scholarly journals Dynamics of a Upright Pole Coupled with Nonlinear Hysteretic Isolators under Harmonic Base Excitation

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yongfeng Cheng ◽  
Hulun Guo ◽  
Zhubing Zhu ◽  
Xiaochao Su ◽  
Yushu Chen
Keyword(s):  
Frequency Response ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Resonant Peak ◽  
Deformation Model ◽  
Base Excitation ◽  
Engineering Structures ◽  
System Parameters ◽  
Resonant Case ◽  
Hysteretic Nonlinearity

Leady isolator shows hysteretic nonlinearity. The isolation efficiency of leady isolator is an important problem in many engineering structures. In this paper, vibrations of a ceramic upright pole coupled with four leady isolators under harmonic base excitation are studied. A hysteretic force-deformation model of leady isolator is derived from experimental results. With this model, the vibration of the pole in rotation is studied. The frequency response is obtained analytically by employing harmonic balance method. The analytical results are agreed well with numerical results. The vibration of the pole is decreased greatly by leady isolator, especially near resonant case. The influences of system parameters on vibration response and resonant peak are discussed in detail.

Nonlinear Frequency Response Analysis of a Multistage Clutch Damper With Multiple Nonlinearities

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Jong-Yun Yoon ◽  
Hwan-Sik Yoon
Keyword(s):  
Frequency Response ◽  
Harmonic Balance ◽  
Piecewise Linear ◽  
Dynamic Performance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Response Analysis ◽  
Nonlinear Frequency ◽  
System Equation ◽  
Nonlinear Frequency Response

This paper presents the nonlinear frequency response of a multistage clutch damper system in the framework of the harmonic balance method. For the numerical analysis, a multistage clutch damper with multiple nonlinearities is modeled as a single degree-of-freedom torsional system subjected to sinusoidal excitations. The nonlinearities include piecewise-linear stiffness, hysteresis, and preload all with asymmetric transition angles. Then, the nonlinear frequency response of the system is numerically obtained by applying the Newton–Raphson method to a system equation formulated by using the harmonic balance method. The resulting nonlinear frequency response is then compared with that obtained by direct numerical simulation of the system in the time domain. Using the simulation results, the stability characteristics and existence of quasi-harmonic response of the system are investigated. Also, the effect of stiffness values on the dynamic performance of the system is examined.

Frequency Response Characteristics of a Revolute Impact Pair

1993 ◽  
Author(s):  
Y. Wang
Keyword(s):  
Frequency Response ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Analytical Techniques ◽  
Single Frequency ◽  
Nonlinear Frequency ◽  
Response Characteristics ◽  
State Response ◽  
Existence And Stability ◽  
Nonlinear Frequency Response

Abstract Clearances in mechanical joints have deteriorating effects on the dynamic behavior of a machine in increasing noise and vibration and reducing the performance. In order to properly characterize these effects and to develop analytical techniques for machine design, it is necessary to investigate the dynamics associated with basic models of impacting systems. In this paper, we develop a method of harmonic balance to study a revolute impact pair. We focus on the characteristics of nonlinear frequency response of the system for a single frequency excitation. These characteristics include multiply-valued steady state response, multiple jump resonances, and existence and stability of these solutions. The effectiveness of the harmonic balance method combined with the Fast Fourier Transform technique is shown through numerical examples.

Vibration Analysis of a Shape Memory Oscillator by Harmonic Balance Method Verified Numerically

2019 ◽  
Vol 29 (03) ◽  
pp. 1930007 ◽  
Author(s):  
Rafal Rusinek ◽  
Joanna Rekas ◽  
Krzysztof Kecik
Keyword(s):  
Shape Memory ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
System Parameters ◽  
Irregular Motion

This paper focuses on periodic solutions for a one-degree-of-freedom oscillator with a spring made of shape memory alloy (SMA). However, when periodic solutions are unstable, irregular motion is identified numerically. The shape memory spring is described by a polynomial characteristic in this model. The harmonic balance method (HBM) is employed to find periodic solutions near the primary resonance. The solutions are confronted with results obtained by the multiple time scales method and numerical simulations. Finally, the effect of system parameters and temperature on the system dynamics is discussed.

Nonlinear dynamics and parametric study of snap through electromagnetic vibration energy harvester using multi-term harmonic balance method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Devarajan Kaliyannan
Keyword(s):  
Analytical Method ◽  
Harmonic Balance ◽  
Energy Harvester ◽  
Harmonic Balance Method ◽  
Electromagnetic Energy ◽  
Balance Method ◽  
Vibration Energy ◽  
Vibration Energy Harvester ◽  
System Parameters ◽  
Electromagnetic Vibration

