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

Father, Son and Holy Ghost

The First Article of Faith of my church is: We believe in God, the Eternal Father, and in His Son, Jesus Christ, and in the Holy Ghost. The Father and Son have glorified bodies. The Holy Ghost is personage of spirit that can dwell in… 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

What is the Greatest Commandment?

Jesus Christ taught the “greatest commandment” in the following Biblical account. Mark 12 [28] And one of the scribes came, and having heard them reasoning together, and perceiving that he had answered them well, asked him, Which is the first commandment of all? [29] And… Read more