Vibration suppression and dynamic behavior analysis of an axially loaded beam with NES and nonlinear elastic supports

2021 ◽  
pp. 107754632110534
Author(s):  
Yuhao Zhao ◽  
Jingtao Du ◽  
Yang Liu
Keyword(s):  
Dynamic Behavior ◽  
Vibration Suppression ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Weight Functions ◽  
Beam Structure ◽  
Beam System ◽  
Residual Matrix ◽  
Axially Loaded ◽  
Nonlinear Elastic

Recently, dynamic analysis of a beam structure with nonlinear energy sink (NES) and various supports is attracting great attention. Most of the existing studies are about the beam structure with NES or nonlinear boundary supports with zero rotational restraint, respectively. However, there is little research accounting for such two types of complex factors simultaneously. In this work, the dynamic behavior of an axially loaded beam with both NES and general boundary supports is modeled and studied. The Galerkin truncated method (GTM) is employed to make the prediction of dynamic behavior of such a beam system, in which the mode functions of axially loaded Euler–Bernoulli beam with linear elastic boundary conditions are selected as the trail and weight functions. Then, the Galerkin condition is used to discretize the nonlinear governing equation of the beam system and establish the residual equations. The Runge–Kutta method is used to solve the residual matrix which consists of residual equations directly, and the harmonic balance method is also used to verify the results from the GTM. The influence of NES on vibration suppression and dynamic behavior of the beam structure is investigated and discussed. Results show that the vibration states of the beam structure can be transformed effectively through the change of NES parameters. On the other hand, the NES with suitable parameters has a beneficial effect on the vibration suppression at both ends of the beam structure.

Dynamic Analysis of 1-Dof and 2-Dof Nonlinear Energy Sink With Geometrically Nonlinear Damping and Combined Stiffness

2021 ◽  
Author(s):  
Yunfa Zhang ◽  
Xianren Kong ◽  
Chengfei Yue ◽  
Huai Xiong
Keyword(s):  
Bifurcation Analysis ◽  
Vibration Suppression ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Nonlinear Damping ◽  
Linear Oscillator ◽  
Frequency Detuning ◽  
Incremental Harmonic Balance Method ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study investigates the dynamics of 1-dof and 2-dof NES with nonlinear damping and combined stiffness connected to a linear oscillator. For the system of 1-dof NES, a truncation damping and failure frequency are revealed through bifurcation analysis using the complex variable averaging method. The frequency detuning interval for the existence of the strongly modulated response (SMR) is also reported . For the system of 2-dof NES, it is reported in a similar bifurcation analysis that the mass distribution between NES affects the maximum value of saddle-node bifurcation. To obtain the periodic solution of the 2-dof NES system with the consideration of frequency detuning, the incremental harmonic balance method (IHB) and Floquet theory are employed. The corresponding response regime is obtained by Poincare mapping, it shows that the responses of the linear oscillator and 2-dof NES are not always consistent, and 2-dof NES can generate extra SMR than 1-dof NES. Finally, the vibration suppression effect of the proposed NES with nonlinear damping and combined stiffness is analyzed and verified by the energy spectrum, and it also shows that the 2-dof NES system demonstrates better performance.

scholarly journals Analysis of the Vibration Suppression of Double-Beam System via Nonlinear Switching Piezoelectric Network

Machines ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 115
Author(s):  
Fengling Zhang ◽  
Jiuzhou Liu ◽  
Jing Tian
Keyword(s):  
Electromechanical Coupling ◽  
Vibration Suppression ◽  
Harmonic Balance Method ◽  
Coupling Model ◽  
Circuit Board ◽  
Beam System ◽  
Double Beam ◽  
Calculation Results ◽  
Nonlinear Switching ◽  
Aero Engines

In this paper, a method to suppress the vibration of a double-beam system with nonlinear synchronized switch damping on the inductor via a network (SSDI-net) is proposed. Unlike the classical linear piezoelectric shunt damping, SSDI-net is a nonlinear piezoelectric damping. A double-beam system with SSDI-net was simplified to a lumped parameter electromechanical coupling model and analyzed by using the multi-harmonic balance method, at first with alternating frequency–time techniques (MHBM/AFT). Then, a new lower-power autonomous switching control circuit board was designed, based on SSD technique, and vibration control experiments using a double-beam system with an SSDI network are conducted, to verify the validity of the proposed analysis method and its calculation results. The nonlinear switching piezoelectric network proposed in this article can increase the voltage inversion factor. Furthermore, future applications of this switching piezoelectric network technology in the vibration suppression of bladed-disk structures in aero engines can reduce the number of switches by at least half and obtain almost the same damping effect.

