In previous work, Mockensturm and Mote investigated the effects of twist on steady motions of an axially moving plate. It was found that twisting produces compressive stresses that increase with twist, aspect ratio, and initial, longitudinal tension. In this work, we study the effects of the stresses and non-flat equilibrium produced by twist on the free response. To accomplish this, the equations of motion are linearized about the equilibrium configuration, yielding a set of three, coupled, linear partial differential equations. The equations are discretized and the free response is predicted from the resulting discrete eigenvalue problem. As a function of twist angle, the natural frequencies first increase and then decrease rapidly to zero as the compressive lateral stresses become sufficiently large to cause wrinkling. The effects of thickness, aspect ratio, and initial tension on natural frequencies are also studied.

Issue Section:
Technical Papers
Keywords:
partial differential equations, linear differential equations, vibrations, eigenvalues and eigenfunctions, torsion
Topics:
Constitutive equations, Eigenfunctions, Eigenvalues, Equations of motion, Equilibrium (Physics), Partial differential equations, Plates (structures), Separation (Technology), Stress, Tension, Vibration, Compressive stress, Kinematics, Deformation, Differential equations, Torsion
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