Equilibria and vibration of a heavy pinched loop

摘要: A thin strip is bent such that the two ends are brought together and clamped (pinched) to form a teardrop shape. The end held at various angles with loop either upright, horizontal, downward, or halfway between these positions. length of increased, resulting equilibrium shapes, as well small in-plane vibrations about equilibrium, investigated analytically experimentally. When buckling occurs critical length, subsequent postbuckling deflections can be large. For other orientations, except hanging one, also become large increased. In analysis, assumed an inextensible elastica which unstrained when straight, its self-weight included. shooting method applied obtain numerical solutions nonlinear boundary value problem linear vibration problem. Polycarbonate strips used in experiments, data acquired laser vibrometer. experimental deflections, frequencies, mode shapes exhibit excellent agreement analytical solutions.