LMI-based hybrid temporal-spatial differential control design for a class of Euler-Bernoulli beam system

2021 ◽  
pp. 095440622110036
Author(s):  
Jiaqi Zhong ◽  
Xiaolei Chen ◽  
Yupeng Yuan ◽  
Jiajia Tan
Keyword(s):  
Vibration Suppression ◽  
Direct Method ◽  
Recursive Algorithm ◽  
Linear Matrix ◽  
Bernoulli Beam ◽  
Hybrid Controller ◽  
Beam System ◽  
Active Vibration ◽  
Differential Control ◽  
Euler Bernoulli Beam

This paper addresses the problem of active vibration suppression for a class of Euler-Bernoulli beam system. The objective of this paper is to design a hybrid temporal-spatial differential controller, which is involved with the in-domain and boundary actuators, such that the closed-loop system is stable. The Lyapunov’s direct method is employed to derive the sufficient condition, which not only can guarantee the stabilization of system, but also can improve the spatial cooperation of actuators. In the framework of the linear matrix inequalities (LMIs) technology, the gain matrices of hybrid controller can obtained by developing a recursive algorithm. Finally, the effectiveness of the proposed methodology is demonstrated by applying a numerical simulation.

The effects of nonlinear energy sink and piezoelectric energy harvester on aeroelastic instability of an airfoil

2021 ◽  
pp. 107754632199358
Author(s):  
Ali Fasihi ◽  
Majid Shahgholi ◽  
Saeed Ghahremani
Keyword(s):  
Energy Harvester ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Dynamical Behavior ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Piezoelectric Energy ◽  
Energy Sink ◽  
Two Degree Of Freedom ◽  
Nonlinear Energy

The potential of absorbing and harvesting energy from a two-degree-of-freedom airfoil using an attachment of a nonlinear energy sink and a piezoelectric energy harvester is investigated. The equations of motion of the airfoil coupled with the attachment are solved using the harmonic balance method. Solutions obtained by this method are compared to the numerical ones of the pseudo-arclength continuation method. The effects of parameters of the integrated nonlinear energy sink-piezoelectric attachment, namely, the attachment location, nonlinear energy sink mass, nonlinear energy sink damping, and nonlinear energy sink stiffness on the dynamical behavior of the airfoil system are studied for both subcritical and supercritical Hopf bifurcation cases. Analyses demonstrate that absorbing vibration and harvesting energy are profoundly affected by the nonlinear energy sink parameters and the location of the attachment.

Nonlinear Normal Modes of a Continuous Cantilever Beam with Nonlinear Energy Sink Absorber

2013 ◽  
Vol 325-326 ◽  
pp. 214-217
Author(s):  
Yong Chen ◽  
Yi Xu
Keyword(s):  
Cantilever Beam ◽  
Vibration Suppression ◽  
Normal Modes ◽  
Nonlinear Energy Sink ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Energy Sink ◽  
Nonlinear Normal ◽  
Nonlinear Energy ◽  
Good Agreement

Using nonlinear energy sink absorber (NESA) is a good countermeasure for vibration suppression in wide board frequency region. The nonlinear normal modes (NNMs) are helpful in dynamics analysis for a NESA-attached system. Being a primary structure, a cantilever beam whose modal functions contain hyperbolic functions is surveyed, in case of being attached with NESA and subjected to a harmonic excitation. With the help of Galerkins method and Raushers method, the NNMs are obtained analytically. The comparison of analytical and numerical results indicates a good agreement, which confirms the existence of the nonlinear normal modes.

scholarly journals Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers

Micromachines ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 575 ◽  
Author(s):  
Aymen Jallouli ◽  
Najib Kacem ◽  
Joseph Lardies
Keyword(s):  
Differential Equations ◽  
Dynamic Behavior ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Ultrasonic Transducers ◽  
Initial Deflection ◽  
Geometric Imperfections ◽  
Resonance Frequencies

In order to investigate the effects of geometric imperfections on the static and dynamic behavior of capacitive micomachined ultrasonic transducers (CMUTs), the governing equations of motion of a circular microplate with initial defection have been derived using the von Kármán plate theory while taking into account the mechanical and electrostatic nonlinearities. The partial differential equations are discretized using the differential quadrature method (DQM) and the resulting coupled nonlinear ordinary differential equations (ODEs) are solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). It is shown that the initial deflection has an impact on the static behavior of the CMUT by increasing its pull-in voltage up to 45%. Moreover, the dynamic behavior is affected by the initial deflection, enabling an increase in the resonance frequencies and the bistability domain and leading to a change of the frequency response from softening to hardening. This model allows MEMS designers to predict the nonlinear behavior of imperfect CMUT and tune its bifurcation topology in order to enhance its performances in terms of bandwidth and generated acoustic power while driving the microplate up to 80% beyond its critical amplitude.

