Question
Download Solution PDFअनुप्रस्थ काट क्षेत्रफल 'A', जड़त्व आघूर्ण 'T' तथा लम्बाई 'L' वाले एक कैंटिलीवर बीम की प्राकृतिक आवृत्ति ω1 है। यदि बीम गलती से दो हिस्सों में टूट जाए, तो शेष कैंटिलीवर बीम की प्राकृतिक आवृत्ति ω2 इस प्रकार होगी कि:-
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
प्राकृतिक आवृत्ति इस प्रकार दी जाती है:
\(\omega = \sqrt {\frac{k_{eq}}{m}} =\sqrt {\frac{g}{\delta }} \;\)
गणना:
दिया गया है:
L1 = L, \(L_2=\frac{L_1}{2}\)
कैंटिलीवर बीम के लिए:
\(\begin{array}{l} \delta = \frac{{P{L^3}}}{{3EI}}\\ \omega = \sqrt {\frac{g}{\delta }} = \sqrt {\frac{{3EIg}}{{P{L^3}}}} \Rightarrow \omega \propto \sqrt {\frac{1}{{{L^3}}}} \\ \frac{{{\omega _2}}}{{{\omega _1}}} = \sqrt {\frac{{L_1^3}}{{L_2^3}}} = \sqrt {\frac{{{L^3}}}{{{{\left( {\frac{L}{2}} \right)}^3}}}} = 2\sqrt2 \\ \therefore\;{\omega _2} > {\omega _1} \end{array}\)
Last updated on Apr 14, 2023
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