  Over the past few years, equation discovery has gained popularity in
different fields of science and engineering. However, existing equation
discovery algorithms rely on the availability of noisy measurements of the
state variables (i.e., displacement {and velocity}). This is a major bottleneck
in structural dynamics, where we often only have access to acceleration
measurements. To that end, this paper introduces a novel equation discovery
algorithm for discovering governing equations of dynamical systems from
acceleration-only measurements. The proposed algorithm employs a library-based
approach for equation discovery. To enable equation discovery from
acceleration-only measurements, we propose a novel Approximate Bayesian
Computation (ABC) model that prioritizes parsimonious models. The efficacy of
the proposed algorithm is illustrated using {four} structural dynamics examples
that include both linear and nonlinear dynamical systems. The case studies
presented illustrate the possible application of the proposed approach for
equation discovery of dynamical systems from acceleration-only measurements.
