Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
(OP)
Does anyone have closed form solutions for the differential equation providing the transient responses x(t)? I pulled out my old differential equations book and used Laplace transforms. The algebra got out of hand! I DO THINK IT'S SOLVABLE!
Tunalover





RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
Or you could take the general solution to a unit impulse and simply discritise the "half-sine" with a number or impulses starting with a very small one, ending with the magnitude of the half sine.
"Simplicity is the ultimate sophistication." L. da Vinci
- Gian
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
TTFN

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RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
Using Laplace transforms, but on undamped system. The sinusoidal pulse is built the way IRstuff described.
I suppressed the general algebraic output because it was messy I suppose. I did include algebraic output in the example values part.
I'm sure it can be done for damped system. But I myself wouldn't do it without computer algebra system. Do you have one of those? If there's value for you (let me know), I can do it on Maple and post the results, but I think the algebraic solution would be too long to be useful to you.
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(2B)+(2B)' ?
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
Thanks for that! I don't have a math program. I tried it the old fashioned way. There is certainly value in the solution as this physical problem is very real with transit drop events. I just don't have the money to poney up for MathCAD (I tried unsuccessfully to install a free trial version of MathCAD Express from PTC).
Tunalover
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
"Simplicity is the ultimate sophistication." L. da Vinci
- Gian
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
Tunalover
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
TTFN

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Need help writing a question or understanding a reply? forum1529: Translation Assistance for Engineers
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
Shock Response Calculator
Have Fun!
James A. Pike
www.xl4sim.com
www.erieztechnologies.com
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
Yes I am aware that the undamped solution is published but my OP was seeking the damped solution. See the OP.
Tunalover
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
You should be able to find the shock response spectra for a half sine pulse for various damping ratios in shock and vibration literature. Just use these spectra to determine the response of your system.
Do you have access to FEA software? You can model a spring mass system and get the response to a half sine pulse.
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
Have Fun!
James A. Pike
www.xl4sim.com
www.erieztechnologies.com
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
Regards,
Howard Bruce Jackson
Tunalover
RE: Single DOF spring-mass-dashpot system excited by half-sine wave shock pulse
Regards,
Howard Bruce Jackson
aka Tunalover
Tunalover