Large amplitude vibrations of imperfect porous-hyperelastic beams via a modified strain energy

Abstract

In this paper, the porous-hyperelastic properties of soft materials are obtained experimentally and a general model for a combination of porosity (of functional type) and hyperelasticity using the Mooney-Rivlin strain energy density is obtained. Porous-hyperelastic samples are fabricated using thermoplastics with different porosities by varying the infill rate of 3D-printing. Following the available standards, the stress-strain behaviour for different samples are obtained and a general model for hyperelastic closed-cell porosity is presented. After obtaining model's characteristics from the experimental testings, a general beam formulation is presented for hyperelastic beams with functional porosity through the length. Both the axial and transverse motions are considered in the model of hyperelastic beams in the framework of the Mooney-Rivlin material model and Hamilton's principle. A geometrical imperfection of the beam is also considered in the formulation. The nonlinear forced vibrations of the imperfect porous-hyperelastic beam are studied by simultaneously solving the axial and transverse nonlinear coupled equations using a dynamic equilibrium technique. It is shown that having a uniform and functional porosity has a significant effect in changing the nonlinear frequency response of the system. Geometrical imperfection leads to a significant coupling between the axial and transverse coordinates when the porosity varies functionally through the length which shows the importance of considering both motions while analysing such structures. The results are useful for better understanding the effects of imperfections in studying the mechanics of soft structures and can be useful in designing soft robotics and artificial organs.