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Multi-harmonic excitations are commonly observed in rotor systems and affect their nonlinear characteristics significantly. However, most of the published nonlinear studies on rotating structures only consider single-harmonic excitation. Compared with single-harmonic issues, multi-harmonic excitations increase the difficulty of calculation and solution exponentially. The purpose of this paper is to establish the nonlinear coupled mechanical model and analyze nonlinear forced vibrations of rotating shells subjected to multi-harmonic excitations in thermal environment. The nonlinear governing equations, considering the Coriolis forces, centrifugal force, initial hoop tension and thermal effect, are obtained by the improved Donnell nonlinear shell theory and Hamilton principle, and then, the multi-mode Galerkin technique is introduced to transform the partial differential equations into multi-degree-of-freedom nonlinear ordinary differential equations (ODEs). Afterward, numerical simulations are conducted by the pseudo-arc-length continuation algorithm. The verification of the solutions with available results in the literature and the convergency of the results are presented. At last, the effects of main factors on nonlinear dynamic response of rotating shells are evaluated. It can be observed that since the multi-DOF coupled system, which is excited by multi-harmonics, exhibits complex nonlinear dynamic responses of rotating shells, the nonlinear multiple internal resonances occur.

The nonlinear response of a water-filled, thin circular cylindrical shell, simply supported at the edges, to multi-harmonic excitation is studied. The shell has opportune dimensions so that the natural frequencies of the two modes (driven and companion) with three circumferential waves are practically double than the natural frequencies of the two modes (driven and companion) with two circumferential waves. This introduces a one-to-one-to-two-to-two internal resonance in the presence of harmonic excitation in the spectral neighbourhood of the natural frequency of the mode with two circumferential waves. Since the system is excited by a multi-harmonic point-load excitation composed by first and second harmonics, very complex nonlinear dynamics is obtained around the resonance of the fundamental mode. In fact, at this frequency, both modes with two and three circumferential waves are driven to resonance and each one is in a one-to-one internal resonance with its companion mode. The nonlinear dynamics is explored by using bifurcation diagrams of Poincaré maps and time responses.

Under the influence of road excitations, the acquisition of optimal time-delayed feedback control parameters is deemed crucial for the improvement of the vibration reduction effect of semi-active vehicle suspension systems. Moreover, different effects on vibration reduction are generally exhibited by vehicle suspension systems based on different time-delayed state feedback control. Therefore, the mechanical model of time-delayed feedback control in semi-active vehicle suspension systems is chosen as the research focus in this paper. Firstly, the optimal values of time-delayed feedback control parameters are derived through an optimization algorithm based on “equivalent harmonic excitation.” Secondly, driven by the optimal values derived from optimization, this study is primarily focused on the investigation of the vibration reduction effect of time delay in a vehicle’s semi-active suspension system under road excitation, thereby revealing the optimal time-delayed feedback control strategy. Finally, the study suggests that a stable state with full time delay within the effective vibration frequency range is more likely to be achieved by the semi-active vehicle suspension system based on time-delayed state feedback control of wheel vertical displacement. Additionally, the optimization efficiencies for vertical seat acceleration, vertical body acceleration, suspension travel, and tire displacement are reported as 97.73%, 98.95%, 47.30%, and 46.38%, respectively.

In this paper, a new technique is proposed to deal with strongly nonlinear stochastic systems with fractional derivative damping and random harmonic excitation. Combining the advantages of Linstedt–Poincaré (L–P) method and multiple scales method, introducing a different frequency expansion form and a time transformation, a series of perturbation equations is obtained according to the powers of parameter. Then, we eliminate the secular producing terms to solve the perturbation equations to derive the second-order approximate solution. Furthermore, the steady-state frequency–amplitude function in deterministic case is analyzed, and the first-order and second-order steady-state moments of the amplitude are also discussed in the presence of random harmonic excitation. In order to explore the effectiveness of the proposed approximate method, two classical examples were proposed to verify the theoretical results through numerical simulations. Especially, the method can be used to investigate some types of extremely strong odd nonlinear terms via the discussions of each example.

