Theoretical and experimental investigations on semi-active quasi-zero-stiffness dynamic vibration absorber

Control forces of delayed third-order critically damped Duffing equation is proposed in this study. The analytical solution is based on the modified HPM. The solution is demonstrated by introducing a proper function used to suppress the vibration of the nonlinear oscillations. The outcome of the modified homotopy expansion by the exponential negative delay parameter reveals that approximations using this technique are more accurate. To test the accuracy of the recommended modified technique, the obtained results are compared with the numerical solution. Excellent agreement with numerical testing is observed. Further, the suggested control function is eligible for establishing highly accurate approximate analytical frequency and periodic solutions. Based on He’s frequency formula a quasi-exact solution for the nonlinear oscillation has been derived. It is effective and simple to utilize analytic tools for nonlinear problems. These results reveal the accuracy and quality of the suggested technique.

Criteria of vibration control in delayed third-order critically damped Duffing oscillation

Vibration absorption is a core research topic in structural dynamics and the mechanics of machines, and antiresonance assignment is an effective solution to such a problem in the presence of harmonic excitation forces Due to recent developments in the theory of feedback control systems, the use of active control approaches to antiresonance assignment has been recently gaining more attention in the literature Therefore, several methods exploiting state feedback or output feedback have been proposed in recent years These techniques that just rely on servo-controlled actuators are becoming an interesting alternative to active approaches that emulate the well-known Tuned Mass Damper in an active (or semi-active) framework This paper reviews and compares the most important approaches, with a greater focus on the methods exploiting the concept of control theory without adding new degrees of freedom in the system The theoretical results, with the underlying theory, are discussed to highlight the key features of each assignment techniques Several numerical examples where different techniques are applied and compared, also providing some analysis usually neglected in the literature, enrich the paper and demonstrate the key concepts

Active Approaches to Vibration Absorption through Antiresonance Assignment: A Comparative Study

In this article, the vibration absorption performances of a vibration absorber with time-delayed feedback control for a low frequency primary system are studied. In order to extend the effective working frequency band of the time-delayed vibration absorber, its stiffness is designed as an adjustable parameter. The stiffness value of the beam-structure absorber can be tuned by a group of stoppers that can change the constraint condition of the beam. First, the mechanical model of the proposed delay-coupled system is established. Then, the stability boundaries of the proposed system are derived. Next, the analytical approximate solutions of the system are obtained to reveal the frequency response functions. Moreover, two parameter design principles for low-frequency nonlinear primary system are proposed based on the antiresonance frequency and optimum condition. The results show that, for the low-frequency nonlinear primary system, according to the design principles, the antiresonance frequency band can be tuned and the vibration amplitude can be reduced to zero due to the effect of time-delayed control. Relevant experimental prototype is constructed to verify the efficacy of the proposed vibration absorber with time-delayed control.

Time-Delayed Feedback Control Design and Its Application for Vibration Absorption

The generalization of equal-peak method for delay-coupled nonlinear system

In this study, a generalized equal-peak principle is established to suppress the multimodal vibration of a multiple-degree-of-freedom (M-DOF) nonlinear system. Based on the proposed generalized principle, the design procedure of the multiple time-delayed vibration absorbers (TDVAs) is carried out. By four conditions in the proposed generalized principle, the objective of suppressing all the resonance peaks around multiple modes to the equal minimum values is realized. For the existence of nonlinearity, the necessary and sufficient conditions in the design procedure can guarantee that the two resonance peaks around each mode are simultaneously equal. Moreover, the two equal resonance peaks are suppressed to minimum values with the minimum peak condition. Two case studies verify the efficiency of the TDVAs designed by the generalized equal-peak principle for multimodal vibration suppression. Due to the multimodal vibration suppression capacity of the proposed TDVAs designed by the generalized equal-peak principle, significant broad frequency band vibration suppression effects are achieved. Thus, TDVAs and the proposed equal-peak principle have potential applications in the fields of high-DOF vibration systems, such as civil engineering, precision machining and aerospace.

Establishment of the equal-peak principle for a multiple-DOF nonlinear system with multiple time-delayed vibration absorbers

For a nonlinear beam under broadband excitations, the multimodal nonlinear resonance phenomena will be induced. To suppress the multimodal nonlinear resonances, the multiple time-delayed vibration absorbers (TDVAs) are introduced. The optimal time-delayed parameters of the TDVAs are determined by the proposed multimodal equal-peak principle consisting of three design criteria. In the proposed three criteria, the stability criterion ensures the stability of the equilibrium state for the system; the extremes equal criterion figures out the time-delayed parameters to realize the equal resonance peaks around each concerned mode; the minimum peak criterion can obtain the optimal time-delayed parameters for the minimum resonance peaks. The results show that the TDVAs designed by the proposed multimodal equal-peak principle consisting of three criteria could simultaneously suppress the resonance peaks of the beam around multiple modes to the equal and minimum values. Besides, the equal resonance peaks are much lower than the absorbers without time-delayed feedback under the same mass constraint. The proposed TDVAs and the multimodal equal-peak principle have wide application prospects in suppressing the multimodal vibrations for nonlinear continuous systems with broad frequency band and large amplitudes excitation in the fields of civil engineering and aerospace.

Hao Meng

Papers

The generalization of equal-peak method for delay-coupled nonlinear system

Time-Delayed Feedback Control Design and Its Application for Vibration Absorption

Establishment of the equal-peak principle for a multiple-DOF nonlinear system with multiple time-delayed vibration absorbers

Multimodal vibration suppression of nonlinear Euler–Bernoulli beam by multiple time-delayed vibration absorbers

Tunable broadband low-frequency band gap of multiple-layer metastructure induced by time-delayed vibration absorbers