Derivation of nonlinear damping from viscoelasticity in case of nonlinear vibrations

2018 ◽  
Vol 97 (3) ◽  
pp. 1785-1797 ◽  
Author(s):  
Marco Amabili
Keyword(s):  
Nonlinear Vibrations ◽  
Nonlinear Damping

Nonlinear Damping in Large-Amplitude Vibrations of Viscoelastic Plates

2019 ◽  
Author(s):  
Marco Amabili ◽  
Prabakaran Balasubramanian ◽  
Giovanni Ferrari
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Frequency ◽  
Nonlinear Vibrations ◽  
Excitation Frequency ◽  
Laser Doppler Vibrometer ◽  
Nonlinear Damping ◽  
Dissipated Energy ◽  
Rectangular Plates ◽  
Lagrange Equations ◽  
Frequency Dependent

Abstract Damping is largely increasing with the vibration amplitude during nonlinear vibrations of rectangular plates. At the same time, soft materials present an increase of their stiffness with the vibration frequency. These two phenomena appear together and are both explained in the framework of the viscoelasticity. While the literature on nonlinear vibrations of plates is very large, these aspects are rarely addressed. The present study uses the fractional solid model to describe the viscoelastic material behaviour. This allows to capture at the same time (i) the increase in the storage modulus with the vibration frequency and (ii) the frequency-dependent nonlinear damping in nonlinear vibrations of rectangular plates. The solution of the nonlinear vibration problems is obtained through Lagrange equations by deriving the potential energy of the plate and the dissipated energy, both geometrically nonlinear and frequency-dependent. The model is then applied to a silicone rubber rectangular plate tested experimentally. The plate was glued to a metal frame and harmonically excited by stepped sine testing at different force levels and the vibration response was measured by a laser Doppler vibrometer. The comparison of numerical and experimental results was satisfactorily carried out for: (i) nonlinear vibration responses in the frequency and time domain at different excitation levels, (ii) dissipated energy versus excitation frequency and excitation force, (iii) storage energy and (iv) loss factor, which is particularly interesting to evaluate the plate dissipation versus frequency at different excitation levels. Finally, the linear and nonlinear damping terms are compared.

scholarly journals The nonlinear vibrations of a vertical hard gyroscopic rotor with nonlinear characteristics

2019 ◽  
Vol 10 (2) ◽  
pp. 529-544 ◽  
Author(s):  
Zharilkassin Iskakov ◽  
Kuatbay Bissembayev
Keyword(s):  
High Velocity ◽  
Nonlinear Vibrations ◽  
Rotational Velocity ◽  
Nonlinear Damping ◽  
Nonlinear Characteristics ◽  
Vibration Isolators ◽  
Absolute Displacement ◽  
Linear Damping ◽  
Force Transmissibility ◽  
The Moment

Abstract. The paper considers an impact of viscous linear and cubic nonlinear damping of the elastic support on nonlinear vibrations of a vertical hard gyroscopic unbalanced rotor, taking into account nonlinear stiffness of the support material. Analyzing the research results shows that linear and cubic nonlinear damping can significantly suppress the resonance peak of the fundamental harmonic, eliminate the jumping phenomena of the nonlinear system. In non-resonance areas where the velocity is higher than the critical one, cubic nonlinear damping, unlike linear one, can slightly suppress amplitude of the rotor vibration. Therefore, in the high-velocity area, only nonlinear damping can maintain performance of a vibration isolator. In resonance area, an increase in linear or cubic nonlinear damping significantly suppresses the ability to absolute displacement. In non-resonance area, where the rotational velocity is lower than the critical one, they have almost no impact on ability to absolute displacement. In high velocity area, an increase in nonlinear damping may slightly increase the moment of force transmissibility, but linear damping has almost no impact on it. The obtained results can be successfully used to produce passive vibration isolators used for damping the vibrations of rotary machines, including gyroscopic ones.

Compensating for Nonisochronism in an Oscillator with Nonlinear Damping Resistance

Vestnik MEI ◽  
2017 ◽  
pp. 87-91
Author(s):  
Pavel A. Stremoukhov ◽  
◽  
Ansar R. Safin ◽  
Aleksey B. Ustinov ◽  
Nicolay N. Udalov ◽  
...  
Keyword(s):  
Nonlinear Damping

Nonlinear damping identification from transient data

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 1625-1632
Author(s):  
C. B. Smith ◽  
N. M. Wereley
Keyword(s):  
Nonlinear Damping ◽  
Transient Data

RANDOMLY FORCED NONLINEAR VIBRATIONS OF LAYERED SKEW PLATES AND SHALLOW SHELLS

1993 ◽  
Author(s):  
R. HEUER ◽  
H. IRSCNIK ◽  
F. ZIEGLER ◽  
FELLOW ASME
Keyword(s):  
Nonlinear Vibrations ◽  
Shallow Shells

Beneficial performance of a quasi-zero stiffness vibration isolator with generalized geometric nonlinear damping

2020 ◽  
pp. 095745652097238
Author(s):  
Chun Cheng ◽  
Ran Ma ◽  
Yan Hu
Keyword(s):  
Damping Ratio ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Equivalent Damping ◽  
Frequency Responses ◽  
Geometric Nonlinear ◽  
Resonant Region ◽  
Force Transmissibility ◽  
Isolation Performance ◽  
Force And Displacement Transmissibility

Generalized geometric nonlinear damping based on the viscous damper with a non-negative velocity exponent is proposed to improve the isolation performance of a quasi-zero stiffness (QZS) vibration isolator in this paper. Firstly, the generalized geometric nonlinear damping characteristic is derived. Then, the amplitude-frequency responses of the QZS vibration isolator under force and base excitations are obtained, respectively, using the averaging method. Parametric analysis of the force and displacement transmissibility is conducted subsequently. At last, two phenomena are explained from the viewpoint of the equivalent damping ratio. The results show that decreasing the velocity exponent of the horizontal damper is beneficial to reduce the force transmissibility in the resonant region. For the case of base excitation, it is beneficial to select a smaller velocity exponent only when the nonlinear damping ratio is relatively large.

Sign in / Sign up

Export Citation Format

Share Document