## Snap-Through Instability of Graphene on Substrates

## Torsional Kinematic Model for Concentric Tube Robots

## Temporal evolution and instability in a viscoelastic dielectric elastomer

## Optomechanics of Soft Materials

## Planar analysis of a quasi-zero stiffness mechanism using inclined linear springs

## A lower bound on snap-through instability of curved beams under thermomechanical loads

## Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System

## Transient behavior of curved structures

## Horizontal stability of a quasi-zero stiffness mechanism using inclined linear springs

## Understanding of the phase transformation from fullerite to amorphous carbon at the microscopic level

## Dynamics of Snapping Beams and Jumping Poppers

## Snap-through instability of graphene on substrates

## Endocytic proteins drive vesicle growth via instability in high membrane tension environment

## Observation of a Snap-Through Instability in Graphene

## Determination of the Bending Rigidity of Graphene via Electrostatic Actuation of Buckled Membranes

## Theory of Sorption Hysteresis in Nanoporous Solids: I. Snap-Through Instabilities

## Elastocapillary Snapping: Capillarity Induces Snap-Through Instabilities in Small Elastic Beams

## Substrate-regulated morphology of graphene

## Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

## Nonlinear Dynamics of Discrete and Continuous Mechanical Systems with Snap-through Instabilities

The primary focus of this dissertation is the characterization of snap-through buckling of discrete and continuous systems. Snap-through buckling occurs as the consequence of two factors, first the destabilization, or more often the disappearance of, an equilibrium position under the change of a system parameter, and second the existence of another stable equilibrium configuration at a remote location in state space. In this sense snap-through buckling is a global dynamic transition as the result of a local static instability.

In order to better understand the static instabilities that lead to snap-through buckling, the behavior of mechanical systems in the vicinity of various local bifurcations is first investigated. Oscillators with saddle-node, pitchfork, and transcritical bifurcations are shown analytically to exhibit several interesting characteristics, particularly in relation to the system damping ratio. A simple mechanical oscillator with a transcritical bifurcation is used to experimentally verify the analytical results. The transcritical bifurcation was selected since it may be used to represent generic bifurcation behavior. It is shown that the damping ratio may be used to predict changes in stability with respect to changing system parameters.

Another useful indicator of snap-through is the presence of chaos in the dynamic response of a system. Chaos is usually associated snap-through...