Beam Bending Natural Frequencies & Mode Shapes

A rocket vehicle behaves as a free-free beam during flight. The vehicle’s body bending modes can be excited by wind gusts, aerodynamic buffeting, thrust offset, maneuvers, etc. Note that the mass and stiffness properties vary along the vehicle’s length. Furthermore, the mass properties change with… Read more

Matlab Tips

This script demonstrates a Matlab anonymous function with variable coefficients. It also performs integration using the quad function, which uses adaptive Simpson quadrature. This example is from an actual engineering problem for beam vibration. L=27.5; beta=4.73004/L; % sigma1=( sinh(beta*L) +sin(beta*L))/(cosh(beta*L) -cos(beta*L)); % core=@(x) ((cosh(beta*x)-cos(beta*x))-sigma1*(sinh(beta*x) -sin(beta*x))).^2;… Read more

Acoustic-Structural Interaction

Preliminary notes for acoustic waves: c = speed of sound f = frequency k = wavenumber lambda = wavelength r = radius wavelength is equal to the speed of sound divided by frequency lambda = c / f wavenumber is equal to two pi divided… Read more

Piezoelectric Shunt Damping

Piezoelectric shunt damping systems reduce structural vibration by shunting an attached piezoelectric transducer with an electrical impedance. Current impedance designs result in a coupled electrical resonance at the target modal frequencies. Piezoelectric transducers (PZTs), in conjunction with appropriate circuitry, can be used as a mechanical… Read more

Vibration Testing & Analysis Standard References

The European Cooperation for Space Standardization http://www.ecss.nl/ Download: ECSS-E-ST-10-03C, Space Engineering: Testing Spacecraft Mechanical Loads Analysis Handbook: ECSS-E-HB-32-26A_19February2013 Slide summary:  ESA_mechanical_loads_handbook_part_1 * * * SMC-S-016, Air Force Space Command, Space and Missile Systems Center, Standard Test Requirements for Launch, Upper-Stage and Space Vehicles, 2014  Download… Read more

Congratulations SpaceX

Dragon Cargo Spacecraft Berths with International Space Station To Sam DiMaggio, Jessica Jensen and all my colleagues at SpaceX… Very Well Done! Great day for America’s commerical space industry! I am pleased that Sam and his engineering staff use my Vibrationdata software and tutorials in… Read more

Rail Impact Shock

Question: MIL-STD-810G, Method 526 Rail Impact, outlines the physical test of an actual system at 4, 6, and 8 mph. Is there an equivalent laboratory shock test for equipment which is to be transported via railroad car? Answer 1: from Tom Irvine U.S. Army TB… Read more

North Korean Rocket Failure

Severe vibrations likely brought down N. Korean rocket By George Leopold 4/13/2012 3:15 PM EDT WASHINGTON – The failure of North Korea’s three-stage Unha-3 rocket on Thursday (March 12) was most likely caused by severe vibrations at an early point in the flight trajectory known… Read more

Aerospace Conference

The 2012 Spacecraft and Launch Vehicle Dynamic Environments Workshop will be held in El Segundo, California, June 19-21. The conference information is give at: Workshop Link I will present a paper: An Alternate Damage Potential Method for Enveloping Nonstationary Random vibration I hope to see… Read more