Here is a chart showing the natural frequencies of piano keys: piano.pdf Here is a paper on some basic music theory: music.pdf * * * See also: Fun with Sound Files Wind Chime Acoustics Tuning Fork Sound and Vibration: tuning.pdf * * * – Tom… Read more
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
This post is a work-in-progress… Frequency Response Function based substructuring (FBS) predicts the dynamic behavior of a coupled system on the basis of free interface FRFs of the uncoupled components. Here is a tutorial paper: Frequency Response Function Substructuring Modal damping requires special consideration: Notes on… Read more
This set of scripts calculates the response of an SDOF system to an applied force PSD. A transfer function is derived. Then its square is applied to the force PSD to calculate the response, using point-by-point multiplication and integration. sdof_ran_force.zip Important note: The following scripts… Read more
Here is a C++ program which generates random numbers for a user-selected distribution. monte_carlo_random.cpp monte_carlo_random.exe The distribution options are: 1. Uniform 2. Normal 3. Rayleigh 4. Weibull 5. Gumbel 6. Binomial The random numbers can then be used in a Monte Carlo analysis. * *… Read more
There is a need to derive a PSD envelope for nonstationary acceleration time histories, including launch vehicle data, which may be similar to that shown in the above figure. A PSD can be derived using rainflow fatigue cycle counting along with a Miners-type relative fatigue… Read more
Question: What is meant exactly by “fatigue exponent”. I generally input a value between 3 (for notched parts) and 6 (for (unnotched ones). Is it right?…I’ve found confusing and contrasting definitions about b and m exponent (among MIL-STD-810 G and various other documents) Answer:… Read more
The Newmark-beta method can be used to solve structural dynamics problems in the time domain, of the form: M (d^2x/dt^2) + C dx/dt + K x = F This method performs direct integration on the mass, damping and stiffness matrices which may be fully-coupled. Here… Read more
The Newmark-beta method can be used to solve structural dynamics problems in the time domain, of the form: M (d^2x/dt^2) + C dx/dt + K x = F This method performs direct integration on the mass, damping and stiffness matrices which may be fully-coupled. Here… Read more
One of my responsibilities to NASA is to provide training sessions and materials as an outreach to the engineering community. Occasionally, I provide onsite training, but these classes are becoming increasingly difficult to organize for a variety of reasons. As an alternative, I am considering… Read more