The spectral density of the nonlinear damping model: single DOF case

1990 ◽  
Vol 35 (12) ◽  
pp. 1320-1329 ◽  
Author(s):  
W. Zhang
Keyword(s):  
Spectral Density ◽  
Nonlinear Damping ◽  
Damping Model

Reduced-Order Nonlinear Damping Model: Formulation and Application to Postflutter Aeroelastic Behavior

AIAA Journal ◽  
2021 ◽  
pp. 1-11
Author(s):  
X. Q. Wang ◽  
Pengchao Song ◽  
Marc P. Mignolet ◽  
P. C. Chen
Keyword(s):  
Nonlinear Damping ◽  
Model Formulation ◽  
Reduced Order ◽  
Damping Model

Life Calculation of First Stage Compressor Blade of a Trainer Aircraft

2012 ◽  
Author(s):  
J. S. Rao ◽  
Narayan Rangarajan ◽  
Rejin Ratnakar ◽  
R. Rzadkowski ◽  
M. Soliński ◽  
...  
Keyword(s):  
Air Force ◽  
Critical Speed ◽  
Iterative Solution ◽  
Nonlinear Damping ◽  
Equivalent Viscous Damping ◽  
Campbell Diagram ◽  
Compressor Rotor ◽  
Institute Of Technology ◽  
The Given ◽  
Damping Model

This paper is concerned with life estimation of a compressor rotor blade of an engine at the Air Force Institute of Technology in Warsaw used in a trainer aircraft. A bird strike is simulated by two or three blade passage blocks in the incoming flow and the pressure field is obtained from a CFD code. For the blade the Campbell diagram is prepared and the critical speeds are identified. The alternating pressures corresponding to the critical speed are obtained from an FFT. A nonlinear damping model is estimated using Lazan’s hysteresis law; the equivalent viscous damping model is determined as a function of reference strain amplitude in the given mode of vibration at the rotational speed. An iterative solution is developed with the nonlinear damping model and the resonant stress and location is determined. The life at this critical speed is determined using a cumulative damage criterion.

A Practical Mathematical Model for Nonlinear Hysteresis of Metal Rubber Isolator

2011 ◽  
Vol 105-107 ◽  
pp. 20-23 ◽  
Author(s):  
Yan Guo Zhou ◽  
Wen Zhong Qu ◽  
Li Xiao
Keyword(s):  
Practical Method ◽  
Nonlinear Damping ◽  
Mathematical Form ◽  
Nonlinear Hysteresis ◽  
Damping Behavior ◽  
Satisfactory Precision ◽  
Practical Engineering ◽  
Metal Rubber ◽  
Damping Model ◽  
Rubber Isolator

The hysteresis dynamic behavior of metal rubber mathematically modeled with a practical method is studied, and the method of parameter separated identification is presented with details. Parameters of the model are identified with the test data of metal rubber, from which the theoretical loops are reconstructed, and the mechanism of the nonlinear damping behavior of the metal rubber is investigated. The theoretical loops and the experimental one are close to each other with satisfactory accuracy. The result shows that with the simple mathematical form and the satisfactory precision, the mixed damping model can be used effectively in practical engineering. This study provides a practical and effective method in modeling and the parameter identification of the metal rubber isolator.

scholarly journals Modeling and Simulation of Linear and Nonlinear MEMS Scale Electromagnetic Energy Harvesters for Random Vibration Environments

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Farid Khan ◽  
Boris Stoeber ◽  
Farrokh Sassani
Keyword(s):  
Resonant Frequency ◽  
Spectral Density ◽  
Output Voltage ◽  
Random Vibration ◽  
Nonlinear Damping ◽  
Electromagnetic Energy ◽  
Mean Square ◽  
Load Voltage ◽  
Energy Harvesters ◽  
Transformation Factor

