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1. Introduction to Harmonic Balance Method (HBM) Analysis
1.1. Harmonic Balance Method Equations
1.1.1. Dynamic Equations of Motion
1.1.2. Equation Solution
1.1.3. Solution Convergence and Stopping Criteria
1.1.4. Alternating Frequency-Time Procedure
1.2. Harmonic Balance Method Cyclic Equations
1.3. References
2. HBM Analysis Overview
2.1. Commands Used in an HBM Analysis
2.2. Terminology Used in an HBM Analysis
3. Modeling an HBM Analysis
3.1. Nonlinear Elements Supported in an HBM Analysis
3.2. Linear Part of the Model
3.3. Limitations
4. Applying Loads and Constraints in an HBM Analysis
5. Solving an HBM Analysis
5.1. HBM Initial Guess
5.2. HBM Solution Controls
5.3. Tips and Best Practices
5.3.1. Node-to-Node Contact Definition
5.3.2. Basic Checks After an HBM analysis
5.3.3. Convergence
5.3.4. Scaling the Solution Vector
6. Postprocessing Results of an HBM Analysis
6.1. HBM Expansion and Postprocessing Tips and Limitations
7. HBM Cyclic Procedure
7.1. HBM Cyclic Analysis: Single Stage Generation Pass
7.2. HBM Cyclic Analysis: Superelements Use Pass
7.3. HBM Cyclic Analysis: Postprocessing
8. Harmonic Balance Method Examples
8.1. Example 1: 1-DOF Duffing Oscillator
8.1.1. Problem Description
8.1.2. Input for the Analysis
8.1.3. Results
8.2. Example 2: Two Cantilever Beams with Frictionless Gap Contact
8.2.1. Problem Description and Modeling
8.2.2. Input for the Analysis
8.2.3. Results
8.3. Example 3: Two Jointed Beams with Frictional Contact Interface
8.3.1. Problem Description
8.3.2. Input for the Analysis
8.3.3. Results
8.4. Example 4: Cyclic Spring-Mass System with Cubic Nonlinearity
8.4.1. Problem Description
8.4.2. Input for the Analysis
8.4.3. Results
8.5. Example 5: Cyclic Model with Solid Elements and Frictional Contact
8.5.1. Problem Description
8.5.2. Input for the Analysis
8.5.3. Results
A. HBM Macros