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TABLE OF CONTENTS SectionPage 1.0Review of Fundamentals Single DOF System1-3 Single DOF System Undamped Free Vibrations 1-5 Single DOF System Damped Free Vibrations1-8 Single DOF System Undamped Forced Vibrations1-12 Single DOF System Damped Forced Vibrations1-14 MSC.Nastran Documentation1-24 Text References on Dynamic Analysis Normal Modes Analysis Overview2-3 2 DOF Equation of Motion using Engineering Approach2-4 Summarizing Some Important Ideas About Normal Modes That Emerge 2-10 Setting the Same Problem using a Matrix Approach 2-11 Case Study 1 – Normal Modes of a 2 DOF Structure 2-17 Workshop 2 – Normal Modes Analysis of a 2 DOF Structure2-44 Extending to Multi DOF Problems2-45 Eigenvalue Extraction Method2-56 Theoretical Approach for MDOF 2-46 Facts Regarding Normal Modes 2-51 Extending to Multi DOF Problems (Cont.) 2-53 Eigenvalue Extraction Method 2-61 Sturm Sequence Theory2-63 Lanczos Method2-64 Case Study 2 – Normal Modes Analysis of a Satellite2-67 Reasons to Calculate Normal Modes2-81 Workshop 13 – Modal Analysis of a Car Chassis2-83 How Accurate is the Normal Modes Analysis2-84 Mesh Density2-85 Workshop 1a to 1c – Normal Modes Analysis with Various Mesh Size2-86

TABLE OF CONTENTS SectionPage 2.0Normal Modes Analysis (cont.) Element Type2-89 Workshop 15a to 15e – Modal Analysis of a Tuning Fork2-90 Mass Distribution2-93 Workshop 14a – Modal Analysis of a Tower2-94 Detail of Joints2-95 Detail of Constraints2-96 Workshop 14b – Modal Analysis of a Tower with Soft Ground Connection2-97 Hand Calculations2-98 Check List for Normal Modes Prior to Doing Further Analysis Mass Modeling Mass Modeling 3-3 Coupled Versus Lumped Mass 3-4 Rod Finite Element Example 3-6 Justification for MSC.Nastran Coupled Mass Convention 3-8 Mass Units3-10 Mass Input Effective Mass Participation Factor Theory4-3 Nastran Case Control Entry4-6 Case Study4-8 Applications in Industry4-18 Workshop 19 – Effective Mass Guyan Reduction Introduction to Dynamic Reduction5-3 Reduction Methods for Dynamics Available with MSC.Nastran 5-4 Static Condensation for Statics5-5 Static Condensation for Dynamics5-8

TABLE OF CONTENTS SectionPage 5.0 Guyan Reduction (continued) Solution Control for Guyan Reduction5-13 Difficulties with Guyan Reduction5-15 Modal Reduction Rigid Body Modes Rigid Body Modes 6-3 Calculation of Rigid Body Modes6-8 Specification of SUPORT Degrees of Freedom6-11 Checking SUPORT Degrees of Freedom6-13 Modal Analysis with Rigid Body Modes Normal Modes Analysis for Pre-Stiffened Structures Normal Modes Analysis for Pre-Stiffened Structures7-3 Case Study: Normal Modes for Pre-Stiff. Str. Using Sol Case Study: Normal Modes for Pre-Stiff. Str. Using Sol Workshop 12a, 12b, 12c Response Method Response Types8-3 Spring Mass System8-4 Transient Analysis8-5 Frequency Response Analysis8-9 Response Types 8-10 Modal and Direct Methods8-11 Patran Menu Choice8-13 Modal and Direct Methods8-14

TABLE OF CONTENTS SectionPage 9.0Damping Overview Damping in Dynamic Analysis 9-3 Viscous Damping Input 9-7 Frequency Dependent Impedance Sample 9-24 Sample using CBUSH Element9-25 Displacement Output for CBUSH Element9-26 Force Output for CBUSH Element9-27 Structural Damping Input 9-28 Modal Damping Input 9-33 Rayleigh Damping Input Transient Response Analysis Introduction to Transient Response Analysis10-3 Direct Transient Response10-4 Case Study – Direct Transient Analysis of a Simple Plate10-11 Workshop 3 – Direct Transient Analysis10-39 Transient Excitation10-41 Transient Excitation Issues TLOAD1 Entry10-50 Load Set Combination – DLOAD10-55 TLOAD2 Entry10-57 Initial Conditions10-60 Damping for Direct Transient Response Analysis10-65 Viscous Damping Versus Structural Damping, SDOF System10-68 Damping for Direct Transient Response Analysis (Cont.)10-73 Damping in Dynamic Analysis10-76 Workshop 17 – Direct Transient Analysis of a Car Model10-86 Modal Transient Response Modal Transient Response without Damping Modal Transient Response with Damping 10-90

TABLE OF CONTENTS SectionPage 10.0Transient Response Analysis (continued) Data Recovery for Modal Transient Response10-94 Modal Transient Response10-95 Mode Truncation Modal Transient Versus Direct Transient Workshop 4 – Modal Transient Analysis Workshop 18 – Modal Transient Analysis of the Tower Model With Seismic Input Frequency Response Analysis Introduction to Frequency Response Analysis11-3 Direct Frequency Response 11-6 Case Study – Direct Frequency Response of a Plate11-9 Workshop 5 – Direct Frequency Response of a Plate11-30 Excitation Definition The RLOAD1 Entry11-34 The RLOAD2 Entry Frequency Response Considerations11-43 Solution Frequencies11-45 Recommendations11-85 Damping for Direct Frequency Response Analysis Modal Frequency Response11-92 Modal Frequency Response without Damping Modal Frequency Response with Damping11-95 Modal Frequency Response (Cont.) Damping in Modal Frequency Response Mode Truncation in Modal Frequency Response Analysis Modal vs. Direct Frequency Response Workshop 16 – Modal Frequency Response of a Car Model Interpreting Frequency Response Results in MSC.Patran11-114

TABLE OF CONTENTS SectionPage 12.0Enforced Motion Enforced Motion12-3 Enforced Motion Equations 12-4 Enforced Motion in Transient Analysis Workshop 8 – Direct Transient Response with Enforced Acceleration (Matrix Partitioning) Enforced Motion for Frequency Response Analysis Random Analysis Classification of Dynamic Environments13-3 Examples of Random Dynamic Environment13-4 Ergodic Random Data13-5 Random Response Analysis 13-6 What is a PSD? 13-8 Summarizing the Input How are Random Results Used ? MSC.Random Overview MSC.Random – Flowchart Case Study Input Format Random Analysis Recommendations Workshop 9 – Random Analysis using MSC.Random13-60 Workshop 11 – Random Vibration Analysis of a Satellite using MSC.Random Response/Shock Spectrum Analysis Response Spectrum Method14-3 Maximum and Relative Response 14-6 Create Response Spectra from Transient Analysis of Large Structure 14-9 Case Study – Create Response Spectra Response Spectrum Analysis Method 14-25

TABLE OF CONTENTS SectionPage 14.0 Response/Shock Spectrum Analysis (continued) Case Study – Response Spectrum Analysis14-31 Workshop 20 – Create Response Spectra for Tower Model with Seismic Input Workshop 21 – Response Spectrum Analysis for Equipment Mounted on Tower Model Enforced Motion, Large Mass Method Enforced Motion 15-3 Using Large Mass Method in Transient Response 15-4 Workshop 7 – Direct Transient Response with Enforced Acceleration 15-7 Enforced Motion in Frequency Response 15-8 Using Large Mass Method in Frequency Response 15-9 Recommendations in Enforced Motion 15-11