Axisymmetric wave propagation in finitely deformed dielectric elastomer tubes

Abstract

Wave propagation in hollow dielectric elastomer cylinders is studied. The quasi-static deformation of the tube owing to a combination of radial electric field and mechanical loading is determined first. Two combinations are accounted for, one at which the tube is free to expand in the axial direction, and another at which the tube is axially pre-stretched and restricted from elongating. Subsequently, longitudinal axisymmetric incremental motions are superposed on the underlying state. The governing equations in the tube and in the surrounding space are formulated and a numerical procedure is used in order to solve the resulting set of equations. The fundamental mode in the frequency spectrum is determined for thin, intermediate and thick wall tubes. The influences of the tube geometry, the mechanical pre-stretch and particularly the electric bias field are examined. An important observation is the ability to manipulate the propagation of the waves by adjusting the electromechanical bias field. This infers the use of dielectric elastomers in tubular configurations as active waveguides or isolators by a proper tuning of the electrostatic stimuli.

Bifurcation of finitely deformed thick-walled electroelastic cylindrical tubes subject to a radial electric field

“…In order to determine when deviations from the perfect cylindrical configuration are possible we use the theory of incremental deformations and electric fields superimposed on an underlying finite deformation and electric field. We note that by including dependence on time the problem of wave propagation in an electroelastic tube can be analyzed, as has been done by Shmuel and deBotton [11], who considered axisymmetric waves for an axially loaded tube with a radial electric field, but no radial mechanical loads. When the wave speed vanishes, corresponding bifurcation results can be obtained.…”

“…In considering the propagation of axisymmetric electroelastic waves in a tube in the absence of pressure Shmuel and deBotton [11] obtained results for vanishing wave speed, which corresponds to bifurcation. Such results can be read off as special cases of the results here corresponding to points in the above figures where the (dashed) zero pressure curves intersect with the corresponding bifurcation curves.…”

“…Such results can be read off as special cases of the results here corresponding to points in the above figures where the (dashed) zero pressure curves intersect with the corresponding bifurcation curves. Note, however, that in [11] an incremental electric field exterior to the body needed to be accounted for. …”

Stacked dielectric tubes with electromechanically controlled radii

“…Kovacs et al (2007) employed this motion in an arm wrestling robot. Another actuation that is based on a cylindrical configuration was proposed by Shmuel and deBotton (2013) and Shmuel (2015). These works studied the propagation of longitudinal and torsional waves in dielectric elastomer tubes.…”

“…These elastomers possess many promising properties such as low density, flexibility, ability to undergo large deformations, fast response and availability. Therefore, EAPs are employed in many actuation-based applications such as artificial muscles (Bar-Cohen, 2001), energy-harvesting M A N U S C R I P T Noy Cohen 2 devices (Springhetti et al, 2014;McKay et al, 2010), micropumps (Rudykh et al, 2012) and tunable wave guides (Shmuel and deBotton, 2013), among others. The actuation is the result of the attraction between two oppositely charged electrodes that are attached to a thin dielectric film.…”