Parameters optimization for a novel dynamic vibration absorber

Nonlinear vibration of a traveling belt with non-homogeneous boundaries

This paper presents an investigation on the nonlinear aeroelastic system of an airfoil with external store by incremental harmonic balance (IHB) method. Besides solving limit cycle (LC) solutions, the IHB method is implemented to obtain quasi-periodic (QP) solutions by introducing multiple irreducible time scales. Steady state responses such as LC and QP oscillations obtained by the presented method are verified by numerical examples. One pair of Floquet multipliers for LC solutions first leave and then enter a unit cycle at complex conjugate values, indicating the existence of a secondary Hopf bifurcation and its reversal one. Along with the fundamental frequency of LC oscillation, an additional frequency arises at the secondary bifurcation, and finally disappears at the reversal bifurcation. The appearance and disappearance of the irreducible frequency cause the steady state responses changing from LC to QP and back to LC oscillation.

Quasi-periodic aeroelastic response analysis of an airfoil with external store by incremental harmonic balance method

A lumped parameter transverse vibration model of a composite plate harvester is analyzed via harmonic balance approaches. The harvester is mainly composed of a piezoelectric circular composite clamped by two steel rings and a proof mass on the plate. The lumped parameter model is a 1.5 degree-of-freedom strongly nonlinear system with a higher order polynomial stiffness. A harmonic balance approach is developed to analyze the system, and the resulting algebraic equations are numerically solved by adopting an arc-length continuation technique. An incremental harmonic balance approach is also developed for the lumped parameter model. The two approaches yield the same results. The amplitude-frequency responses produced by the harmonic balance approach are validated by the numerical integrations and the experimental data. The investigation reveals that there coexist hardening and softening characteristics in the amplitude-frequency response curves under sufficiently large excitations. The harvester with the coexistence of hardening and softening nonlinearities can outperform not only linear energy harvesters, but also typical hardening nonlinear energy harvesters.

Nonlinear vibration analysis of a circular composite plate harvester via harmonic balance

The present work explores nonlinear dynamics of a supercritically moving beam under the 3:1 internal resonance condition. Responses are very different with those without internal resonance. Based on the direct multiple scale method, resonances for the first-two natural modes are identified to exist in three cases. The first one is that the pulsating speed frequency closes to two times of the first natural frequency. Under this condition, responses for natural modes are distinctly coupled as response curves are twisted. The internal resonance plays an essential role in energy transmission between related modes. It not only arouses a double-jumping phenomenon, but also reduces the typical parametric responses to zero astoundingly. Besides, the internal resonance changes the critical pulsating speed and produces some saddle-node bifurcations. In the case of the pulsating speed frequency closing to two times of the second natural frequency, only the second natural mode could be excited. The response occurs in the form of a typical parametric resonance. The third case is the pulsating speed frequency closing to the sum of the first-two natural frequencies. Different with the first two cases, quasi-periodic responses are found in the form of beat vibrations. Amplitude and the frequency of beats are affected by the pulsating speed, the internal resonance condition and also the pulsating frequency. Contributions of them are quite different. This paper is instructive to the study of vibration of other gyroscopic continuous systems, such as pipes conveying fluid and rotation continua.

Internal resonance of a supercritically axially moving beam subjected to the pulsating speed

A New Incremental Harmonic Balance Method With Two Time Scales for Quasi-Periodic Motions of an Axially Moving Beam With Internal Resonance Under Single-Tone External Excitation


 Periodic and period-doubling vibrations in a gear transmission system subjected to forced excitations with multi-piecewise linear functions are investigated in this work by using the incremental harmonic balance (IHB) method. The nonlinear ordinary differential equations that govern vibration of the gear transmission system are formulated by employing the Newton's second law. Analytical results reveal abundant interesting phenomena, including jumps, bifurcations, softening-spring behaviors, and primary, super-harmonic, and sub-harmonic resonances, which have not been exhibited in existing investigations on nonlinear vibrations of gear transmission systems. Nonlinear phenomena and resonances of the gear transmission system are revealed by considering different numbers of degrees of freedom of the system. The bifurcations containing saddle-node, period-doubling, and Hopf bifurcations are observed in frequency response curves. The period-doubling phenomena are characterized with phase-plane diagrams and Fourier spectra. Further, analytical results obtained by the IHB method match very well with those from numerical integration.

Jianliang Huang

Papers

A New Incremental Harmonic Balance Method With Two Time Scales for Quasi-Periodic Motions of an Axially Moving Beam With Internal Resonance Under Single-Tone External Excitation

Nonlinear Vibration of a Multi-Degree-of-Freedom Gear Transmission System with Multi-Piecewise Linear Functions

Event-driven Gauss quadrature and stability analysis for fast alternating frequency-time harmonic balance of non-smooth systems