LEADER 05402nam 2200685Ia 450 001 9911020228003321 005 20200520144314.0 010 $a9786612371424 010 $a9781282371422 010 $a1282371428 010 $a9780470823767 010 $a0470823763 010 $a9780470823750 010 $a0470823755 035 $a(CKB)1000000000799979 035 $a(EBL)469607 035 $a(OCoLC)646819591 035 $a(SSID)ssj0000366097 035 $a(PQKBManifestationID)11278608 035 $a(PQKBTitleCode)TC0000366097 035 $a(PQKBWorkID)10415129 035 $a(PQKB)10537747 035 $a(MiAaPQ)EBC469607 035 $a(PPN)190783486 035 $a(Perlego)2775862 035 $a(EXLCZ)991000000000799979 100 $a20090423d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpectral element method in structural dynamics /$fUsik Lee 210 $aSingapore ;$aHoboken, NJ $cJ. Wiley & Sons Asia$dc2009 215 $a1 online resource (470 p.) 300 $aIncludes index. 311 08$a9780470823743 311 08$a0470823747 327 $aSPECTRAL ELEMENT METHOD IN STRUCTURAL DYNAMICS; Contents; Preface; Part One: Introduction to the Spectral Element Method and Spectral Analysis of Signals; 1 Introduction; 1.1 Theoretical Background; 1.1.1 Finite Element Method; 1.1.2 Dynamic Stiffness Method; 1.1.3 Spectral Analysis Method; 1.1.4 Spectral Element Method; 1.1.5 Advantages and Disadvantages of SEM; 1.2 Historical Background; 2 Spectral Analysis of Signals; 2.1 Fourier Series; 2.2 Discrete Fourier Transform and the FFT; 2.2.1 Discrete Fourier Transform (DFT); 2.2.2 Fast Fourier Transform (FFT); 2.3 Aliasing; 2.3.1 Aliasing Error 327 $a2.3.2 Remedy for Aliasing2.4 Leakage; 2.4.1 Leakage Error; 2.4.2 Artificial Damping; 2.5 Picket-Fence Effect; 2.6 Zero Padding; 2.6.1 Improving Interpolation in the Transformed Domain; 2.6.2 Remedy for Wraparound Error; 2.7 Gibbs Phenomenon; 2.8 General Procedure of DFT Processing; 2.9 DFTs of Typical Functions; 2.9.1 Product of Two Functions; 2.9.2 Derivative of a Function; 2.9.3 Other Typical Functions; Part Two: Theory of Spectral Element Method; 3 Methods of Spectral Element Formulation; 3.1 Force-Displacement Relation Method; 3.2 Variational Method; 3.3 State-Vector Equation Method 327 $a3.4 Reduction from the Finite Models4 Spectral Element Analysis Method; 4.1 Formulation of Spectral Element Equation; 4.1.1 Computation of Wavenumbers and Wavemodes; 4.1.2 Computation of Spectral Nodal Forces; 4.2 Assembly and the Imposition of Boundary Conditions; 4.3 Eigenvalue Problem and Eigensolutions; 4.4 Dynamic Responses with Null Initial Conditions; 4.4.1 Frequency-Domain and Time-Domain Responses; 4.4.2 Equivalence between Spectral Element Equation and Convolution Integral; 4.5 Dynamic Responses with Arbitrary Initial Conditions 327 $a4.5.1 Discrete Systems with Arbitrary Initial Conditions4.5.2 Continuous Systems with Arbitrary Initial Conditions; 4.6 Dynamic Responses of Nonlinear Systems; 4.6.1 Discrete Systems with Arbitrary Initial Conditions; 4.6.2 Continuous Systems with Arbitrary Initial Conditions; Part Three: Applications of Spectral Element Method; 5 Dynamics of Beams and Plates; 5.1 Beams; 5.1.1 Spectral Element Equation; 5.1.2 Two-Element Method; 5.2 Levy-Type Plates; 5.2.1 Equation of Motion; 5.2.2 Spectral Element Modeling; 5.2.3 Equivalent 1-D Structure Representation; 5.2.4 Computation of Dynamic Responses 327 $aAppendix 5.A: Finite Element Model of Bernoulli-Euler Beam6 Flow-Induced Vibrations of Pipelines; 6.1 Theory of Pipe Dynamics; 6.1.1 Equations of Motion of the Pipeline; 6.1.2 Fluid-Dynamics Equations; 6.1.3 Governing Equations for Pipe Dynamics; 6.2 Pipelines Conveying Internal Steady Fluid; 6.2.1 Governing Equations; 6.2.2 Spectral Element Modeling; 6.2.3 Finite Element Model; 6.3 Pipelines Conveying Internal Unsteady Fluid; 6.3.1 Governing Equations; 6.3.2 Spectral Element Modeling; 6.3.3 Finite Element Model; Appendix 6.A: Finite Element Matrices: Steady Fluid 327 $aAppendix 6.B: Finite Element Matrices: Unsteady Fluid 330 $aSpectral Element Method in Structural Dynamics is a concise and timely introduction to the spectral element method (SEM) as a means of solving problems in structural dynamics, wave propagations, and other related fields. The book consists of three key sections. In the first part, background knowledge is set up for the readers by reviewing previous work in the area and by providing the fundamentals for the spectral analysis of signals. In the second part, the theory of spectral element method is provided, focusing on how to formulate spectral element models and how to conduct spectral el 606 $aStructural dynamics$xMathematics 606 $aStructural frames$xMathematical models 606 $aSpectral theory (Mathematics) 615 0$aStructural dynamics$xMathematics. 615 0$aStructural frames$xMathematical models. 615 0$aSpectral theory (Mathematics) 676 $a624.171 700 $aLee$b Usik$01838606 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911020228003321 996 $aSpectral element method in structural dynamics$94417628 997 $aUNINA