  This paper focuses on the escape problem of a harmonically-forced classical
particle from a purely-quartic truncated potential well. The latter corresponds
to various engineering systems that involve purely cubic restoring force and
absence of linear stiffness even under the assumption of small oscillations,
such as pre-tensioned metal wires and springs, and compliant structural
components made of polymer materials. This, in contrast to previous studies
where the equivalent potential well could be treated as linear at first
approximation under the assumption of small perturbations. Due to the strong
nonlinearity of the current potential well, traditional analytical methods are
inapplicable for describing the transient bounded and escape dynamics of the
particle. The latter is analyzed in the framework of isolated resonance
approximation by canonical transformation to action-angle (AA) variables and
the corresponding reduced resonance manifold (RM). The escape envelope is
formulated analytically. Surprisingly, despite the essential nonlinearity of
the well, it exhibits a universal property of a sharp minimum due to the
existence of multiple intersecting escape mechanisms. Unlike previous studies,
three underlying mechanisms that govern the transient dynamics of the particle
were identified: two maximum mechanisms and a saddle mechanism. The first two
correspond to a gradual increase in the system's response amplitude for a
proportional increase in the excitation intensity, and the latter corresponds
to an abrupt increase in the system's response and therefore more potentially
hazardous. The response of the particle is described in terms of energy-based
response curves. The maximal transient energy is predicted analytically over
the space of excitation parameters and described using iso-energy contours. All
theoretical predictions are in complete agreement with numerical results.
