Determination of Response Statistics of Single Degree of Nonlinear Random Structure with Nonlinear Damping Characteristic and Nonlinear Elastic Characteristic

2021 ◽  
pp. 53-61
Author(s):  
Petre Stan ◽  
Marinica Stan
Keyword(s):  
Elastic Characteristic ◽  
Nonlinear Damping ◽  
Random Structure ◽  
Single Degree ◽  
Nonlinear Elastic

A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Bin Tang ◽  
M. J. Brennan
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Dependent Term ◽  
Quadratic Damping

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration.

The Measurement of Nonlinear Damping in Single-Degree-of-Freedom Systems

1991 ◽  
Vol 113 (1) ◽  
pp. 132-140 ◽  
Author(s):  
H. J. Rice ◽  
J. A. Fitzpatrick
Keyword(s):  
Nonlinear Distortion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Crucial Importance ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Wide Range ◽  
Impulse Excitation ◽  
Excitation Techniques ◽  
Quadratic Damping

The measurement and correct modelling of damping is of crucial importance in the prediction of the dynamical performance of systems for a wide range of engineering applications. In most cases, however, the experimental methods used to measure damping coefficients are extremely basic and, in general, poorly reported. This paper shows that damping is a deceptive parameter which is prone to subtle nonlinear distortion which often appears to satisfy general linear criteria. An efficient experimental method which provides for the measurement of both the linear and nonlinear damping for a single-degree-of-freedom system is proposed. The results from a numerical simulation study of a model with “drag” type quadratic damping are shown to give reliable estimates of parameters of the system when both random and impulse excitation techniques are used.

Primary Resonance of a Vehicle Suspension System With Nonlinear Stiffness and Nonlinear Damping

2006 ◽  
Author(s):  
Shaohua Li ◽  
Shaopu Yang
Keyword(s):  
Primary Resonance ◽  
Singularity Theory ◽  
Nonlinear Damping ◽  
Suspension System ◽  
Vehicle Suspension ◽  
Model Parameters ◽  
Nonlinear Stiffness ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Vehicle Suspension System

In this work, primary resonance of a single-degree-of-freedom (SDOF) vehicle suspension system with nonlinear stiffness and nonlinear damping under multi-frequency excitations is investigated. The primary resonance equation is obtained by average method, and then the system’s bifurcation behaviors are studied by singularity theory. In addition, the effect of changing physical model parameters on the system’s primary resonance is studied.

Exact determination of critical damping in multiple exponential kernel-based viscoelastic single-degree-of-freedom systems

2019 ◽  
Vol 24 (12) ◽  
pp. 3843-3861 ◽  
Author(s):  
Mario Lázaro
Keyword(s):  
Past History ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Critical Curves ◽  
History Of ◽  
Definition Of ◽  
Analytical Expressions ◽  
Critical Damping

In this paper, exact closed forms of critical damping manifolds for multiple-kernel-based nonviscous single-degree-of-freedom oscillators are derived. The dissipative forces are assumed to depend on the past history of the velocity response via hereditary exponential kernels. The damping model depends on several parameters, considered variables in the context of this paper. Those parameter combinations which establish thresholds between induced overdamped and underdamped motion are called critical damping manifolds. If such manifolds are represented on a coordinate plane of two damping parameters, then they are named critical curves, so that overdamped regions are bounded by them. Analytical expressions of critical curves are deduced in parametric form, considering certain local nondimensional parameters based on the Laplace variable in the frequency domain. The definition of the new parameter (called the critical parameter) is supported by several theoretical results. The proposed expressions are validated through numerical examples showing perfect fitting of the determined critical curves and overdamped regions.

