Response And Dvnamic Stability Of Delectric Elastomer Spherical/Cylindrical Shell

Due to the advantages of large voltage-induced deformation,fast response,strong environmental adaptability and excellent bionic performance,dielectric elastomer is considered as an ideal material for manufacturing soft machines.Dielectric elastomer structures easily appear failures when operating in applications.The existing studies mainly focus on static and quasi-static situations and the results generally cannot be used for dynamic situation.In the present thesis,the response and dynamic stability of dielectric elastomer spherical shell and cylindrical shell subjected to electrical and mechanical loads are investigated.For dielectric elastomer spherical shell,firstly,the dynamical equation with respect to the stretch ratio of the structure subjected to electrical and mechanical loads is derived according to the principle of virtual work.The free energy function is expressed as the summation of the dielectric energy and the elastic energy described by the Mooney-Rivlin model.Then,the dynamical response of the dielectric elastomer spherical shell is numerically analyzed.The relation between the peak value of stationary response and the voltage/pressure is analytically derived through the first integral of system.The intersection point of the relation curve and the static equilibrium curve gives the critical voltage/pressure.The dynamic stability of the spherical dielectric elastomer shell under different situations is discussed in detail.For any given voltage,there exists a threshold of material constant,below which the structure will remain stable forever.A similar threshold of material constant exists for any pressure with the value of nonzero.For the case with absent pressure,however,there always exists a critical voltage,beyond which the structure will be dynamically unstable.It is also found that pre-stretch will improve the dynamic stability of the dielectric elastomer spherical shell.For the dielectric elastomer cylindrical shell,the dynamical equation with respect to the stretch ratio for the inner diameter with of the structure under electromechanical coupling is established with the application of infinitesimal method and the boundary conditions.The neo-Hookean model is adopted for the elastic strain energy of the system.The equilibrium position,quasi-static stability,dynamic response and dynamic stability of the stretch ratio of the system subjected to electrical and mechanical loads are analyzed.The effects of pressure,voltage,geometric parameter and pre-stretch on the stability are also discussed.The results show that there exist critical pressure and critical voltage of quasi-static instability and dynamic instability.It is found that the critical values of quasi-static instability are greater than the corresponding critical values of the dynamic instability.With the increase of the thickness parameter,both of the critical values of quasi-static instability and dynamic instability increase.Pre-stretch can improve the dynamic stability domain of the system.