scholarly journals Complex response analysis of a non-smooth oscillator under harmonic and random excitations

2021 ◽  
Vol 42 (5) ◽  
pp. 641-648
Author(s):  
Shichao Ma ◽  
Xin Ning ◽  
Liang Wang ◽  
Wantao Jia ◽  
Wei Xu
Keyword(s):  
Excitation Frequency ◽  
System Stability ◽  
Response Analysis ◽  
External Excitation ◽  
Stochastic Response ◽  
Impact Oscillator ◽  
Nonlinear Parameters ◽  
Bifurcation Phenomena ◽  
Mc Simulation ◽  
Smooth System

AbstractIt is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces, making it challenging to carry out the research of this category of complex systems with non-smooth characteristics. To address this problem, by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation, a modified conducting process has proposed. Taking the multiple nonlinear parameters, the non-smooth parameters, and the external excitation frequency into consideration, the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed. It can be found that the system parameters can make the system stability topology change. The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo (MC) simulation. Consequently, the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.

scholarly journals Stereo-DIC Measurements of a Vibrating Bladed Disk: In-Depth Analysis of Full-Field Deformed Shapes

2021 ◽  
Vol 11 (12) ◽  
pp. 5430
Author(s):  
Paolo Neri ◽  
Alessandro Paoli ◽  
Ciro Santus
Keyword(s):  
Single Point ◽  
Excitation Frequency ◽  
Phase Variation ◽  
Operating Conditions ◽  
Image Correlation ◽  
Response Analysis ◽  
Full Field ◽  
Low Speed ◽  
Bladed Disk ◽  
Depth Analysis

Vibration measurements of turbomachinery components are of utmost importance to characterize the dynamic behavior of rotating machines, thus preventing undesired operating conditions. Local techniques such as strain gauges or laser Doppler vibrometers are usually adopted to collect vibration data. However, these approaches provide single-point and generally 1D measurements. The present work proposes an optical technique, which uses two low-speed cameras, a multimedia projector, and three-dimensional digital image correlation (3D-DIC) to provide full-field measurements of a bladed disk undergoing harmonic response analysis (i.e., pure sinusoidal excitation) in the kHz range. The proposed approach exploits a downsampling strategy to overcome the limitations introduced by low-speed cameras. The developed experimental setup was used to measure the response of a bladed disk subjected to an excitation frequency above 6 kHz, providing a deep insight in the deformed shapes, in terms of amplitude and phase distributions, which could not be feasible with single-point sensors. Results demonstrated the system’s effectiveness in measuring amplitudes of few microns, also evidencing blade mistuning effects. A deeper insight into the deformed shape analysis was provided by considering the phase maps on the entire blisk geometry, and phase variation lines were observed on the blades for high excitation frequency.

scholarly journals Analysis of moored ship oscillations in waves

2020 ◽  
Author(s):  
Д.П. Ковалев ◽  
П.Д. Ковалев ◽  
А.С. Борисов
Keyword(s):  
Dynamic System ◽  
Sea Level ◽  
Order Differential Equation ◽  
External Excitation ◽  
Impact Oscillator ◽  
Mooring Lines ◽  
Sea Level Fluctuations ◽  
Port Area ◽  
Sea Level Fluctuation ◽  
The Impact

В работе рассмотрены особенности колебаний пришвартованного судна для основных портов Сахалинской области, поскольку качка судна у причала может представлять опасность и приводить к повреждению судна или швартовых линий. По данным натурных измерений морского волнения в портовых бухтах рассчитаны спектры колебаний уровня и определены периоды существующих в них волн для диапазона периодов от 2 с до 30 минут. Произведен расчет периодов собственных колебаний (качки) двух типов судов, преимущественно швартующихся в портах. С учетом полученных результатов выполнено моделирование движения судов при волнении как динамической с системы внешним возбуждающим воздействием на основе дифференциального уравнения второго порядка. Показано влияние коэффициента вязкого демпфирования и жесткости швартовых на реакцию динамической системы без удара о причал и для режима ударного осциллятора. Установлено, что в случае прихода в район порта Корсаков длинноволновой зыби движения судна могут переходить в хаотические. The paper considers the peculiarities of moored vessel oscillations for the main ports of the Sakhalin region, since the pitching of the vessel at the berth can be dangerous and lead to damages of the vessel or mooring lines. Spectra of sea level fluctuations and periods of waves in port bays were calculated using sea level fluctuation measurements obtained in the range from 2 seconds to 30 minutes. Calculations of resonance periods (pitching) of two types of vessels mainly moored in ports were done. Taking into consideration these results the simulation of the vessel movement in waves as a dynamic system with an external excitation was performed on the base of second-order differential equation. The influence of viscous damping coefficient and mooring stiffness on the response of the dynamic system is shown for two cases: for system without impact and for the impact oscillator mode. It is established that in the event of a long-wave swell coming to the Korsakov port area, the vessels movements may become chaotic.

