In this paper, we examine Khinchin’s entropy for two weakly nonlinear systems of oscillators. We study a system of coupled Duffing oscillators and a set of Henon–Heiles oscillators. It is shown that the general method of deriving the Khinchin’s entropy for linear systems can be modified to account for weak nonlinearities. Nonlinearities are modeled as nonlinear springs. To calculate the Khinchin’s entropy, one needs to obtain an analytical expression of the system’s phase volume. We use a perturbation method to do so, and verify the results against the numerical calculation of the phase volume. It is shown that such an approach is valid for weakly nonlinear systems. In an extension of the author’s previous work for linear systems, a mixing entropy is defined for these two oscillators. The mixing entropy is the result of the generation of entropy when two systems are combined to create a complex system. It is illustrated that mixing entropy is always non-negative. The mixing entropy provides insight into the energy behavior of each system. The limitation of statistical energy analysis motivates this study. Using the thermodynamic relationship of temperature and entropy, and Khinchin’s entropy, one can define a vibrational temperature. Vibrational temperature can be used to derive the power flow proportionality, which is the backbone of the statistical energy analysis. Although this paper is motivated by statistical energy analysis application, it is not devoted to the statistical energy analysis of nonlinear systems.

In this paper, we use the Monte Carlo simulation to study aeroelastic behavior caused by non-random uncertain free-stream velocity. For sampling, we use the interval process method. Each family of samples is defined by a correlation function and upper and lower bounds. By using this sampling method, there is no need for constructing precise probability distribution functions; therefore, this method is suitable for practical engineering applications. We studied the aeroelastic behavior of an airfoil and a high aspect-ratio wing.

Electrostatic energy harvesters convert kinetic energy into electrical energy via variable capacitors. Efforts to improve their power output are hampered by a lack of understanding of the fundamental limit for energy conversion efficiency. In heat engines, the theoretical limit of conversion efficiency is intrinsically related to entropy and the second law of thermodynamics. Laying the foundation for similar concepts for kinetic energy harvesters may be necessary for establishing a conversion efficiency limit. Thus, the mixing entropy concept is borrowed from statistical mechanics and is adapted here, for the first time, to characterize the energy transfer between coupled mechanical–electrical oscillators. The investigated system is composed of a spring-mass coupled to an inductance-capacitor circuit via a variable capacitor. Combining the two subsystems (electrical and mechanical) generates entropy, referred to as mixing entropy. A non-dimensional study of the governing equations of the systems and their energy terms is carried out. Trends in mixing entropy are compared with trends in the total energy of the system, assuming a conservative system, weak coupling between electrical and mechanical domains, and identical natural frequency of the two oscillators. It is found that mixing entropy can predict the peak in effectiveness of the energy transfer between the two domains. For the cases studied, the maximum mixing entropy and effectiveness values occur when the ratio of the mechanical domain energy to the total energy of the system is 67%. The maximum effectiveness is independent of the initial conditions and depends on the squared ratio of the natural frequency of the nominal coupling capacitor to the natural frequency of the mechanical system.