A mathematical model in three-dimensional piezoelectric continuum to predict non-linear responses of piezoceramic materials
Abstract It has been experimentally observed that the piezoceramic materials exhibit different types of non-linearities under different combinations of electrical and mechanical fields. When excited near resonance in the presence of weak electric fields, they exhibit typical non-linearities similar...
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| Veröffentlicht in: | Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science Journal of mechanical engineering science, 2008-11, Vol.222 (11), p.2251-2268 |
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| container_title | Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science |
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| creator | Samal, M K Seshu, P von Wagner, U Hagedorn, P Dutta, B K Kushwaha, H S |
| description | Abstract
It has been experimentally observed that the piezoceramic materials exhibit different types of non-linearities under different combinations of electrical and mechanical fields. When excited near resonance in the presence of weak electric fields, they exhibit typical non-linearities similar to a Duffing oscillator such as jump phenomena and the presence of superharmonics in the response spectra. In this work, these non-linearities have been modelled for a generalized three-dimensional piezoelectric continuum using higher-order quadratic and cubic terms in the electric enthalpy density function and the virtual work. The identification of the parameters of the model requires a closed form solution for non-linear response of a simplified geometry. A simple proportional damping formulation has been used in the model. Experiments have been conducted on rectangular and cylindrical geometries of piezoceramic PIC 181 at different magnitudes of applied electric fields and results have been compared with those of simulation. |
| doi_str_mv | 10.1243/09544062JMES1002 |
| format | Article |
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It has been experimentally observed that the piezoceramic materials exhibit different types of non-linearities under different combinations of electrical and mechanical fields. When excited near resonance in the presence of weak electric fields, they exhibit typical non-linearities similar to a Duffing oscillator such as jump phenomena and the presence of superharmonics in the response spectra. In this work, these non-linearities have been modelled for a generalized three-dimensional piezoelectric continuum using higher-order quadratic and cubic terms in the electric enthalpy density function and the virtual work. The identification of the parameters of the model requires a closed form solution for non-linear response of a simplified geometry. A simple proportional damping formulation has been used in the model. Experiments have been conducted on rectangular and cylindrical geometries of piezoceramic PIC 181 at different magnitudes of applied electric fields and results have been compared with those of simulation.</description><identifier>ISSN: 0954-4062</identifier><identifier>EISSN: 2041-2983</identifier><identifier>DOI: 10.1243/09544062JMES1002</identifier><language>eng</language><publisher>London, England: SAGE Publications</publisher><subject>Ceramics ; Computer simulation ; Damping ; Duffing oscillators ; Electric fields ; Electricity ; Enthalpy ; Exact solutions ; Mathematical models ; Mechanical engineering ; Nonlinear equations ; Nonlinearity ; Parameter identification ; Piezoelectric ceramics ; Piezoelectricity ; Superharmonics ; Three dimensional models</subject><ispartof>Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science, 2008-11, Vol.222 (11), p.2251-2268</ispartof><rights>2008 Institution of Mechanical Engineers</rights><rights>Copyright Professional Engineering Publishing Ltd Nov 2008</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c399t-cf86579195cd1ea5f94e9fc325eb25e44ebf80dd1f824a90c60e71f702b716523</citedby><cites>FETCH-LOGICAL-c399t-cf86579195cd1ea5f94e9fc325eb25e44ebf80dd1f824a90c60e71f702b716523</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://journals.sagepub.com/doi/pdf/10.1243/09544062JMES1002$$EPDF$$P50$$Gsage$$H</linktopdf><linktohtml>$$Uhttps://journals.sagepub.com/doi/10.1243/09544062JMES1002$$EHTML$$P50$$Gsage$$H</linktohtml><link.rule.ids>314,780,784,21819,27924,27925,43621,43622</link.rule.ids></links><search><creatorcontrib>Samal, M K</creatorcontrib><creatorcontrib>Seshu, P</creatorcontrib><creatorcontrib>von Wagner, U</creatorcontrib><creatorcontrib>Hagedorn, P</creatorcontrib><creatorcontrib>Dutta, B K</creatorcontrib><creatorcontrib>Kushwaha, H S</creatorcontrib><title>A mathematical model in three-dimensional piezoelectric continuum to predict non-linear responses of piezoceramic materials</title><title>Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science</title><description>Abstract