Vibration Analysis of Nonlinear Isolator’s Characteristics by ADAMS

2012 ◽  
Vol 152-154 ◽  
pp. 1077-1081 ◽  
Author(s):  
Zhao Qi He ◽  
Yu Chao Song ◽  
Hong Liang Yu
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Isolation ◽  
Excitation Frequency ◽  
Vibration Isolator ◽  
Vibration System ◽  
Linear Vibration ◽  
External Excitation ◽  
Mass Model ◽  
Adams Software ◽  
Isolation Systems

A nonlinear spring-mass model is established to study the dynamic characteristics of nonlinear vibration isolator. By use of ADAMS software, the influence of stiffness, foundation displacement excitation and frequency of external excitation on the nonlinear vibration isolation systems are analyzed. Results indicate that the linear vibration system needs 4s to achieve stability, but the nonlinear vibration system only needs 0.1s. The response value increases with the increase of excitation frequency, the response pick value increases by 61.58% and 102.35% and each corresponding stable value increases by 159.35% and 309.87%.

A Study on the Leakage and Rotordynamic Performance of a Long Labyrinth Seal Under Mainly Air Conditions

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs
Keyword(s):  
Silicone Oil ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Labyrinth Seal ◽  
System Stability ◽  
Test Fluid ◽  
Liquid Volume ◽  
Frequency Dependent ◽  
Frequency Independent ◽  
The Impact

Abstract This paper investigates the impact of liquid presence in air on the leakage and rotordynamic coefficients of a long (length-to-diameter ratio L/D = 0.747) teeth-on-stator labyrinth seal. The test fluid is a mixture of air and silicone oil (PSF-5cSt). Tests are carried out at inlet pressure Pi = 62.1 bars, three pressure ratios from 0.21 to 0.46, three speeds from 10 to 20 krpm, and six inlet liquid volume fractions (LVFs) from 0% to 15%. Complex dynamic-stiffness coefficients Hij are measured. The real parts of Hij are too frequency dependent to be fitted by frequency-independent stiffness and virtual-mass coefficients. Therefore, this paper presents frequency-dependent direct stiffness KΩ and cross-coupled stiffness kΩ. The imaginary parts of Hij produce frequency-independent direct damping C. Test results show that, under both pure- and mainly air conditions, the leakage mass flowrate m˙ of the test seal steadily increases as inlet LVF increases. KΩ is negative under all test conditions, and the magnitude of KΩ increases as inlet LVF increases, leading to a larger negative centering force on the associated compressor rotor. Under pure-air conditions, kΩ is a small negative value. Injecting oil into the air increases kΩ slightly and make the magnitude of kΩ closer to zero. Under mainly air conditions, increasing inlet LVF from 2% to 15% has little impact on kΩ. C normally increases as inlet LVF increases. The value of the effective damping Ceff = C − kΩ/Ω near 0.5ω is of significant interest to the system stability since an unstable centrifugal compressor may precess at approximately 0.5ω. Ω denotes the excitation frequency. The oil presence in the air has little impact on the value of Ceff near 0.5ω. Also, the liquid presence does not change the insensitiveness of m˙, KΩ, kΩ, C, and Ceff to change in ω; i.e., under both pure- and mainly air conditions, changes in ω has little impact on m˙, KΩ, kΩ, C, and Ceff.

Stochastic Response Analysis and Reliability-Based Design Optimization of Nonlinear Electromechanical Energy Harvesters with Fractional Derivative Elements

2020 ◽  
Author(s):  
Ioannis Petromichelakis ◽  
Apostolos F. Psaros ◽  
Ioannis A. Kougioumtzoglou
Keyword(s):  
Fractional Derivative ◽  
Design Optimization ◽  
Response Analysis ◽  
Reliability Based Design Optimization ◽  
Stochastic Response ◽  
Energy Harvesters ◽  
Reliability Based Design ◽  
Singular Diffusion ◽  
Electromechanical Energy ◽  
Definition Of

Abstract A methodology based on the Wiener path integral technique (WPI) is developed for stochastic response determination and reliability-based design optimization of a class of nonlinear electromechanical energy harvesters endowed with fractional derivative elements. In this regard, first, the WPI technique is appropriately adapted and enhanced to account both for the singular diffusion matrix and for the fractional derivative modeling of the capacitance in the coupled electromechanical governing equations. Next, a reliability-based design optimization problem is formulated and solved, in conjunction with the WPI technique, for determining the optimal parameters of the harvester. It is noted that the herein proposed definition of the failure probability constraint is particularly suitable for harvester configurations subject to space limitations. Several numerical examples are included, while comparisons with pertinent Monte Carlo simulation data demonstrate the satisfactory performance of the methodology.

