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Excel Method for Complex Dynamic Analysis

This guide presents a comprehensive Excel-based approach for analyzing complex dynamic systems, specifically focusing on a falling sandbag scenario with drag. The methodology leverages fundamental motion formulas to derive velocity and acceleration over time, integrating variable position and acceleration effects. With an emphasis on accuracy and error reduction, this document outlines the step-by-step setup needed to model the system, incorporating integration formulas and providing insights into improving results. Ideal for engineering students and professionals aiming to enhance their analytical capabilities using spreadsheet tools.

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Excel Method for Complex Dynamic Analysis

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  1. Excel Method for Complex Dynamic Analysis Boehm February, 2014

  2. Example 2.5Acceleration Depends on Velocity a = g – cv2 v2 y2 = vdv (g – cv2) v1 x dx 1 = ln(x2-a/b) (a+bx2) 2c Best Integration formula I could find Good Luck proceeding to a Solution Falling Sandbag with Drag

  3. Problem 2.1.28 Shows Integration Steps

  4. Spreadsheet Method uses basic motion formulas l Velocity -y Direction l Time V2 = V1 + at = V1 + (V2 – V1)/Δt

  5. Setting Up Formulas and Spreadsheet Problem Statement: Given: a = (g – cv2) where c = 6 x 10-4 ID Balloon’s Position g IRD y Formulas for Spreadsheet v=vi + (g-cvi2) x (delta t) Sandbag’s Position dy=vdt + (g-cv2)dt2/2 y=yi+dy A B D E F G H I J C 1 2 3 4 5

  6. Excel Approach to Integrating a Solution Error = 1.5% Error = .065%

  7. Reducing Delta Time Gives Better Accuracy

  8. 20 a (m/s2) Problem 2.1.19 Non-Constant Acceleration 0 1 2 4 40 Time (sec) Velocity Acceleration 1 Time (sec) 2

  9. Textbook Approach to Solution

  10. Set up the First Three Rows, thenPull down rows until t = 2 seconds A B C D E F G 1 2 3

  11. Acceleration is a function of Position F=ma = -kx a = -kx/m V2 = v1 + a1t X2 = x1 + v1t + a1t2/2

  12. Spring Problem 3.1.37

  13. Is a 1% Error Band Acceptable? • The vast majority of these analyses are used to determine design loads or performance requirements • Factors of 1.5 to 3 are then added for safety and robustness • Generally, analyses requiring complete accuracy, like Satellite re-entry rocket burns, are based on test results of the hardware involved. • MATLAB-type tools are used to refine the Spreadsheet method

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