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The model of a clamped-clamped Euler-Bernoulli beam is presented in order to study nonlinear vibration control of electrostatically actuated nanobeam with nanocapacitive sensor, considering primary and superharmonic resonances. The capacitance of nanobeam capacitor changes with the nanobeam deformation. The nanocapacitive sensor is applied to extract vibration signals and to transform enlarged signals into controller to control nanobeam vibrations. The method of multiple scales is used to obtain the first-order approximate solutions and derive the amplitude-frequency equation. The nonlinear vibration characteristics and amplitude-frequency response of nanobeam vibration system are studied under different excitation voltage, feedback gains, and damping. The relationships between amplitude and system parameters are discussed in detail. The presented analytical and numerical simulations show that dynamic response of nanobeam is stable when the appropriate parameters are chosen. This investigation provides a better understanding of the nonlinear vibration of nanoelectromechanical systems devices based on nanobeam.

The existing available research outcomes on vibration attenuation control for time-delay feedback indicate that, for the delay dynamic vibration absorber with fixed time-delay control parameters, under harmonic excitation, a good vibration attenuation control effect occurs on the vibration of the main system. However, the effect is not obvious for complex excitation. Aiming at the above problems, in a short time interval, a harmonic excitation with the same displacement size as the complex excitation was established. Then, by calculating its equivalent amplitude and equivalent frequency, a harmonic equivalent method for complex excitation was proposed in this paper. The time-delay parameters were adjusted according to the equivalent frequency of harmonic equivalent excitation in real time; therefore, a good vibration attenuation control effect was obtained through the delay dynamic vibration absorber in the discrete time interval. In this paper, research on a time-varying delay dynamic vibration absorber was conducted by taking the two-degree-of-freedom vibration system with a delay dynamic vibration absorber as an example. The simulation results show that the proposed control method can reduce the vibration of the main system by about 30% compared with the passive vibration absorber. This can obviously improve the performance of the time-delay dynamic vibration absorber. It provides a new technical idea for the design of vehicle active frame system.

Frequency stabilization can overcome the dependence of resonance frequency on amplitude in nonlinear microelectromechanical systems, which is potentially useful in nonlinear mass sensor. In this paper, the physical conditions for frequency stabilization are presented theoretically, and the influence of system parameters on frequency stabilization is analyzed. Firstly, a nonlinear mechanically coupled resonant structure is designed with a nonlinear force composed of a pair of bias voltages and an alternating current (AC) harmonic load. We study coupled-mode vibration and derive the expression of resonance frequency in the nonlinear regime by utilizing perturbation and bifurcation analysis. It is found that improving the quality factor of the system is crucial to realize the frequency stabilization. Typically, stochastic dynamic equation is introduced to prove that the coupled resonant structure can overcome the influence of voltage fluctuation on resonance frequency and improve the robustness of the sensor. In addition, a novel parameter identification method is proposed by using frequency stabilization and bifurcation jumping, which effectively avoids resonance frequency shifts caused by driving voltage. Finally, numerical studies are introduced to verify the mass detection method. The results in this paper can be used to guide the design of a nonlinear sensor.

As the key component to transmit power and torque, the fault diagnosis of rotating machinery is crucial to guarantee the reliable operation of mechanical equipment. Regrettably, sample class imbalance is a common phenomenon in industrial applications, which causes large cross-domain distribution discrepancies for domain adaptation (DA) and results in performance degradation for most of the existing mechanical fault diagnosis approaches. To address this issue, a novel DA approach that simultaneously reduces the cross-domain distribution difference and the geometric difference is proposed, which is defined as MRMI. This work contains three parts to improve the sample class imbalance issue: (1) A novel distance metric method (MVD) is proposed and applied to improve the performance of marginal distribution adaptation. (2) Manifold regularization is combined with instance reweighting to simultaneously explore the intrinsic manifold structure and remove irrelevant source-domain samples adaptively. (3) The ℓ2-norm regularization is applied as the data preprocessing tool to improve the model generalization performance. The gear and rolling bearing datasets with class imbalanced samples are applied to validate the reliability of MRMI. According to the fault diagnosis results, MRMI can significantly outperform competitive approaches under the condition of sample class imbalance.