Monday, April 28, 2014

SDOF Drop Shock Online Calculator

This is the second in a series of shock response online calculators.  The calculator below or here will determine the shock response to a dropped weight.  The spring and damper are mass-less and, therefore, the results are valid for both the case of 1) the spring/damper attached to the bottom of the weight and dropped onto a hard surface and 2) the rigid weight dropped onto the spring/damper.  This version is limited to one vertical degree of freedom.

The input includes the weight, drop height, spring constant, viscous damping value, gravitational constant and initial velocity if not zero.

The calculations include un-damped natural frequency of the weight on the spring, critical damping value, damping ratio, time to initial impact, maximum upward (-) direction acceleration, maximum downward (+) acceleration and maximum deflection after impact.

Several response cycles are charted.  The charted response is limited to the pre-coded number of time steps which is dependent on the drop height and natural time period.  A caution note is activated if the limit is exceeded.  The results are still valid with the caution but the time response will have fewer than the normally charted number of response cycles.

The calculation does not require that the weight adheres to the spring/damper at impact and beyond and therefore can "bounce."

Any consistent set of dimensional units can be used that is consistent with Hz and seconds.

For no damping the the maximum displacement will match the theoretical value to within 1% where W/k=Δ2/2(h+Δ).

Future versions will address nonlinear springs, multiple degrees-of-freedom, non-viscous damper types and more.

Tuesday, April 15, 2014

Shock Response Online Calculator

Here is an online calculator for the theoretical shock response to a base input.  It has pre-coded options for 1/2 sine, triangular, rectangular and saw-tooth pulses where peak amplitude in g's and time pulse in seconds are input.  It also has an option for a user input spectrum with up to 20 time points. The suspended system includes the suspended weight on a linear spring (k) and viscous damper (c).  A gravitational constant is also needed.  Any consistent set of units with seconds and cycles per second (Hz)are required.

Output includes a chart of the input shock and shock response versus time. The un-damped natural frequency, critical damping ratio and peak response-to-peak input are also output.

Some baseline cases where the analytical solution is known.

1) if a rectangular shock pulse is applied to an undamped system with a natural period of 2 times the pulse time the response is 2 times the input shock level.
2) if a 1/2 sine shock pulse is applied to an un-damped system with a natural period of approximately 1.7 times the pulse time the response is approximately 1.7 times the input level.