In this article, flexural vibration and its power flow of an axially loaded beam with arbitrary boundary and non-uniform elastic foundation are analyzed via energy principle in conjunction with Rayleigh–Ritz procedure. A general solution is assumed as a modified version of Fourier series supplemented with boundary-smoothing auxiliary terms. Effects of axial load and elastic foundation of the beam are taken into account in terms of potential energy in system Lagrangian. Critical load of this axially loaded beam is obtained under elastic boundary condition and non-uniform foundation. Numerical examples are then presented to demonstrate the reliability and effectiveness of the established model by comparing results with those available in literature or calculated using finite element method. Results show that the current model can make an accurate dynamic analysis for the elastically restrained beam with axial load and non-uniform elastic foundation. Influence of some important factors, including boundary restraint, axial load, and non-uniform foundation, on the vibration characteristics and power flow transmission are studied and addressed. It is found that the supporting condition has a significant influence on power flow distribution across the whole beam, in which the shear force component plays a dominant role for the power flow transmission.

This study presents a new bistable energy harvester utilizing the lever mechanism, and investigates its dynamic behaviors under two Gaussian-type stochastic excitations: white and exponentially correlated Gaussian noises. Fokker–Planck–Kolmogorov equation is used to predict analytical results of the system’s probability distribution function, which are also numerically validated by Euler–Maruyama (E–M) algorithm. For the white noise excitation, the bistable nonlinearity does not affect the average of the harvested power, but the lever mechanism can significantly improve it if the lever parameters transcend an invariant boundary which identifies the performance improvement region. For the exponentially correlated noise, both the bistable nonlinearity and lever parameters affect the average power. The performance improvement region is insensitive to the excitation intensity, but its boundary varies corresponding to different correlation coefficients of the excitation; the smaller correlation coefficient, the broader region. In addition, time history responses of the harvester’s actuation displacement and velocity are numerically obtained to verify the analytical findings. The results reveal that for some small lever parameters, large-amplitude crossing-well response may lead to smaller actuation velocity, which degrades the average of the harvested power. Hence, better energy harvesting requires larger level parameters to enhance the actuation velocity.