Here is a method for converting modal damping to a damping coefficient matrix for all modes. It is based on a pseudo inversion of the modal damping matrix. The resulting coefficient matrix will be fully populated. The damping terms will not necessary corresponding to physical dashpots,… 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
A transfer function is a type of frequency response function (FRF) that gives the steady-state response to a force input as a function of frequency. Transfer functions for structural dynamics problems can be calculated from the natural frequencies, modal damping ratios and normal modes. This… Read more
A vibration absorber is a tuned spring-mass system which reduces the vibration of a harmonically excited system. Here is a paper for an applied force: Vibration Absorber Here is a Matlab script and its supporting function: vibration_absorber_trans.m mratio.m * * * Here is a paper… Read more
In Holland during World War II, the Casper ten Boom family used their home as a hiding place for those hunted by the Nazis. This was their way of living out their Christian faith. Four members of the family lost their lives for providing this… Read more
Good Timber by Douglas Malloch The tree that never had to fight For sun and sky and air and light, But stood out in the open plain And always got its share of rain, Never became a forest king But lived and died a scrubby… Read more
There is a need in certain structural dynamics finite element analysis problems to perform a response analysis in the time domain. This would be the case, for example, if the stiffness was non-linear. Loss-of-clearance or contact between two adjacent vibrating parts is another analysis example.… Read more
Consider a single-degree-of-freedom system subjected to base excitation where the input is an arbitrary time history. The response of the system can be calculated via a digital recursive filtering relationship, which is the numerical engine embedded in the SRS calculation. This is done for… Read more
Finding the the natural frequencies of a continuous beam, plate, membrane or even an acoustical volume requires solving for the eigenvalue roots of a characteristic equation, which may contain trigonometric or Bessel functions. Matlab provides an fzero function which can be used for this purpose.… Read more
The Transamerica Pyramind has a Fundamental Frequency of 0.3 Hz * * * Here are some papers which give natural frequencies and damping values for sample tall buildings: Damping in Tall Buildings and Towers: tall_building_damping.pdf The Damping Characteristics of Bolted and Welded Joints: bolted_joint_damping.pdf Transamerica… Read more