Equivalent representation form of oscillators with elastic and damping nonlinear terms

In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others

Psychometric Properties of the Personal Wellbeing Index in Brazilian and Chilean Adolescents Including Spirituality and Religion = Propriedades Psicométricas do Personal Wellbeing Index em Adolescentes Brasileiros e Chilenos Incluindo Espiritualidade e Religião

This study compared the 7-item Personal Wellbeing Index (PWI) with two other versions which include the domains “Spirituality” and “Religion”, separately, in a sample of Brazilian (n = 1.047) and Chilean (n = 1.053) adolescents. A comparison of psychometric properties between the PWI versions was carried out through multigroup confi rmatory factor analysis showing adequate adjustments (CFI > .95, RMSEA < .08), whereas the item spirituality presented better performance. For the analysis of the differential contribution of each domain to the notion of global satisfaction, a regression on the item Overall Life Satisfaction (OLS) was applied using structural equations. It isrecommended the inclusion of the item spirituality in the original scale, considering the importance of such domain in both cultures