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                <forename type="first">Rafael</forename>
                <surname>de Oliveira Teloli</surname>
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                <forename type="first">Luis Gustavo</forename>
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            <idno type="halRefHtml">&lt;i&gt;IX Congresso Nacional de Engenharia Mecânica (CONEM 2016)&lt;/i&gt;, Aug 2016, Fortaleza, Brazil</idno>
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                <title xml:lang="en">Use of Restoring Surface Method to Estimate a Stochastic Model of a Nonlinear Beam with Cubic Stiffness</title>
                <title xml:lang="pt">Uso do método de superfície de resposta para estimar um modelo estocástico de uma viga não linear com rigidez cúbica</title>
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                <title level="m">IX Congresso Nacional de Engenharia Mecânica (CONEM 2016)</title>
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                  <title>IX Congresso Nacional de Engenharia Mecânica (CONEM 2016)</title>
                  <date type="start">2016-08-21</date>
                  <date type="end">2016-08-25</date>
                  <settlement>Fortaleza</settlement>
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                <term xml:lang="en">Restoring Surface Method</term>
                <term xml:lang="en">Uncertainty Quantification</term>
                <term xml:lang="en">Nonlinear Vibration</term>
                <term xml:lang="pt">Método de Superficie de Resposta</term>
                <term xml:lang="pt">Quantificão de Incertezas</term>
                <term xml:lang="pt">Vibração não linear</term>
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              <p>The goal of this work is to identify the probability density function associated with the parameters that describe the linear and nonlinear vibrating behavior considering uncertainties quantification. The method was tested in a clamped-free aluminum beam with nonlinear hardening behavior. The nonlinear behavior was caused due to the magnetic interaction between the magnet and a steel mass conected to the free end of the aluminumbeam. The identification process is hybrid and nonparametric. When the level of force amplitude applied is low, the restoring force is null. In these operating conditions, modal analysis are used to extract the modal parameters. However, when the level of force amplitude is high, the restoring force must include nonlinear terms. Thus, the identification of the nonlinear coefficient is performed using the restoring surface method. Experimental tests were carried out several times on different days and conditions to consider uncertainties in the acquired data and the identified parameters for each measurement. Therefore, the probability density function of each parameter was estimated. A stochastic model of the system is obtained and validated with the experimental responses to verify the model reliability for different regimes of motion.</p>
            </abstract>
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              <p>A meta deste trabalhó e identificar funções densidade de probabilidade associadas aos parâmetros que descrevem o comportamento vibratório em regime linear e não linear de uma viga assumindo as incertezas existentes. O métodó e testado em uma viga de alumínio com condição de contorno engastada-livre com forte mecanismo de não linearidade polinomial associado a endurecimento da rigidez. Este comportamento não linearé linearé acionado através da interação magnética entre uma massa de ferro conectada na ponta livre da viga e imãs presos na extremidade livre da estrutura. O processo de identificação utilizadó e híbrido e não paramétrico. Com baixos níveis de amplitude da força de excitação, a força elástica de restauraçãó e nula. Nestas condições de operação, técnicas de análise modal são utilizadas para extrair parâmetros modais. Já para elevados níveis de excitação a força de restauração deve incluir termos não lineares. Assim, a identificação do coeficiente não linear será feita pelo método de superfície de resposta. Os testes experimentais foram realizados diversas vezes considerando diferentes dias e condições para considerar incertezas nos dados adquiridos e com os pa-râmetros identificados para cada realização. Assim, se estimam funções densidades de probabilidade de cada parâmetro identificado com cada método. Um modelo estocástico do sistemá e obtido e validado com as repostas experimentais previstas para verificação da confiabilidade do modelo frente a diferentes regimes de vibração. Palavras-chave: Vibração Não Linear, Quantificação de Incertezas, Método de Superfície de Resposta.</p>
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