Experimental Forced Response Analysis of Two-Degree-of-Freedom Piecewise-Linear Systems With a Gap

2020 ◽  
Author(s):  
Akira Saito ◽  
Junta Umemoto ◽  
Kohei Noguchi ◽  
Meng-Hsuan Tien ◽  
Kiran D’Souza
Keyword(s):  
Piecewise Linear ◽  
Excitation Frequency ◽  
Forced Response ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Phase Portraits ◽  
Response Analysis ◽  
Experimental Setup ◽  
The Masses ◽  
Two Degree Of Freedom

Abstract In this paper, an experimental forced response analysis for a two degree of freedom piecewise-linear oscillator is discussed. First, a mathematical model of the piecewise linear oscillator is presented. Second, the experimental setup developed for the forced response study is presented. The experimental setup is capable of investigating a two degree of freedom piecewise linear oscillator model. The piecewise linearity is achieved by attaching mechanical stops between two masses that move along common shafts. Forced response tests have been conducted, and the results are presented. Discussion of characteristics of the oscillators are provided based on frequency response, spectrogram, time histories, phase portraits, and Poincaré sections. Period doubling bifurcation has been observed when the excitation frequency changes from a frequency with multiple contacts between the masses to a frequency with single contact between the masses occurs.

Numerical and Experimental Research on Periodic Solution Stability of Inclined Rotor Journal Bearing System

2011 ◽  
Author(s):  
Dashuai Qian ◽  
Zhansheng Liu ◽  
Jiajia Yan ◽  
Liquan Sun ◽  
Yongliang Wang
Keyword(s):  
Periodic Solution ◽  
Journal Bearing ◽  
Rotor System ◽  
Experimental Results ◽  
System Stability ◽  
Response Analysis ◽  
Solution Stability ◽  
Special Cases ◽  
Rotor Journal ◽  
Bearing System

Rotor bearing systems on ships usually work in inclined states when ships are swaying in wave and wind. The inclined status will affect the lubricant condition of journal bearing and bring about changes of the dynamic characteristics of the rotor system. To study the periodic solution stability of inclined rotor journal bearing system, Capone’s short bearing model is employed to describe the journal bearing support properties. Considering the inclination induced change of bearing radial load, the dynamic equation of inclined rotor system is established by using finite element method. The periodic solution stability is discussed based on bifurcation and response analysis. With the increase of rotating speed, instability of period-1 motion happens and oil whirl occurs. The motion then develops into a kind of quasi-periodic motion. Two special cases of inclined rotor system, the horizontal and the vertical cases, are compared and discussed. Both of the numerical and the experimental results show that the periodic solution unstable threshold decreases with the increase of rotor inclination angle. At last, some experimental results about influences of experiments conditions on rotor system stability are given.

A Study for Rotordynamic and Leakage Characteristics of a Long-Honeycomb Seal With Two-Phase, Mainly Air Mixtures

2019 ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs
Keyword(s):  
Volume Fraction ◽  
Silicone Oil ◽  
Pressure Ratio ◽  
Excitation Frequency ◽  
System Stability ◽  
Test Fluid ◽  
Liquid Volume ◽  
Liquid Volume Fraction ◽  
Honeycomb Seal ◽  
The Impact

Abstract This paper investigates the impact of the oil (silicone oil PSF-5cSt) presence in the air on the leakage and rotordynamic characteristics of a long-honeycomb seal with length-to-diameter ratio L/D = 0.748 and diameter D = 114.656 mm. Tests are carried out with inlet pressure Pi = 70.7 bars, pressure ratio PR = 0.35 and 0.25, inlet liquid volume fraction LVF = 0%, 3.5%, and 7%, and shaft speed ω = 10, 15, and 20 krpm. During the tests, the seal is centered. Test results show that leakage mass flow rate ṁ increases (as expected) as inlet LVF increases. Increasing inlet LVF makes direct stiffness K increase more rapidly with increasing excitation frequency Ω. Increasing inlet LVF has a negligible effect on K at low Ω values, but increases K at high Ω values. The value of effective damping Ceff at about 0.5ω is an indicator to the system stability since an unstable centrifugal compressor rotor can precess at about 0.5ω. Increasing inlet LVF increases the value of Ceff at about 0.5ω, reducing the possibility of sub-synchronous vibrations SSVs at about 0.5ω. San Andrés’s model is used to produce predictions. The model assumes that the test fluid in the seal clearance is an isothermal-homogenous mixture. The model adequately predicts ṁ, K, and the value of Ceff at about 0.5ω.

scholarly journals Stochastic Response of Tension Leg Platform to Wave and Current Forces

1989 ◽  
Vol 111 (4) ◽  
pp. 221-230 ◽  
Author(s):  
A. Ertas ◽  
J.-H. Lee
Keyword(s):  
Constant Current ◽  
Response Analysis ◽  
Stochastic Dynamic ◽  
Superposition Method ◽  
Random Waves ◽  
Stochastic Response ◽  
Tension Leg Platform ◽  
Single Degree Of Freedom ◽  
Simulation Techniques ◽  
Wave Induced

The linear analysis in the frequency domain is presented for the surge motion of a tension leg platform (TLP) in the case of random waves only and random waves with constant current. A single-degree-of-freedom model of a TLP is employed for response. The superposition method, one of the simulation techniques, is applied to random sea wave, and the response analysis of TLP in time is developed with wave velocity and wave acceleration simulations. Wave-induced forces are calculated using the modified Morison equation, which takes into account relative motion. Computational methods for both analyses are developed, and the results of stochastic, dynamic response of the TLP, with and without the presence of current, are presented and compared.

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