Using Parameter Expansion Method and Min-Max Approach for the Analytical Investigation of Vibrating Micro-Beams Pre-Deformed by an Electric Field
Two powerful analytical methods called Parameter Expansion method (PEM) and Min-Max approach (MMA) are used to obtain the analytical solution of micro-beams actuated by an electric field. The nonlinear equation of motion has both even and odd nonlinearities. It is shown that two terms in series expa...
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| Veröffentlicht in: | Advances in structural engineering 2013-04, Vol.16 (4), p.681-687 |
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| container_title | Advances in structural engineering |
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| creator | Sedighi, Hamid M. Reza, Arash Zare, Jamal |
| description | Two powerful analytical methods called Parameter Expansion method (PEM) and Min-Max approach (MMA) are used to obtain the analytical solution of micro-beams actuated by an electric field. The nonlinear equation of motion has both even and odd nonlinearities. It is shown that two terms in series expansions of PEM are adequate to achieve a highly accurate solution of mentioned system. Comparison of the obtained solutions using numerical method shows the accuracy of the analytical procedures. It is proved that the approximated solutions using PEM are in more agreement with numerical results in comparison with MMA. |
| doi_str_mv | 10.1260/1369-4332.16.4.681 |
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The nonlinear equation of motion has both even and odd nonlinearities. It is shown that two terms in series expansions of PEM are adequate to achieve a highly accurate solution of mentioned system. Comparison of the obtained solutions using numerical method shows the accuracy of the analytical procedures. 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The nonlinear equation of motion has both even and odd nonlinearities. It is shown that two terms in series expansions of PEM are adequate to achieve a highly accurate solution of mentioned system. Comparison of the obtained solutions using numerical method shows the accuracy of the analytical procedures. It is proved that the approximated solutions using PEM are in more agreement with numerical results in comparison with MMA.</description><subject>Approximation</subject><subject>Electric fields</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Nonlinear equations</subject><subject>Polymethyl methacrylates</subject><subject>Series expansion</subject><subject>Structural engineering</subject><issn>1369-4332</issn><issn>2048-4011</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEqXwA6y8ZJPWY6dOuizQAhIRLChba5JMWqM8ip2i9jP4Y1wVsURejCzdczVzGLsGMQKpxRiUnkaxUnIEehSPdAonbCBFnEaxADhlg7_AObvw_kMIkEkCA_a99LZd8Vd02FBPjs93G2y97VqeUb_uSo5tyTPbRhnu-GyzcR0Wa151jvdr4rMW631vC6z5U_tFvrcr7A9wV_F3m7vwCe2ZLVwX3RI2nr86iu4p8A2VPN-Hej6vqeidLfjCUl1esrMKa09Xv3PIlov5291j9Pzy8HQ3e44KJUUfTZICJjqdygkJXVUEZVqFl1AuFMlK5JCiQqQpUBzHaTkRWqi8xDRJSCIkashujr3hpM9tWN001hdU19hSt_UGVCI1AKhpiMpjNJzhvaPKbJxt0O0NCHPwbw56zUGvAW1iE_wHaHyEPK7IfHRbF1z5_4gfA6mHlQ</recordid><startdate>20130401</startdate><enddate>20130401</enddate><creator>Sedighi, Hamid M.</creator><creator>Reza, Arash</creator><creator>Zare, Jamal</creator><general>SAGE Publications</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>20130401</creationdate><title>Using Parameter Expansion Method and Min-Max Approach for the Analytical Investigation of Vibrating Micro-Beams Pre-Deformed by an Electric Field</title><author>Sedighi, Hamid M. ; Reza, Arash ; Zare, Jamal</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c320t-57c1568925e06ffe1d8f8f87eb03e2f0b18a3aae91e4448d50603bda877e2a173</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Approximation</topic><topic>Electric fields</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Nonlinear equations</topic><topic>Polymethyl methacrylates</topic><topic>Series expansion</topic><topic>Structural engineering</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sedighi, Hamid M.</creatorcontrib><creatorcontrib>Reza, Arash</creatorcontrib><creatorcontrib>Zare, Jamal</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Advances in structural engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sedighi, Hamid M.</au><au>Reza, Arash</au><au>Zare, Jamal</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Using Parameter Expansion Method and Min-Max Approach for the Analytical Investigation of Vibrating Micro-Beams Pre-Deformed by an Electric Field</atitle><jtitle>Advances in structural engineering</jtitle><date>2013-04-01</date><risdate>2013</risdate><volume>16</volume><issue>4</issue><spage>681</spage><epage>687</epage><pages>681-687</pages><issn>1369-4332</issn><eissn>2048-4011</eissn><abstract>Two powerful analytical methods called Parameter Expansion method (PEM) and Min-Max approach (MMA) are used to obtain the analytical solution of micro-beams actuated by an electric field. 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| subjects | Approximation Electric fields Mathematical analysis Mathematical models Nonlinear equations Polymethyl methacrylates Series expansion Structural engineering |
| title | Using Parameter Expansion Method and Min-Max Approach for the Analytical Investigation of Vibrating Micro-Beams Pre-Deformed by an Electric Field |
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