Here is a paper which gives a derivation of the mass and stiffness matrices for beam bending: beam_FEM.pdf * * * Here is a Matlab script for the modal analysis of a straight beam. beam.zip * * * Here is Matlab script for the modal… Read more
Shock and vibration environments produce dynamic stresses which can cause material failure in structures. The potential failure modes include fatigue, yielding, and ultimate stress limit. F.V. Hunt wrote a seminal paper on this subject, titled “Stress and Stress Limits on the Attainable Velocity in Mechanical… Read more
Here is a Matlab GUI script and reference paper for calculating the longitudinal natural frequencies of a beam or rod. beam_longitudinal.zip Long.pdf * * * See also: Beam Bending Frequencies – Tom Irvine
These Matlab scripts calculate the natural frequencies of a beam via the finite element method: beam_base_accel_fea.zip They also have options for base excitation: 1. frequency response function 2. half-sine base input 3. arbitrary base input A ramp invariant digital recursive relationship is used for the… Read more
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
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