Key to our approach is measuring how arches vibrate. Rock arches are relatively simple mechanical structures with measurable resonant frequencies and mode shapes. The first resonant frequency is termed the fundamental frequency, but any number of higher-mode oscillations are possible. Resonant frequencies are a function of mass and stiffness, and monitoring over time can reveal evidence of internal change.
We measure resonant frequencies from records of ambient motion using ultra-sensitive broadband seismometers. Excitation of the ground occurs from a combination of global earth noise (e.g. ocean waves) and local sources (e.g. wind). Analyzing the Fourier spectra of ambient vibration data, we search for peaks in power and associated frequencies. We also study the polarization of vibration at distinct frequencies.
Modal analysis helps us understand the resonant modes for arches with complex geometry. We generate 3D models from field measurements and input these into finite-element numerical simulation to predict the resonant mode shapes and frequencies, and attempt to match field data. Our goal is to match the fundamental frequency and higher-order modes, some of which take interesting shapes.
Pictured are preliminary results of modal analysis for Delicate Arch. The 3D model was generated from laser scanning data (1). We show the first two predicted modes of vibration: Mode 1 is the first out-of-plane bending, while Mode 2 is the first in-plane bending; click here for more modes! Field data will be used verify these results and calibrate model parameters to match measured resonant frequencies.
We work at a number of prominent sites in Arches and Canyonlands National Parks and surrounding areas. Our work is permitted and partly supported by the National Park Service. We are funded by the National Science Foundation and by the University of Utah.