Space Elevator Climber-Induced Tether Resonance

Climber

Climb speed 0.10

Vibration amplitude 0.50

Vibration frequency 2.0 Hz

Structural damping 0.15

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Climber altitude

Direction

Ascending

Local wave speed c(x)

—

Peak lateral sway

0.0%

Round-trip / forcing period ratio

—

How it works

The tether is modelled as a taut string obeying the 1-D wave equation with position-dependent tension T(x), the same PDE used in real space-elevator dynamics studies:

μ ∂²y/∂t² = ∂/∂x( T(x) ∂y/∂x ) − γ ∂y/∂t + F(x,t)
local wave speed: c(x) = √(T(x)/μ)

T(x) rises from the anchor toward geostationary altitude (where the tether's outward centrifugal pull balances Earth's gravity) and falls off again toward the counterweight — so waves travel faster through the high-tension middle section than near either end, exactly as they would on a real tapered cable.

The climbing vehicle is treated as a moving point force F(x,t) = A·sin(2πft) applied at its own position x_c(t), representing the small lateral kicks a real climber injects through roller-track imperfections and motor vibration as it ascends. The tether is fixed (y = 0) at the anchor station and at the counterweight.

Climb speed — how fast the point force moves along the tether; it bounces between anchor and counterweight, alternating ascent/descent.
Vibration amplitude / frequency — the strength and frequency of the forcing the climber injects.
Structural damping — the γ term; higher values bleed energy out of the tether faster, suppressing resonant buildup.
Round-trip / forcing period ratio — the wave's travel time from anchor to counterweight and back, divided by the forcing period. When this ratio lands near a small integer, the climber's kicks arrive in phase with reflected waves and the sway amplitude grows — the same resonance risk that motivates real climber speed-profiles designed to avoid exciting the tether's natural modes.

Tether (displacement ×40) Climber Earth anchor

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