Copolymerization of two bromine containing methacrylate monomers with methylmethacrylate. Determination of reactivity ratios by in situ quantitative 1H NMR monitoring

e-Polymers ◽  
2007 ◽  
Vol 7 (1) ◽  
Author(s):  
Ichim Ionut Cameliu ◽  
Marius Ciprian Rusu ◽  
Mihai Rusu ◽  
Popa Marcel ◽  
Christelle Delaite ◽  
...  
Keyword(s):  
Side Chain ◽  
Random Structure ◽  
Reactivity Ratios ◽  
Medical Implants ◽  
Propyl Methacrylate ◽  
H Nmr ◽  
Methacrylate Monomers ◽  
Methacrylic Monomers

AbstractAn important method used to make medical implants radiologically visible is based on introduction of radiopaque bromine or iodine containing methacrylic monomers. Thus, 2-(2-bromopropionyloxy) propyl methacrylate (BPPM) and 2-(2-bromoisobutyryloxy) propyl methacrylate (BIPM) were synthesized with the aim to use them as radiopaque agents. The free radical initiated copolymerization of BPPM and BIPM with methyl methacrylate (MMA) were performed directly in a thermostatic cell of the NMR spectrometer. The copolymer compositions obtained from 1H NMR spectra led to the determination of the reactivity ratios (rMMA = 1.08 ± 0.12; rBPPM = 1.01 ± 0.13 and rMMA = 0.95 ± 0.09; rBIPM = 0.95 ± 0.1). The reactivity ratios of these two monomers is similar to that of MMA suggesting that the length of the bromine containing monomers side chain does not affect significantly the reactivity of the methacrylic double bond. From the results we conclude the copolymers to have random structure.

Application of the Random Melnikov Method for Single-Degree-of-Freedom Vessel Rolls Motion

2010 ◽  
Author(s):  
Kaiye Hu ◽  
Yong Ding ◽  
Hongwei Wang ◽  
Jide Li
Keyword(s):  
Global Stability ◽  
Global Bifurcation ◽  
Melnikov Method ◽  
Threshold Value ◽  
Homoclinic Orbits ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Bounded Noise ◽  
Single Degree Of Freedom ◽  
Single Degree

Basing on the nonlinear dynamics theory, the global stability of ship in stochastic beam sea is researched by the global bifurcation method. In this paper, bounded noise is first briefly introduced. Bounded noise is a harmonic function with constant random frequency and phase. It has finite power and its spectral shape can be made to fit a target spectrum, such as Pierson-Moskowitz spectrum, by adjusting its parameters. This paper considered the stochastic excitation term as bounded noise and the influence of nonlinear damping and nonlinear righting moment, setup the random single degree of freedom nonlinear rolling equation. Then the random Melnikov process for the nonlinear system with homoclinic orbits under both dissipative and bounded noise perturbations is derived. The random Melnikov mean-square criterion is used to analysis the global stability of this system. The research indicates that the bounded noise can approximately simulate the wave excitation and if the noise exceeds the threshold value, the ship will undergo stochastic chaotic motion. That will lead ships to instability and even to capsizing.

scholarly journals DYNAMICS FEATURES OF A VIBRATING MACHINE WITH ELASTIC ELEMENT HAVING EXPONENTIAL CHARACTERISTIC OF RESILIENT FORCE

2021 ◽  
pp. 59-62
Author(s):  
Grigory Altshul ◽  
Alexander Gouskov ◽  
Grigory PanovkoAlexander Shokhin ◽  
Alexander Shokhin
Keyword(s):  
Supply Voltage ◽  
Elastic Characteristic ◽  
Vibration Exciter ◽  
Static Characteristics ◽  
Power Supply Voltage ◽  
Resonant Amplitude ◽  
Processed Material ◽  
Working Element ◽  
The Stability ◽  
Nonlinear Elastic

The article analyzes the possibility of using nonlinear elastic elements as a suspension of the working element of resonant vibrating machines with two unbalance vibration exciters is analyzed. The elastic characteristic of the suspension is described by an exponential law, which ensures that the natural frequency remains unchanged regardless of the system mass. Static characteristics of the vibration exciter motors are taken into account. A system of differential equations describing movement of the system depending on the processed material mass is obtained. Amplitude-frequency characteristics depending on the power supply voltage, as well as on the debalance rotational speed are obtained for different values of material mass. The stability of the obtained periodic solutions is analyzed. The constancy of resonant amplitude and frequency of the working element vibrations at various values of material mass is shown. The results obtained confirm the advisability of using an equalfrequency suspension of the working element for resonant vibrating machines.

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