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		<id>https://www.scipedia.com/wd/index.php?action=history&amp;feed=atom&amp;title=Baran_2025a</id>
		<title>Baran 2025a - Revision history</title>
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		<updated>2026-05-05T15:40:28Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
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		<id>https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315856&amp;oldid=prev</id>
		<title>Scipediacontent at 09:55, 6 February 2025</title>
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				<updated>2025-02-06T09:55:19Z</updated>
		
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 09:55, 6 February 2025&lt;/td&gt;
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		<author><name>Scipediacontent</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315769&amp;oldid=prev</id>
		<title>Scipediacontent at 09:25, 22 January 2025</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315769&amp;oldid=prev"/>
				<updated>2025-01-22T09:25:18Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 09:25, 22 January 2025&lt;/td&gt;
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		<author><name>Scipediacontent</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315749&amp;oldid=prev</id>
		<title>Scipediacontent at 10:06, 21 January 2025</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315749&amp;oldid=prev"/>
				<updated>2025-01-21T10:06:03Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 10:06, 21 January 2025&lt;/td&gt;
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		<author><name>Scipediacontent</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315700&amp;oldid=prev</id>
		<title>Onate: Onate moved page Review 240050339233 to Baran 2025a</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315700&amp;oldid=prev"/>
				<updated>2025-01-20T09:26:15Z</updated>
		
		<summary type="html">&lt;p&gt;Onate moved page &lt;a href=&quot;/public/Review_240050339233&quot; class=&quot;mw-redirect&quot; title=&quot;Review 240050339233&quot;&gt;Review 240050339233&lt;/a&gt; to &lt;a href=&quot;/public/Baran_2025a&quot; title=&quot;Baran 2025a&quot;&gt;Baran 2025a&lt;/a&gt;&lt;/p&gt;
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				&lt;td colspan='1' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 09:26, 20 January 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan='2' style='text-align: center;' lang='en'&gt;&lt;div class=&quot;mw-diff-empty&quot;&gt;(No difference)&lt;/div&gt;
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		<author><name>Onate</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315480&amp;oldid=prev</id>
		<title>JSanchez: JSanchez moved page Draft Sanchez Pinedo 219738722 to Review 240050339233</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315480&amp;oldid=prev"/>
				<updated>2025-01-07T11:52:07Z</updated>
		
		<summary type="html">&lt;p&gt;JSanchez moved page &lt;a href=&quot;/public/Draft_Sanchez_Pinedo_219738722&quot; class=&quot;mw-redirect&quot; title=&quot;Draft Sanchez Pinedo 219738722&quot;&gt;Draft Sanchez Pinedo 219738722&lt;/a&gt; to &lt;a href=&quot;/public/Review_240050339233&quot; class=&quot;mw-redirect&quot; title=&quot;Review 240050339233&quot;&gt;Review 240050339233&lt;/a&gt;&lt;/p&gt;
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				&lt;td colspan='1' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 11:52, 7 January 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan='2' style='text-align: center;' lang='en'&gt;&lt;div class=&quot;mw-diff-empty&quot;&gt;(No difference)&lt;/div&gt;
&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>JSanchez</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315479&amp;oldid=prev</id>
		<title>JSanchez: Created page with &quot; == Abstract ==  In this paper, we present a method using Haar wavelets for solving axially functionally graded (FG) Timoshenko beam equations with non-uniform cross-sections....&quot;</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Baran_2025a&amp;diff=315479&amp;oldid=prev"/>
				<updated>2025-01-07T11:52:05Z</updated>
		
		<summary type="html">&lt;p&gt;Created page with &amp;quot; == Abstract ==  In this paper, we present a method using Haar wavelets for solving axially functionally graded (FG) Timoshenko beam equations with non-uniform cross-sections....&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&lt;br /&gt;
== Abstract ==&lt;br /&gt;
&lt;br /&gt;
In this paper, we present a method using Haar wavelets for solving axially functionally graded (FG) Timoshenko beam equations with non-uniform cross-sections. We compare two different approaches to the solution. The first approach involves approximating the resulting function (i.e., rotation) of the differential equation with a polynomial function using Haar wavelets, which is a classical application in the Haar wavelet method. The second method employs an auxiliary function that uses Haar wavelets, but the rotation or deflection do not directly equal the sought function. The rotation and deflection are derived from this auxiliary function. In both methods, the coupled governing equations are transformed into a single governing equation. Using the Haar wavelet method, this single differential equation transforms into a system of linear algebraic equations. For different boundary conditions, the roots of the characteristic polynomial equation obtained from the system of linear algebraic equations are solved to determine the lowest to highest-order natural frequencies. Our results show that the use of auxiliary function is faster and more consistent with the results available in the literature. We presented several natural frequency predictions of Timoshenko beams with different taper ratios and support conditions that have not been detailed in the literature before.OPEN ACCESS Received: 04/09/2024 Accepted: 07/11/2024&lt;br /&gt;
&lt;br /&gt;
== Full document ==&lt;br /&gt;
&amp;lt;pdf&amp;gt;Media:Draft_Sanchez Pinedo_219738722-6482-document.pdf&amp;lt;/pdf&amp;gt;&lt;/div&gt;</summary>
		<author><name>JSanchez</name></author>	</entry>

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