It has been experimentally observed that the piezoceramic materials exhibit different types of non-linearities under different combinations of electrical and mechanical fields. When excited near resonance in the presence of weak electric fields, they exhibit typical non-linearities similar to a Duffing oscillator such as jump phenomena and the presence of superharmonics in the response spectra. In this work, these non-linearities have been modelled for a generalized three-dimensional piezoelectric continuum using higher-order quadratic and cubic terms in the electric enthalpy density function and the virtual work. The identification of the parameters of the model requires a closed form solution for non-linear response of a simplified geometry. A simple proportional damping formulation has been used in the model. Experiments have been conducted on rectangular and cylindrical geometries of piezoceramic PIC 181 at different magnitudes of applied electric fields and results have been compared with those of simulation.</description><subject>Ceramics</subject><subject>Computer simulation</subject><subject>Damping</subject><subject>Duffing oscillators</subject><subject>Electric fields</subject><subject>Electricity</subject><subject>Enthalpy</subject><subject>Exact solutions</subject><subject>Mathematical models</subject><subject>Mechanical engineering</subject><subject>Nonlinear equations</subject><subject>Nonlinearity</subject><subject>Parameter identification</subject><subject>Piezoelectric ceramics</subject><subject>Piezoelectricity</subject><subject>Superharmonics</subject><subject>Three dimensional models</subject><issn>0954-4062</issn><issn>2041-2983</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kUtP3TAQha0KpF6g-y4tkNpVwONHEi8RojxExaLtOvJ1xsUosVM7WQB_Hke3iwqJWhrP4nznjDRDyGdgp8ClOGNaSclqfvv98gcwxj-QDWcSKq5bsUc2q1yt-kdykPMjK4_XakNezulo5gcsn7dmoGPscaA-0PkhIVa9HzFkH0ORJo_PEQe0c_KW2hhmH5ZlpHOkU8Le25mGGKrBBzSJJsxTDBkzjW5ntZjMWJxlFCZvhnxE9l1p-OlvPyS_vl3-vLiu7u6vbi7O7yortJ4r69paNRq0sj2gUU5L1M4KrnBbSkrcupb1PbiWS6OZrRk24BrGtw3UiotD8nWXO6X4Z8E8d6PPFofBBIxL7hopBEBT60J--S8plJZ1DVDA4zfgY1xS2VLuuJCataDWtJP3INDAhBKSrVFsR9kUc07ouin50aSnDli3nrZ7e9piqXaWbH7jP6Hv8a9y4qTq</recordid><startdate>20081101</startdate><enddate>20081101</enddate><creator>Samal, M K</creator><creator>Seshu, P</creator><creator>von Wagner, U</creator><creator>Hagedorn, P</creator><creator>Dutta, B K</creator><creator>Kushwaha, H S</creator><general>SAGE Publications</general><general>SAGE PUBLICATIONS, INC</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>3V.</scope><scope>7XB</scope><scope>88I</scope><scope>8AF</scope><scope>8AO</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M2P</scope><scope>M7S</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20081101</creationdate><title>A mathematical model in three-dimensional piezoelectric continuum to predict non-linear responses of piezoceramic materials</title><author>Samal, M K ; Seshu, P ; von Wagner, U ; Hagedorn, P ; Dutta, B K ; Kushwaha, H S</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c399t-cf86579195cd1ea5f94e9fc325eb25e44ebf80dd1f824a90c60e71f702b716523</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Ceramics</topic><topic>Computer simulation</topic><topic>Damping</topic><topic>Duffing oscillators</topic><topic>Electric fields</topic><topic>Electricity</topic><topic>Enthalpy</topic><topic>Exact solutions</topic><topic>Mathematical models</topic><topic>Mechanical engineering</topic><topic>Nonlinear equations</topic><topic>Nonlinearity</topic><topic>Parameter identification</topic><topic>Piezoelectric ceramics</topic><topic>Piezoelectricity</topic><topic>Superharmonics</topic><topic>Three dimensional models</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Samal, M K</creatorcontrib><creatorcontrib>Seshu, P</creatorcontrib><creatorcontrib>von Wagner, U</creatorcontrib><creatorcontrib>Hagedorn, P</creatorcontrib><creatorcontrib>Dutta, B K</creatorcontrib><creatorcontrib>Kushwaha, H S</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>ProQuest Central (Corporate)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>STEM Database</collection><collection>ProQuest Pharma Collection</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Science Journals</collection><collection>Engineering Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><collection>ProQuest Central Basic</collection><jtitle>Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Samal, M K</au><au>Seshu, P</au><au>von Wagner, U</au><au>Hagedorn, P</au><au>Dutta, B K</au><au>Kushwaha, H S</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A mathematical model in three-dimensional piezoelectric continuum to predict non-linear responses of piezoceramic materials</atitle><jtitle>Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science</jtitle><date>2008-11-01</date><risdate>2008</risdate><volume>222</volume><issue>11</issue><spage>2251</spage><epage>2268</epage><pages>2251-2268</pages><issn>0954-4062</issn><eissn>2041-2983</eissn><abstract>Abstract
It has been experimentally observed that the piezoceramic materials exhibit different types of non-linearities under different combinations of electrical and mechanical fields. When excited near resonance in the presence of weak electric fields, they exhibit typical non-linearities similar to a Duffing oscillator such as jump phenomena and the presence of superharmonics in the response spectra. In this work, these non-linearities have been modelled for a generalized three-dimensional piezoelectric continuum using higher-order quadratic and cubic terms in the electric enthalpy density function and the virtual work. The identification of the parameters of the model requires a closed form solution for non-linear response of a simplified geometry. A simple proportional damping formulation has been used in the model. Experiments have been conducted on rectangular and cylindrical geometries of piezoceramic PIC 181 at different magnitudes of applied electric fields and results have been compared with those of simulation.</abstract><cop>London, England</cop><pub>SAGE Publications</pub><doi>10.1243/09544062JMES1002</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Ceramics Computer simulation Damping Duffing oscillators Electric fields Electricity Enthalpy Exact solutions Mathematical models Mechanical engineering Nonlinear equations Nonlinearity Parameter identification Piezoelectric ceramics Piezoelectricity Superharmonics Three dimensional models |
| title | A mathematical model in three-dimensional piezoelectric continuum to predict non-linear responses of piezoceramic materials |
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