Study Neo-Hookean and Yeoh Hyper-Elastic Models in Dielectric Elastomer-Based Micro-Beam Resonators

Abstract

Micro-bridge resonator with dielectric elastomer that is sandwiched between two electrodes is studied here with geometric and material nonlinearity. Geometric nonlinearity is introduced with Von-Karman strain-displacement relationship. For material nonlinearity that is modeled rarely in articles, two hyper-elastic models are used here. Governing equation of motion for Neo-Hookean and Yeoh models are derived through Hamilton's principle. These equations show that Neo-Hookean is not a suitable model for this case because of inadequate terms, but the Yeoh one is. Governing equation in Yeoh model is solved by analytical Lindstedt-Poincare method. Time history of micro-beam is presented in different modes and it is shown good agreement with numerical method. It is seen that increasing of mode number leads to increasing of frequency. In addition, the influence of different parameters on nonlinear normalized frequency is illustrated.

A perturbation analysis in nonlinear free vibration of a microbeam reinforced by shape memory alloy layer based on the modified couple stress theory

“…Also, the fourth-order Runge–Kutta method is used to accurately validate the results of the Lindstedt–Poincare method with respect to material and geometric properties. To evaluate the error between the numerical method and the analytical approach and the closeness of two methods, integral absolute error has been used (Barforooshi and Mohammadi, 2016). In this method, the error integral between the analytical and numerical method in time is calculated, and the results are presented in terms of percentages as shown in Table 6.…”

Free vibration of a hyper-elastic microbeam using a new “augmented Biderman model”

“…They used the finite element model to check the accuracy of the reduced order model. Danaee Barforooshi and Karami Mohammadi (2016) considered a hyperelastic microbeam with geometric and material nonlinearity. Geometric nonlinearity was introduced by von Kármán and Yeoh, and neo-Hookean models were used for the material nonlinearity.…”

On the stability of internally pressurized thick-walled spherical and cylindrical shells made of functionally graded incompressible hyperelastic material

“…Different strain energy functions are used to model hyperelastic behavior of these materials and there are numerous efforts in the literature on the derivation and/or fitting of various forms of strainenergy functions, such as works of Mooney (1940), Blatz and Ko (1962), Yeoh (1993), Ogden (1972), Beatty (1987). Presenting precise constitutive model to describe hyperelastic behavior of rubber like material is the subject of a lot of researches in the recent years such as works by Anani and Alizadeh (2011), Bao et al (2003), Silva and Bittencourt (2008), Pereira and Bittencourt (2010), Pascon and Coda (2013), Coelho et al (2014), Santos et al (2015), Tomita et al (2008) and Barforooshi and Mohammadi (2016) As functionally graded rubber is the subject of this study it should be noted that graded rubber like materials were created by Ikeda et al (1998) in the laboratory for the first time, a while after these materials have attracted the attention of investigators for modeling these materials behavior under mechanical and geometrical boundary conditions. Some important and novel researches about analysis of inhomogeneous rubber like materials structures are presented in details by Bilgili (2003Bilgili ( ,2004, Batra (2006), Batra and Bahrami (2009), Rahimi (2015,2016).…”