Nonlinear Transverse Vibration of a Hyperelastic Beam Under Harmonically Varying Axial Loading

Nonlinear transverse vibration of a hyperelastic beam under a harmonically varying axial load is analyzed in this work. Equations of motion of the beam are derived via the extended Hamilton's principle, where transverse vibration is coupled with longitudinal vibration. The governing equation of nonlinear transverse vibration of the beam is obtained by decoupling the equations of motion. By applying the Galerkin method, the governing equation transforms to a series of nonlinear ordinary differential equations (ODEs). Response of the beam is obtained via three different methods: the Runge–Kutta method, multiple scales method, and harmonic balance method. Time histories, phase-plane portraits, fast Fourier transforms (FFTs), and amplitude–frequency responses of nonlinear transverse vibration of the beam are obtained. Comparison of results from the three methods is made. Results from the multiple scales method are in good agreement with those from the harmonic balance and Runge–Kutta methods when the amplitude of vibration is small. Effects of the material parameter and geometrical parameter of the beam on its amplitude–frequency responses are analyzed.

Nonlinear vibration mechanism for fabrication of crimped nanofibers with bubble electrospinning and stuffer box crimping method

This paper aims to produce nanoscale crimped fibers using stuffer box crimping and bubble electrospinning. Nanofibers are originally obtained via a ruptured bubble and then crimped with the stuffer box crimping method. During this spinning process, the governing equations for nonlinear transverse vibration of an axially moving viscoelastic beam with finite deformation are established using the Hamiltonian principle. The crimp frequency is affected by many factors, including spinning conditions and mechanical properties of fibers. The obtained governing equations can be further used for numerical or analytical study of the crimping mechanism.