In this paper, the mechanical model of two-degree-of-freedom vehicle semi-active suspension system based on time-delayed feedback control with vertical acceleration of the vehicle body was studied. With frequency-domain analysis method, the optimization of time-delayed feedback control parameters of vehicle suspension system in effective frequency band was studied, and a set of optimization method of time-delayed feedback control parameters based on “equivalent harmonic excitation” was proposed. The time-domain simulation results of vehicle suspension system show that compared with the passive control, the time-delayed feedback control based on the vertical acceleration of the vehicle body under the optimal time-delayed feedback control effectively broadens the vibration absorption bandwidth of the vehicle suspension system. The ride comfort and stability of the vehicle under random road excitation are significantly improved, which provides a theoretical basis for the selection of time-delayed feedback control strategy and the optimal design of time-delayed feedback control parameters of vehicle suspension system.

This paper is dedicated to the fundamental research of the mechanical model of a 1/4-vehicle semi-active suspension system with time-delayed state feedback control during wheel vertical displacement. The strategy combining the “equivalent harmonic excitation” optimization algorithm with the particle swarm optimization algorithm is proposed in this paper. Through the optimization and solution of time-delayed feedback control parameters of the 1/4 vehicle semi-active suspension system, the dynamic response of the vehicle suspension system before and after parameter optimization is studied. The research results indicate that, compared to passive control, time-delayed feedback control of wheel vertical displacement can significantly improve the smoothness, handling stability, and safety of vehicle operation.

Considering the low accuracy and low efficiency of the traditional calibration method for base strain sensitivity of accelerometers, a novel base strain sensitivity calibration system with steady harmonic excitation is proposed. The required cantilever beam for calibration is driven by an electromagnetic exciter to generate a base strain varying in a steady harmonic pattern. By applying a Wheatstone bridge circuit, the generated strain with low distortion can be measured. The measurement system with a compensation function can automatically calibrate the base strain sensitivity. The amplitude linearity and frequency response characteristics of the base strain sensitivity in two accelerometers are obtained experimentally, and the uncertainty in the results is 2% ( k = 2).

A bistable nonlinear energy sink (BNES) conceived for the passive vibration control of beam and plate structures under harmonic excitation is investigated. By applying an Incremental Harmonic Balance (IHB) method together with an adjusted arc-length continuation technique, the frequency and amplitude responses are obtained, and their respective trends are discussed in detail from three aspects. The simplest single-mode dynamics is first considered with a special focus on the coupled effect of the cubic nonlinear stiffness and the negative linear stiffness, where an analytical treatment using complex-averaging method is also applied to obtain the slow invariant manifold for understanding the underlying dynamics. Then the multi-mode dynamics of the beam are discussed in variation of each parameter. As a result, a simple step-by-step design rule for the BNES is summarized. Finally, the obtained results and design criteria of the BNES in the beam case are extended to a 2D plate, realizing a broadband control for multi-mode plate vibration. It is found that compared to a traditional cubic one, a BNES can have a better performance both on the frequency and amplitude point of view.

In this study, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the graphene nanoplatelets (GPLs)-reinforced composite (GPLRC) annular plate subject to an external harmonic load. Using Hamilton’s principle and the von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the annular plate subject to a harmonic excitation. The fundamental and golden results of this paper could be that the chaotic motion and nonlinear frequency of the annular plate are hardly dependent on the value of the length to thickness ratio (lGPL/wGPL) of the GPLs. Moreover, utilizing GPLs in the shapes close to square (lGPL/wGPL = 1) presents higher frequency of the annular plate. Also, increase in lGPL/tGPL indicates that using GPLs with lower thickness relative to its length provides better frequency response

Purpose – The purpose of this paper is to propose a novel hybrid excitation permanent magnet synchronous generator (HEPMSG) utilizing tooth harmonic for excitation, the structural features and operation principle of which are also described. Design/methodology/approach – To obtain the operation performance quickly, this paper derives the mathematical model of the machine system represented by circuit, and analyzes the operation mode of rectifier circuit in the tooth harmonic excitation system, then the standard state equations for each operation mode are obtained. Combining the inductance parameter of this machine with the load resistance and inductance, the armature current waveform, the field current waveform and tooth harmonic winding current waveform are obtained by using the numerical method to solve the standard state equation. Findings – Comparing with the experimental results, the availability of the principle and the validity of the model of the machine system are verified. Practical implications – This HEPMSG is a new brushless self-excited and self-regulated generator, which is suitable for an independent power source. Originality/value – Unlike the existing hybrid excitation permanent magnet machine, this HEPMSG utilized the inherent tooth harmonic EMF of the rotor to adjust the air-gap magnetic field of the permanent magnet machine.