Nonlinear vibration absorption for a flexible arm via a virtual vibration absorber

The application of the magnetorheological elastomer (MRE) to nonlinear vibration control for a flexible arm is investigated in this paper. A semiactive control method is suggested to reduce vibration via the internal resonance and the MRE. To establish a vibration energy transfer channel, a tuned vibration absorber based on the MRE is developed. Through adjusting the coil current, the frequency of the vibration absorber can be readily controlled by the external magnetic field, thereby maintaining the internal resonance condition with the flexible arm. By the perturbation analysis, it is proven that the internal resonance can be successfully established between the flexible arm and the MRE vibration absorber, and the vibration energy of the flexible arm can be transferred to and dissipated by the MRE vibration absorber. Through numerical simulations, virtual prototyping simulations, and experimental investigation, it is verified that the proposed method and the suggested MRE vibration absorber are effective in controlling nonlinear vibration of the flexible arm.

Analysis of free non-linear vibrations of a viscoelastic plate under the conditions of different internal resonances

Dynamics of a mass–spring–beam with 0:1:1 internal resonance using the analytical and continuation method

Non-linear damped vibrations of a cylindrical shell subjected to the different conditions of the combinational internal resonance are investigated. Its viscous properties are described by Riemann-Liouville fractional derivative. The displacement functions are determined in terms of eigenfunctions of linear vibrations. The procedure resulting in decoupling linear parts of equations is proposed with the further utilization of the method of multiple time scales for solving nonlinear governing equations of motion, in so doing the amplitude functions are expanded into power series in terms of the small parameter and depend on different time scales. It is shown that the phenomenon of internal resonance can be very critical, since in a circular cylindrical shell the internal additive and difference combinational resonances are always present. The influence of viscosity on the energy exchange mechanism is analyzed. It is shown that each mode is characterized by its damping coefficient connected with the natural frequency by the exponential relationship with a negative fractional exponent.

Nonlinear dynamics of a foldable multibeam structure with one to two internal resonances

Dynamics of regenerative chatter and internal resonance in milling process with structural and cutting force nonlinearities

A frequency up-converting, wide band vibration energy harvesting (VEH) mechanism via 1:2 internal resonance is proposed for the first time in this work. By introducing a constant magnetic field to break the symmetry of the structure and introducing the secondary nonlinear coupling stiffness, the internal coupling of the first two bending modes is realized. Using the frequency up-converting effect of 1: 2 internal resonance, the vibration energy collection efficiency is improved exponentially; using the quadratic stiffness nonlinearity to realize the bilateral frequency broadening, the effective bandwidth of the vibration energy collection is broadened significantly. Numerical and experimental results indicate that the peak-splitting effect of the 1: 2 internal resonance can bidirectionally widen the relative bandwidth of vibrational energy harvesting, with a 200% increase in energy harvesting efficiency owing to frequency up-conversion.

The study investigated the steady state response of a piezoelectric pipe conveying fluid under external and internal resonances in the supercritical regime of fluid velocity. Internal resonance conditions between the first and second frequency modes were studied at a specific flow velocity in the supercritical regime. The Galerkin method and the multiple scale method were used to extract the vibration amplitude versus the excitation frequency and amplitude. The steady state solutions lost stability through saddle-node and Hopf bifurcations, leading to periodic, double periodic, multi-periodic, and chaotic behaviors in the forced and frequency response curves. Time response, FFT, phase portrait, and Lyapunov exponents were presented to predict the unstable regions of the piezo-pipe system between the Hopf points. The Wolf algorithm was utilized to evaluate the Lyapunov exponents. Additionally, a fuzzy terminal sliding mode controller was designed in the chaotic region of the piezoelectric pipe conveying fluid, and its parameters were optimized using the genetic algorithm. The controller effectively stabilized the chaotic motion of the system, demonstrating better performance than the sliding mode control in numerical results.

A formulation for computing resonant nonlinear normal modes (NNMs) is developed for discrete and continuous systems. In a canonical framework, internal resonance conditions are immediately recognized by identifying commensurable linearized natural frequencies of these systems. Additionally, a canonical formulation allows for a single (linearized modal) coordinate to parameterize all other coordinates during a resonant NNM response. Energy-based NNM methodologies are applied to a canonical set of equations and asymptotic solutions are sought. In order to account for the resonant modal interactions, it will be shown that high-order terms in the O(1) solutions must be considered (in the absence of internal resonances, a linear expansion at O(1) is sufficient). Two applications (‘3:1’ resonances in a two-degree-of-freedom system and ‘3:1’ resonance in a hinged-clamped beam) are then considered by which to demonstrate the resonant NNM methodology. It is shown that for some responses, nonlinear modal relations do not exist in the context of physical coordinates and thus a transformation to a canonical framework is necessary in order to appropriately define NNM relations.

Nonlinear dynamic analysis of flexible workpiece and tool in turning operation with delay and internal resonance

Vibrational Spectra:Principles and Applications with emphasis on optical activity

High-efficient internal resonance energy harvesting: Modelling and experimental study

Two-to-one internal resonance in the higher-order modes of a MEMS beam: Experimental investigation and theoretical analysis via local stability theory

Flexible manipulators have received wide attention because they are more realistic than their rigid counterparts in many practical conditions. The control of the motion and vibration of an elastic model has inspired many studies in the past decades. In this paper, a finite element model is developed and used for the modeling of the single-link flexible arm. A new adaptive genetic algorithm (AGA) is proposed to optimize the feedback gains of a proportional derivative (PD) controller for the control of the motion and vibration of the flexible arm. The proposed technique is based on a new adaptive mutation operator to adjust the probability of mutation of each chromosome based on the average fitness value at each generation. The results are compared with those obtained by applying simple GA and a direct evaluation of the objective function in the domain. It has been shown that the new developed adaptive mechanism is faster in convergence and the obtained solutions are of higher fitness values. Compared analysis shows the effectiveness of the proposed adaptive GA over traditional genetic algorithms that have the defects of premature convergence and stagnation when applied in optimization problems. Three different objective functions based on minimizing the error function are tested and compared. Multi-objective error fitness function combined with AGA has given the best system response. Simulation results demonstrate the effectiveness of the proposed technique which encourages for further research into the application of the technique in controlling multiple link flexible robots for further applications.

Internal resonance of a flexible beam in a spatial tethered system