Description
SPRINGER Fundamentals Of Structural Dynamics Theory And Computation (Hb 2022) by HJELMSTAD K.D.
This text closes the gap between traditional textbooks on structural dynamics and how structural dynamics is practiced in a world driven by commercial software, where performance-based design is increasingly important. The book emphasizes numerical methods, nonlinear response of structures, and the analysis of continuous systems (e.g., wave propagation). Fundamentals of Structural Dynamics: Theory and Computation builds the theory of structural dynamics from simple single-degree-of-freedom systems through complex nonlinear beams and frames in a consistent theoretical context supported by an extensive set of MATLAB codes that not only illustrate and support the principles, but provide powerful tools for exploration. The book is designed for students learning structural dynamics for the first time but also serves as a reference for professionals throughout their careers. 1 Foundations of Dynamics1.1 Kinematics of particles1.2 Kinetics of particles1.3 Power, work, and energy1.4 Conservation of energy1.5 Dynamics of rigid bodies1.6 Example1.7 The Euler{Lagrange equations1.8 Summary2 Numerical Solution of Ordinary Di_erential Equations2.1 Why numerical methods?2.2 Practical implementation2.3 Analysis of a first order equation2.4 Analysis of second order di_erential equations2.4.1 The central di_erence method2.4.2 The generalized trapezoidal rule2.4.3 Newmark's method2.5 Performance of the methods2.6 Summary3 Single-Degree-of-Freedom Systems3.1 The SDOF oscillator3.2 Undamped free vibration 3.3 Damped free vibration3.4 Forced vibration3.4.1 Suddenly applied constant load3.4.2 Sinusoidal load3.4.3 General periodic loading 3.5 Earthquake ground motion3.6 Nonlinear responsexiiixiv Contents3.7 Integrating the equation of motion3.8 Example4 Systems with Multiple Degrees of Freedom4.1 The 2{DOF system as a warm-up problem4.2 The shear building4.3 Free vibration of the NDOF system4.3.1 Orthogonality of the eigenvectors4.3.2 Initial conditions4.4 Structural damping4.4.1 Modal damping4.4.2 Rayleigh damping4.4.3 Caughey damping4.4.4 Non-classical damping4.5 Damped forced vibration of the NDOF system4.6 Resonance in NDOF systems4.7 Numerical integration of the NDOF equations5 Nonlinear Response of NDOF Systems5.1 A point of departure5.2 The shear building, revisited5.3 The principle of virtual work5.4 Nonlinear dynamic computations5.5 Assembly of equations5.6 Adding damping to the equations of motion5.7 The structure of the NDOF code5.8 Implementation6 Earthquake Response of NDOF Systems6.1 Special case of the elastic system6.2 Modal recombination6.3 Response spectrum methods6.4 Implementation6.5 Example7 Special Methods for Large Systems7.1 Ritz projection onto a smaller subspace7.2 Static correction method7.3 Summary8 Dynamic Analysis of Truss Structures8.1 What is a truss?8.2 Element kinematics8.3 Element and nodal static equilibrium8.4 The principle of virtual work8.5 Constitutive models for axial forceContents xv8.6 Solving the static equations of equilibrium8.7 Dynamic analysis of truss structures8.8 Distributed element mass8.9 Earthquake response of truss structures8.10 Implementation8.11 Example9 Axial Wave Propagation9.1 The axial bar problem9.2 Motion without applied loading9.3 Classical solution by separation of variables9.4 Modal analysis with applied loads9.5 The Ritz method and _nite element analysis9.5.1 Dynamic principle of virtual work9.5.2 Finite element functions9.5.3 A slightly di_erent formulation9.5.4 Boundary conditions9.5.5 Higher order interpolation9.5.6 Initial conditions9.6 Axial bar dynamics code10 