Large loads due to fluid-structure interaction can lead to high bending stresses and fatigue failure in wings and wind turbine blades. A solution for the mentioned problem is using a bistable composite laminate for load alleviation. A bistable composite laminate is capable of attaining two statically stable shapes, and it can be designed to alleviate a critical load, such as wind gust, by snapping from one stable position to the other. Piezocomposite actuators can be used to reverse the snapthrough and bring back the structure to its original optimal aerodynamic shape, after the gust load is alleviated. However, there will always be a limit on the size of the piezocomposite actuator used; hence, severe force and energy constraints exist to achieve the snap-through. In this context, this paper focuses on the minimum required actuation energy for performing snapthrough of a bistable structure. The paper shows how the required energy for cross-well transfer varies as a function of damping ratio and frequency ratio at specific harmonic force amplitude when the system is externally disturbed with a bandlimited noise signal. A band-limited noise signal is chosen to model external/ambient disturbances. This paper uses the Duffing-Holmes equation as a one-degree-of-freedom representative model of a bistable structure. This equation is numerically solved to calculate the required energy for crosswell oscillation under different system and forcing conditions. Various non-dimensional parameters are used to highlight interesting phenomena. It is found that the domain of low energy regions decreases by increasing the level of noise.