Estimation of the probability of two consecutive passages through resonance during the descent of an asymmetric rigid body in a rarefied atmosphere

A two-frequency nonlinear system of ordinary differential equations is considered. This system describes the perturbed motion of a rigid body with considerable asymmetry in a rarefied atmosphere. It is known that when the frequencies of this system of equations coincide, the phenomena of capture or passage through the principal resonance, which have a random nature, are possible. In this case, the probability of a passage through the resonance is calculated from the initial conditions on the separatrix. The objective of this study is to obtain an expression for estimating the probability of two consecutive passages through the resonance regions during the descent in the rarefied atmosphere of Mars of a rigid body with significant geometric and aerodynamic asymmetry.

Forced-self-excited System of Iced Transmission Lines under Planar Harmonic Excitations

This paper is concerned with the analysis of the self-excited vibrations and forced vibrations of the iced transmission lines. By introducing the external excitation load, the effect of dynamic wind on the nonlinear vibration equations of motion is reflected by vertical aerodynamic force. The approximate analytical solution of the non-resonance, and the amplitude frequency response relation of the principal resonance of the forced self-excited system are obtained by using the multiple scale method. With the increase in excitation amplitude, the nonlinearity of the system is enhanced, and the forced-self-excited system experiences three vibration stages (self-excited vibration, the superposition form of self-excited vibration and forced vibration, forced vibration controlled by nonlinear damping). Among them, the accuracy of the approximate analytical solution decreases with the increase of the nonlinear strength. And the excitation amplitude is greater than the critical value, the quenching phenomenon appear in the forced-self-excited system, and the discriminant formula is derived in this paper. In addition, the frequency of excitation term determines the vibration form of the system. The principal resonance, super-harmonic resonance and sub-harmonic resonance of the forced-self-excited system are analyzed by using different excitation frequencies. Compared with the principal resonance and the harmonic resonance, the meaningful transition from periodic response to quasi periodic response is easy to appear with the condition of the 1/3-order sub-harmonic and the 3-order super-harmonic. The conclusions would be helpful to the practical engineering of the iced transmission lines. More important, as a combination of Duffing equation and Rayleigh equation, the forced-self-excited system also has high theoretical research value.

Biodynamic Response of Seated Human Body to Roll Vibration and Correlation between Roll and Lateral Directions

Within 30 Hz, the discomfort caused by whole-body vibration in rotational direction is higher than vertical vibration at similar equivalent magnitude. Roll vibration, in particular, produces greater discomfort comparing with pitch and yaw vibrations. It is critical to understand the biodynamic characteristics of seated human body under roll vibration for both comfort assessment and vibration control. Experiments are carried out to obtain the biodynamic response of seated human body under random roll vibrations at four r.m.s. magnitude levels. It is found that the principal resonance in the roll apparent inertia is about 1 Hz, but varied from 0.7 to 1.5 Hz depending on the magnitude of vibration (0.5 to 2.0 rad/s2), and the secondary resonance locates around 3 Hz with a much lower modulus. It is noted that the human response to roll vibration has some features in common with that in the lateral direction. Two lumped parameter models are developed and calibrated to study the correlation between the two excitation axials. The equivalent relationships of magnitude and phase between roll and lateral vibrations are obtained on condition that they produce similar rotational responses of the upper human body. It suggests an equivalence approach between translational and rotational vibrations that can benefit the comfort assessment when exposed to multiaxial excitations.

Improving energy harvesting in excited Duffing harvester device using a delayed piezoelectric coupling

The present work examines the influence of time delay introduced in the piezoelectric circuit of an excited Duffing harvester device with hardening stiffness on the vibration and voltage amplitudes. Specifically, we seek to exploit a delayed electrical circuit of the harvester to enhance its performance. We consider the case of a monostable system and we use a perturbation technique to approximate the periodic response and the corresponding voltage amplitude near the principal resonance. It is shown that for appropriate values of delay amplitude, the energy harvesting performance is improved over a certain range of coupling parameters and excitation frequencies. Numerical simulation is conducted to support the analytical predictions.