Axial vibration of an artificial muscle

Significant number of muscles can be assumed to be of longitudinal type where the length is much higher than its cross-section. Usual motion of the longitudinal muscles is axial due to its contraction and dilatation. Our aim is to investigate the axial vibration of such muscles. The artificial muscle is formed whose physical model is a clamped-free beam. Characteristics of the muscle material are obtained experimentally and the data are applied for the rheological model. It is obvious that the stress-strain properties are strong nonlinear. The beam is assumed to be fixed at one end and free for axial motion at the other end. Mathematical model of motion is supposed as a partial truly strong nonlinear differential equation. In the paper an analytical procedure for approximate solving of the equation is developed. Using a suitable transformation the equation is rewritten into two strong nonlinear ordinary second order differential equations. Analyzing the solution, the influence of the geometric properties, but also of material properties and boundary conditions on the motion is considered. Special attention is given to frequency of vibration of the beam. Effect of the order of nonlinearity and of the initial conditions on the frequencies is widely analyzed.