The simulation results for electromagnetic energy harvesters (EMEHs) under broad band stationary Gaussian random excitations indicate the importance of both a high transformation factor and a high mechanical quality factor to achieve favourable mean power, mean square load voltage, and output spectral density. The optimum load is different for random vibrations and for sinusoidal vibration. Reducing the total damping ratio under band-limited random excitation yields a higher mean square load voltage. Reduced bandwidth resulting from decreased mechanical damping can be compensated by increasing the electrical damping (transformation factor) leading to a higher mean square load voltage and power. Nonlinear EMEHs with a Duffing spring and with linear plus cubic damping are modeled using the method of statistical linearization. These nonlinear EMEHs exhibit approximately linear behaviour under low levels of broadband stationary Gaussian random vibration; however, at higher levels of such excitation the central (resonant) frequency of the spectral density of the output voltage shifts due to the increased nonlinear stiffness and the bandwidth broadens slightly. Nonlinear EMEHs exhibit lower maximum output voltage and central frequency of the spectral density with nonlinear damping compared to linear damping. Stronger nonlinear damping yields broader bandwidths at stable resonant frequency.

Virtual Spring-Damping System for Flow Induced Motion Experiments

2015 ◽  
Author(s):  
Hai Sun ◽  
Marinos P. Bernitsas ◽  
Eun Soo Kim ◽  
Michael M. Bernitsas
Keyword(s):  
Hydrodynamic Force ◽  
Water Channel ◽  
Nonlinear Damping ◽  
Flow Speed ◽  
Spring Constant ◽  
Optical Encoder ◽  
Induced Motion ◽  
Real Linear ◽  
The University ◽  
Damping Model

The research objective of the Marine Renewable Energy Lab (MRELab) is to design multi-cylinder VIVACE Converters and optimize their power output for a broad range of velocities. For a given geometric and mass configuration of a school of cylinders, each point on the power envelope, at a given flow-speed, is a function of the spring constant and damping. Conducting tests with real springs and dampers requires lengthy preparation for each set of experiments. A more efficient way to conduct experiments faster and accurately is developed based on a controller embedded virtual spring-damping system (Vck) that des not include the hydrodynamic force in the closed loop. Each oscillator consists of one Vck, one interchangeable cylinder moving on submerged roller blocks and driven by the fluid flow, and connected to the controller through belts and pulleys. It is designed to achieve the desired static/dynamic friction through the Vck. An Arduino embedded board controls a servomotor with an optical encoder, which enables real-time position/speed measurement. A system identification (SI) methodology is developed making possible to identify the damping model of any oscillator, which is typically much more complicated than the classical linear viscous model. Upon completion of the SI process for an oscillator, the actual nonlinear damping model is subtracted using the controller and leaving the system with zero damping. Then, a mathematically linear damping model is added, thus, resulting in a system with real linear viscous damping. This process enables changing the spring constant and harnessing damping through the controller instantly. Experiments are then conducted with both real spring dampers and Vck to validate the process. All FIM experiments are conducted in the Low Turbulence Free Surface Water Channel of the University of Michigan at 16,000<Re<140,000. The main findings are: (a) The Vck system was developed keeping the hydrodynamic force out of the control loop and, thus, not biasing the FIM. (b) The agreement between real and virtual springs and dampers was excellent in FIM measurements over the entire range of spring constants and velocities tested. (c) The lag due to the controller was minimal and significantly reduced compared to the first generation of Vck built in the MRELab.

A New Damping Model for Nonlinear Stiffness Systems With Variable Preload Displacements and Constant Amplitude Decay Ratios

1994 ◽  
Vol 116 (1) ◽  
pp. 257-263 ◽  
Author(s):  
T. Xu ◽  
G. G. Lowen
Keyword(s):  
Energy Loss ◽  
Mathematical Description ◽  
Nonlinear Damping ◽  
Damping Coefficient ◽  
Nonlinear Stiffness ◽  
Constant Amplitude ◽  
Damping Force ◽  
Damping Model ◽  
Good Agreement

This study of the behavior of nonlinear stiffness systems with variable preload displacements and constant amplitude decay ratios showed that the energy loss per cycle is dependent on these preload displacements. By introducing a nonlinear damping force, which is a function of both displacement and velocity, the associated work per cycle can be made approximately the same function of the preload displacement as is the case for the energy loss. In this manner, it becomes possible to make the resulting damping coefficient essentially independent of the preload displacement. This new damping model was incorporated into the mathematical description of an over-running sprag clutch. Confirming experimentation showed very good agreement with computed results.

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