SIEMENS Basic Dynamic Analysis User's Guide Contents Proprietary & Restricted Rights Notice . 11 About this Book . 1-1 Fundamentals of Dynamic Analysis . 2-1 Overview . 2-2 Dynamic Analysis Versus Static Analysis . 2-2 Equations of Motion . 2-2 Velocity and Acceleration . 2-3 Single Degree-of-Freedom System . 2-3 Dynamic and Static Degrees-of-Freedom . 2-3 Equation of Motion . 2-3 Inertia Force . 2-4 Viscous Damping . 2-4 Elastic Force . 2-4 Applied Load . 2-4 Solution of the Equation of Motion . 2-4 Free Vibration Analysis . 2-5 Circular Natural Frequency . 2-5 Natural Frequency . 2-5 Damping Types . 2-7 Underdamped System . 2-7 Forced Vibration Analysis . 2-8 Dynamic Amplification Factor for No Damping . 2-9 Dynamic Amplification Factor with Damping . 2-11 Dynamic Analysis Process . 2-12 Dynamic Analysis Types . 2-14 Overview of Real Eigenvalue Analysis . 2-14 Overview of Frequency Response Analysis . 2-14 Overview of Transient Response analysis . 2-14 Finite Element Input Data . 3-1 Overview . 3-2 Mass Input . 3-2 Lumped and Coupled Mass . 3-2 CROD Element Stiffness Matrix . 3-4 CROD Lumped Mass Matrix . 3-4 CROD Coupled Mass Matrix . 3-5 Lumped Mass Versus Coupled Mass Example . 3-5 CBAR, CBEAM Lumped Mass . 3-7 CBAR, CBEAM Coupled Mass . 3-7 NX Nastran Mass Input . 3-8 Basic Dynamic Analysis User's Guide 3 CoContentsntents Nonstructural Mass . 3-8 Damping Input . 3-8 Viscous and Structural Damping . 3-9 The Effect of Damping . 3-11 Structural Damping Specification . 3-11 Viscous Damping Specification . 3-11 Units in Dynamic Analysis . 3-12 Contact Conditions in Dynamic Solutions . 3-13 Direct Matrix Input . 3-14 External Matrices . 3-14 Direct Matrix Input . 3-15 Real Eigenvalue Analysis (SOL 103) . 4-1 Overview of Real Eigenvalue Analysis . 4-2 Natural Frequencies . 4-2 Mode Shapes . 4-2 Reasons to Compute Normal Modes . 4-4 Overview of Normal Modes Analysis . 4-4 Mode Shape Normalization . 4-9 Eigenvalue Extraction Methods . 4-11 Lanczos Method . 4-12 RDMODES Method . 4-12 Householder Methods . 4-12 Modified Householder Methods . 4-12 Automatic Householder Methods . 4-13 Sturm Modified Inverse Power Method . 4-13 Comparison of Methods . 4-13 User Interface for Real Eigenvalue Analysis . 4-14 User Interface for the Lanczos Method . 4-14 User Interface for the Other Methods . 4-16 Input Requirements for Normal Modes Analysis . 4-18 Executive Control Section . 4-19 Case Control Section . 4-19 Bulk Data Section . 4-20 Examples . 4-20 Two-DOF Model ..