Abstract Vibration energy harvester (VEH) has proven to be a favorable potential technique to supply continuous energy from ambient vibrations and its performance is greatly influenced by the design of potential structures. A snap-through mechanism is used in an electromagnetic energy harvester to improve its effectiveness. It mainly comprises of three springs that are configured so that the potential energy of the system has two stable equilibrium points. In this work, a harmonically base excited snap-through electromagnetic vibration energy harvester is investigated by analytical and semi-analytical method. The approximate analytical outcomes are qualitatively and quantitatively supported by semi-analytical method using multi-term harmonic balance method (MHBM).The bifurcation diagram of response current shows that snap-through electromagnetic vibration energy harvesters exhibits periodic intrawell, interwell and chaotic motion when the system parameters are varied. The influence of system parameters on the response of snap-through electromagnetic vibration energy harvester are examined. Nonlinearity produced by the snap-through oscillator improves energy harvesting so that the snap-through electromagnetic energy harvester can outperform the linear energy harvester in the similar size under harmonic excitation. A fitness function was formulated and optimization of the selected parameters was done using genetic algorithm. The parametric optimization leads to a considerable improvement in the harvested current from the system.

Relationship between harmonic balance method and non-linear output frequency response function approach

2007 ◽  
Vol 221 (12) ◽  
pp. 1533-1543 ◽  
Author(s):  
Z K Peng ◽  
Z Q Lang
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Harmonic Balance ◽  
Frequency Response Function ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Output Frequency ◽  
Non Linear ◽  
Harmonic Components ◽  
The Relationship

The current paper is concerned with the investigation of the relationship between the harmonic balance method (HBM) and the non-linear output frequency response function (NOFRF) approach in the analysis of non-linear systems. Both are applied to the Duffing's oscillator to demonstrate their relationships. The results reveal that, if the Volterra series representation of a non-linear system is convergent, the harmonic components calculated by the NOFRFs are a solution of the HBM. Moreover, the simulation studies show that, in the convergent cases, the NOFRF method can give more accurate results for the higher-harmonic components than the HBM. The relationship investigated in the current study between the two methods should help researchers and engineers to understand the HBM and the NOFRF methods.

Nonlinear System Identification of a MEMS Dual-Backplate Capacitance Microphone by Harmonic Balance Method

2005 ◽  
Author(s):  
Jian Liu ◽  
David T. Martin ◽  
Karthik Kadirvel ◽  
Toshikazu Nishida ◽  
Louis N. Cattafesta ◽  
...  
Keyword(s):  
Steady State ◽  
Governing Equation ◽  
Harmonic Balance ◽  
Nonlinear System Identification ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Algebraic Equations ◽  
Nonlinear Identification ◽  
System Parameters ◽  
Mems Microphone

This paper presents the nonlinear identification of system parameters for a capacitive dual-backplate MEMS microphone. First, the microphone is modeled by a single-degree-of-freedom (SDOF) second order differential equation with electrostatic and cubic mechanical nonlinearities. A harmonic balance nonlinear identification approach is then applied to the governing equation to obtain a set of algebraic equations that relate the unknown system parameters to the steady-state response of the microphone under the harmonic excitation. The microphone is experimentally characterized and a nonlinear least-squares technique is implemented to identify the system parameters from experimental data. The experimentally extracted bandwidth of the microphone is over 218 kHz. Finally, numerical simulations of the governing equation are performed, using the identified system parameters, to validate the accuracy of the approximate solution. The differences between the properties of the integrated measured center velocity and simulated center displacement responses in the steady state are less than 1%.

scholarly journals Bifurcation Analysis of a Spacecraft Structure Using the Harmonic Balance Method

2015 ◽  
Author(s):  
T. Detroux ◽  
L. Renson ◽  
L. Masset ◽  
J. P. Noël ◽  
G. Kerschen
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Models ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
System Parameters ◽  
The Past ◽  
Classical Formulation ◽  
Detection And Tracking ◽  
Numerical Tool ◽  
Quasiperiodic Oscillations

The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. The present paper proposes to extend the method to the detection and tracking of bifurcations in the codimension-2 system parameters space. To validate the methodology, the forced response of a real spacecraft is examined. The paper first provides some numerical evidence of the presence of quasiperiodic oscillations and isolated solutions. It then demonstrates how the tracking of Neimark-Sacker and fold bifurcations can help get a deeper understanding of these attractors.

Harmonic Balance Analysis for the Oscillations of Magnetic Levitation

2014 ◽  
Vol 672-674 ◽  
pp. 1554-1557
Author(s):  
Zu Yao Wang
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Frequency Response ◽  
Harmonic Balance ◽  
Magnetic Levitation ◽  
Harmonic Balance Method ◽  
Weakly Nonlinear ◽  
Amplitude Frequency Response ◽  
Strongly Nonlinear System ◽  
Balance Analysis

This paper investigates a design and analysis of a novel energy harvester that uses magnetic levitation to produce an oscillator with a tunable resonance. The governing equation of the system which could be derived based on the Newton’s second law is reduced to the form of a Duffing’s equation. The system steady-state amplitude frequency response relationship is analyzed by harmonic balance and numerical simulation, respectively. In the weakly nonlinear system, the curve of amplitude frequency response using harmonic balance method accords with the curve using numerical simulation;and in the strongly nonlinear system, the curve using harmonic balance basically accords with the curve using numerical simulation as well.

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