Theoretical and experimental studies of a novel nested oscillator with a high-damping characteristic

2020 ◽  
pp. 107754632094378
Author(s):  
Haiping Liu ◽  
Kaili Xiao ◽  
PengPeng Zhao ◽  
Dongmei Zhu
Keyword(s):  
Resonant Frequency ◽  
Vibration Suppression ◽  
Damping Ratio ◽  
Experimental Studies ◽  
Harmonic Balance Method ◽  
Design Parameters ◽  
Base Excitation ◽  
Oscillation System ◽  
Equivalent Damping ◽  
Vibration Transmissibility

Stiffness and damping of a structure usually show the opposite change so that the resonant frequency and the static load bearing capacity of a mechanical system often exhibit contradiction. To solve this dilemma, a novel high-damping oscillator which is constructed by a nested diamond structure with the purpose of enhancing the damping property is proposed in this study without reducing the overall systematic stiffness. The mathematical model and geometrical relationships are established at first. And then, the steady-state solutions under base excitation are derived by using the harmonic balance method and further verified by numerical simulation. In addition, the effects of some design parameters on the equivalent damping ratio for the high-damping oscillator are studied to reveal the nonlinear characteristic. Besides, the natural frequency of the nonlinear oscillator is also presented and investigated. By using the displacement transmissibility and comparing with the traditional linear isolator with the same overall stiffness, the vibration suppression performance of the high-damping oscillator is addressed. The obtained calculating results demonstrate that the vibration control performance of the high-damping oscillator outperforms the linear counterpart around resonant frequency. Moreover, the influences of systematic parameters of the high-damping oscillator for the base excitation case on the vibration transmissibility are also discussed, respectively. Finally, an experimental campaign is conducted on an in-house-built test rig to corroborate the accuracy of the analytical solutions of the high-damping oscillation system. The results discussed in this study provide a useful guideline, which can help to design this class of high-damping oscillation system.

Basic Optimization Methodology for the Design of Friction Damping in Blade Shrouds

2013 ◽  
Author(s):  
Michal Hajžman ◽  
Luděk Pešek ◽  
Jan Brůha ◽  
Vladimír Zeman ◽  
Drahomír Rychecký
Keyword(s):  
Vibration Suppression ◽  
Harmonic Balance Method ◽  
Rigid Bodies ◽  
Geometrical Parameters ◽  
Bending Vibration ◽  
Friction Forces ◽  
Normal Contact ◽  
Friction Element ◽  
Experimental Stand ◽  
Optimization Methodology

This paper is focused on the optimization of friction element parameters in blade shrouds for various types of excitation. In order to create and validate a proper modelling methodology an experimental stand and a numerical simulation of blades interaction by means of a friction element placed in the shrouds were prepared. Mathematical models are based on the finite element method combined with rigid bodies. The interaction of the friction element and blades is described by normal contact and tangential friction forces derived for particular geometrical parameters of the studied mechanical system. The models can be analyzed both in frequency domain (by the harmonic balance method) or in time domain (by the numerical integration). The results of the optimization of friction element parameters with respect to the bending vibration suppression are documented in the paper. Another contact modelling approach intended for more complex contact surfaces is based on the decomposition of a contact surface into a set of elementary areas and on the expression of contact and friction forces between these areas. All methodologies are implemented in the MATLAB system and the results for the chosen test cases are compared with the results obtained by a measurement or by the ANSYS software.

A Non-Traditional Variant Nonlinear Energy Sink: Transient Responses

2019 ◽  
Author(s):  
Youzuo Jin ◽  
Kefu Liu ◽  
Deli Li ◽  
Liuyang Xiong ◽  
Lihua Tang
Keyword(s):  
Energy Harvester ◽  
Vibration Suppression ◽  
System Modeling ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Transient Responses ◽  
Continuous Contact ◽  
Magnet Coil ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract In this paper, a non-traditional variant nonlinear energy sink (NES) is developed for simultaneous vibration suppression and energy harvesting in a broad frequency band. The non-traditional variant NES consists of a cantilever beam attached by a pair of magnets at its free end, a pair of the so-called continuous-contact blocks, and a pair of coils. The beam is placed between the continuous-contact blocks. The constraint of the continuous-contact blocks forces the beam to deflect nonlinearly. Each of the magnet-coil pairs forms an electromagnetic energy harvester. Different from a traditional way that attaches the coils to the primary mass, the developed setup has the coils fixed to the base. First, the developed apparatus is described. Subsequently, the system modeling and parameter identification are addressed. The performance of the apparatus under transient responses is examined by using computer simulation. The results show that the proposed apparatus behaves similarly as the NES with the following features: 1:1 resonance, targeted energy transfer, initial energy dependence, etc.

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