This problem is really freaking me out..any help appreciated

Problem 1. Evaluate the effect of three tests below on a single degree of freedom system:

a) Sine sweep @0.5 g from 5 to 200 Hz with a sweep rate of 0.5 oct/min (assume zeta=0.02)

b) 100g 6ms half sine pulse (assume zeta =0)

c) 500g 1ms half sine pulse (assume zeta =0)

Plot the effect of each test on one graph (acceleration vs natural frequency). Also provide a short discussion on your conclusion. also discuss whether these are peak stresses or fatigue stress tests.

Provide matlab scripts.

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I have no idea about the first part but I tried to write the script for second part as given below:

clear;
f=167;
fn=1;
i=1;
while fn<=1000
  a=-981*f*f/((2*fn*fn)-(2*f*f));
  acc(i)=a;
  x(i)=fn;
  i=i+1;
  fn=fn+0.5;
end;
q=[acc'];
plot(x',q);
xlabel('Natural frequency(Hertz)');
ylabel('Peak Acceleration(M/Sec^2)');

[Oleg Komarov]

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers

Answer 1

[Walter Roberson]

Hint:

x = 1:0.5:1000;
acc = zeros(1,length(x));
for i = 1:length(x)
  acc(i) =-981*f*f/((2*x(i)*x(i))-(2*f*f));
end

which can be further optimized to:

x = 1:0.5:1000;
acc = -981/2 * f.^2 ./ (x.^2-f.^2);

[psyx21]

Thanks alot for the reply friends.. but i'm not sure whether my script is correct or not... please let me know if possible...:)

[Walter Roberson]

Let me put it this way: I see no relationship between the code you presented and any of (a), (b), or (c) .

Where did you get the number 167 from? Where did the 981 come from?

100 g would be 980.665 m/s not 981, and 6 ms is 1000/6 = 166.666666<etc> HZ, not 167 Hz.

How much of a difference do these make? The make an infinite difference at t = 167, which produces -infinity with your values but produces -122460.66433566 with the more accurate values.

It is not obvious to me that your acceleration formula has the correct form at all, but I have not studied that field. I don't see, for example, where the half-sine shape is taken in to account.

[psyx21]

This formula is for base excitation using sine wave, and taking damping(zeta)=0, I got this formula.

[psyx21]

Please try to provide some solution to this problem asap...thanks friends i am really thankful to you all:)

[Walter Roberson]

The answer for (c) should be an easy modification of your other solution (if it is correct).

It seems to me that a "single degree of freedom system" could include systems with rotational freedom, not just systems with linear freedom.

[psyx21]

We just have to consider base excitation using sine wave pulse..