Dynamics of Planar Beams: Theory10.1 Beam kinematics10.1.1 Motion of a beam cross section10.1.2 Strain{displacement relationships10.1.3 Normal and shear strain10.2 Beam kinetics10.3 Constitutive equations10.4 Equations of motion10.4.1 Balance of linear momentum10.4.2 Balance of angular momentum10.5 Summary of beam equations10.6 Linear beam theory10.6.1 Linearized kinematics10.6.2 Linearized kinetics10.6.3 Linear equations of motion10.6.4 Boundary conditions10.6.5 Initial conditions11 Wave Propagation in Beams11.1 Propagation of a train of sinusoidal waves11.1.1 Bernoulli{Euler beam11.1.2 Rayleigh beam11.1.3 Timoshenko beam11.2 Solution by separation of variablesxvi Contents11.3 The Bernoulli{Euler beam 11.3.1 Implementing boundary conditions11.3.2 Natural frequencies11.3.3 Orthogonality of the eigenfunctions11.3.4 Implementing the initial conditions11.3.5 Modal vibration11.3.6 Other boundary conditions11.3.7 Wave propagation11.3.8 Example: Simple{simple beam11.4 The Rayleigh beam11.4.1 Simple{simple Rayleigh beam11.4.2 Orthogonality relationships11.4.3 Wave propagation: Simple{simple beam11.4.4 Other boundary conditions11.4.5 Implementation11.5 The Timoshenko beam11.5.1 Simple{simple beam11.5.2 Wave propagation11.5.3 Numerical example11.6 Summary12 Finite Element Analysis of Linear Beams12.1 The dynamic principle of virtual work12.1.1 The Ritz approximation12.1.2 Initial conditions12.1.3 Selection of Ritz functions12.1.4 Beam _nite element functions12.1.5 Ritz functions and degrees of freedom12.1.6 Local to global mapping12.1.7 Element matrices and assembly12.2 The Rayleigh beam12.2.1 Virtual work for the Rayleigh beam12.2.2 Finite element discretization12.2.3 Initial conditions for wave propagation12.2.4 The Rayleigh beam code12.2.5 Example 12.3 The Timoshenko beam12.3.1 Virtual work for the Timoshenko beam12.3.2 Finite element discretization12.3.3 The Timoshenko beam code12.3.4 Veri_cation of element performance12.3.5 Wave propagation in the Timoshenko beamContents xvii13 Nonlinear Dynamic Analysis of Planar Beams13.1 Equations of motion13.2 The principle of virtual work13.3 Tangent functional13.4 Finite element discretization13.5 Static analysis of nonlinear planar beams13.5.1 Solution by Newton's method13.5.2 Static implementation13.5.3 Veri_cation of static code13.6 Dynamic analysis of nonlinear planar beams13.6.1 Solution of the nonlinear di_erential equations13.6.2 Dynamic implementation13.6.3 Example13.7 Summary14 Dynamic Analysis of Planar Frames14.1 What is a frame?14.2 Equations of motion14.3 Inelasticity14.3.1 Numerical integration of the rate equations14.3.2 Material tangent14.3.3 Internal variables14.3.4 Speci_c model for implementation14.4 Element matrices 14.4.1 Finite element discretization14.4.2 Local to global transformation14.5 Static verification14.6 Dynamics of frames14.6.1 Earthquake ground motion14.6.2 Implementation14.6.3 Examples14.6.4 Sample input functionA Newton's MethodA.1 LinearizationA.2 Systems of equationsB The Directional DerivativeB.1 Ordinary functionsB.2 FunctionalsC The Eigenvalue ProblemC.1 The algebraic eigenvalue problemC.2 The QR algorithmC.3 Eigenvalue problems for large systemsC.4 Subspace iterationxviii ContentsD Finite Element InterpolationD.1 Polynomial interpolationD.2 Lagrangian interpolationD.3 Ritz functions with hp interpolationD.4 Lagrangian shape functionsD.5 C0 Bubble functionsD.6 C1 Bubble functionsE Data Structures for Finite Element CodesE.1 Structure geometry and topologyE.2 Structures with only nodal DOFE.3 Structures with non-nodal DOFF Numerical QuadratureF.1 Trapezoidal ruleF.2 Simpson's ruleF.3 Gaussian quadratureF.4 ImplementationF.5 ExamplesIndex