Inextensibility and Its Effect on the Number of Equilibria of Shallow Buckled Beams

A buckled beam with shallow rise under lateral constraint is considered. The initial rise results from a prescribed end displacement. The beam is modeled as inextensible, and analytical solutions of the equilibria are obtained from a constrained energy minimization problem. For simplicity, the results are derived for the archetypal beam with pinned ends. It is found that there are an infinite number of zero lateral-load equilibria, each corresponding to an Euler buckling mode. A numerical model is used to verify the accuracy of the model and also to explore the effects of extensibility.

Wave Propagation in a Network of Buckled Beams Directly and Parametrically Excited at One End

Wave propagation in a network of buckled beams, which represents a finite dissipative periodic structure with quadratic and cubic nonlinearities, is studied. The aforementioned structure is harmonically driven externally and parametrically at one end with forcing frequencies lying within its stop band, one above and one below. Numerical calculations show the occurrence of supratransmission, a sudden increase in the energy transmitted across the finite structure, after a certain forcing amplitude of the external excitation. In essence, this nonlinear wave propagation mechanism for the discrete nonlinear periodic structure occurs due to loss of stability of the periodic solutions that are initially localized to the driven end of the structure (nonlinear instability). It is found that small parametric excitation can considerably decrease the required threshold for the onset of energy transmission within the stop band.

Zero Torque Compliant Mechanisms Employing Pre-buckled Beams

The concept of a statically balanced mechanism with a single rotational degree-of-freedom is presented. The proposed device achieves static balancing by combining positive stiffness elements and negative stiffness elements within an annular domain. Two designs are discussed. The first is composed of an Archimedean spiral and two pinned-pinned pre-buckled beams. The overall mechanism is modeled via an analytical approach and the element dimensions are optimized. The optimal configuration is then tested through finite element analysis (FEA). A second approach replaces the spiral beam with elastic custom-shaped spline beams. A FEA optimization is performed to determine the shape and size of such spline beams. The behavior of the negators is used as reference for the optimization so as to achieve a complete balancing. A physical prototype of each configuration is machined and tested. The comparison between predicted and acquired data confirmed the efficacy of the design methods.