bøgehastighet

Bøgehastighet, in Norwegian, roughly translates to bending velocity and refers to the rate at which the bending of a structure changes over time. It is a concept used in structural dynamics, biomechanics, and robotics to describe how quickly a beam, arm, or other flexible element changes its bending shape under time-varying loads.

In a continuous beam, bøgehastighet can be described in two related ways. One is the time derivative of the cross-sectional rotation: ωb(x,t) = ∂θ(x,t)/∂t, where θ(x,t) is the angle of the cross-section relative to a reference direction. Another is the rate of change of curvature: ∂κ/∂t, with κ(x,t) = ∂θ/∂x being the curvature. In Euler-Bernoulli beam theory, κ is approximately the second spatial derivative of transverse deflection w(x,t), so bøgehastighet relates to how quickly the deflection pattern evolves over time.

Contexts of use include dynamic analysis of slender structures under impacts or rapidly varying loads, where higher bending velocities lead to inertial and damping effects and influence fatigue, strength, and stability. In biomechanics, bøgehastighet describes how fast joints or limbs bend; in robotics, it concerns the speed of bending in flexible actuators or links.

Typical units are radians per second for angular bending velocity, or per second (1/s) for curvature rate, with alternative expressions in degrees per second depending on the measurement. Measurement methods combine experimental techniques such as high-speed imaging or digital image correlation with computational modeling to extract θ(x,t) or κ(x,t) over time. See also bending moment, curvature, and dynamic beam theory.