenvalues and eigenvectors sensitivity analysisA few considerations on the structure and properties of the matrices M, K and CUnrestrained systems: Rigid-body modesDamped systems: Proportional and nonproportional dampingGeneralised and complex eigenvalue problems: Reduction to standard formSummary and commentsMore MDOF systems: Forced vibration and response analysisIntroductionMode superpositionHarmonic excitation: Proportional viscous dampingTime-domain and frequency-domain responseSystems with rigid-body modesThe case of nonproportional viscous dampingMDOF systems with hysteretic dampingA few remarks on other solution strategies: Laplace transform and direct integrationFrequency response functions of a -DOF systemSummary and commentsContinuous systemsIntroductionThe flexible string in transverse motionFree vibration of a finite string: Standing waves and normal modesAxial and torsional vibrations of rodsFlexural (bending) vibrations of beamsA two-dimensional continuous system: The flexible membraneThe differential eigenvalue problemBending vibrations of thin platesForced vibration and response analysis: The modal approachSome final considerations: Alternative form of FRFs and the introduction of dampingSummary and commentsMDOF and continuous systems: Approximate methodsIntroductionThe rayleigh quotientThe Rayleigh-Ritz methodSummary and commentsExperimental modal analysisIntroductionExperimental modal analysis: Overview of the fundamentalsModal testing proceduresA few selected topics in experimental modal analysisSummary and commentsProbability and statistics: Preliminaries to random vibrationsIntroductionOn the concept of probabilityProbability: Axiomatic formulation and some resultsRandom variables and distribution functionsRandom vectorsMore on conditional probabilityConvergences and the law of large numbersA few remarks on probability and statisticsStochastic processes and random vibrationsIntroductionThe concept of random processBasic calculus of random processesSpectral representation of random processesResponse of linear systems to random excitationStationary narrowband processes: A few selected topicsSummary and commentsAppendicesReferencesIndex