Effect of Dynamic Soft Elasticity on Vibration of Embedded Nematic Elastomer Timoshenko Beams

2018 ◽  
Vol 10 (05) ◽  
pp. 1850058 ◽  
Author(s):  
Dong Zhao ◽  
Ying Liu
Keyword(s):  
Low Frequency ◽  
Beam Theory ◽  
Timoshenko Beams ◽  
Analysis Method ◽  
Anisotropic Parameter ◽  
Nematic Elastomer ◽  
Dissipation Mechanism ◽  
Viscous Media ◽  
Complex Modal Analysis ◽  
Soft Elasticity

This paper addresses the transverse vibration of a nematic elastomer (NE) beam embedded in soft viscoelastic surroundings with the aim to clarify a new dissipation mechanism caused by dynamic soft elasticity of this soft material. Based on the viscoelasticity theory of NEs in low-frequency limit and the Timoshenko beam theory, the governing equation of motion is derived by using the Hamilton principle and energy method, and is solved by the complex modal analysis method. The dependence of vibration property on the intrinsic parameters of NEs (director rotation time, rubber relaxation time, anisotropic parameter) and foundation (spring, shear and damping constants) are discussed in detail. The results show that dynamic soft elasticity leads to anomalous anisotropy of energy transfer and attenuation. The relative stiffer foundation would restraint the rubber dissipation of viscoelastic beams, but has less influence on the director rotation dissipation, which is particular for NE beams. This study would provide a useful guidance in the dynamic design of NE apparatus embedded in soft viscous media.

Effects of director rotation relaxation on viscoelastic wave dispersion in nematic elastomer beams

2018 ◽  
Vol 24 (4) ◽  
pp. 1103-1115 ◽  
Author(s):  
Dong Zhao ◽  
Ying Liu
Keyword(s):  
Wave Motion ◽  
Relaxation Times ◽  
Low Frequency ◽  
Wave Dispersion ◽  
Frequency Limit ◽  
Anisotropic Parameter ◽  
Acoustic Design ◽  
Phase Velocities ◽  
Nematic Elastomer ◽  
Viscoelastic Wave

In this paper, the transverse wave dispersion in a nematic elastomer (NE) Timoshenko beam is studied by considering anisotropy and viscoelasticity of NEs in the low frequency limit. Firstly, the characteristic equations of wave motion in an NE beam are derived, and then numerically solved to obtain the corresponding phase velocities and attenuation factors. The influences of anisotropic parameter, director rotation and rubber relaxation times on the wave dispersion in an NE beam are discussed. Results show that unlike the situation in general isotropic viscoelastic beam, non-classical viscoelastic wave dispersion is found in NE beams. Geometric dispersion is restrained with the vanishing of cut-off frequencies for shear waves due to director rotation relaxation of NEs. This unique property promises prospective applications of NE beams in optic or acoustic design.

Analytical Solution for Rotational Rub-Impact Plate Under Thermal Shock

2016 ◽  
Vol 32 (3) ◽  
pp. 297-311
Author(s):  
T.-Y. Zhao ◽  
H.-Q. Yuan ◽  
B.-B. Li ◽  
Z.-J. Li ◽  
L.-M. Liu
Keyword(s):  
Thermal Shock ◽  
High Frequency ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Cantilever Plate ◽  
Analysis Method ◽  
Multiple Frequency ◽  
Width Direction ◽  
Blade Tip ◽  
High Frequency Vibrations

AbstractThe analysis method is developed to obtain dynamic characteristics of the rotating cantilever plate with thermal shock and tip-rub. Based on the variational principle, equations of motion are derived considering the differences between rubbing forces in the width direction of the plate. The transverse deformation is decomposed into quasi-static deformation of the cantilever plate with thermal shock and dynamic deformation of the rubbing plate under thermal shock. Then deformations are obtained through the calculation of modal characteristics of rotating cantilever plate and temperature distribution function. Special attention is paid to the influence of tip-rub and thermal shock on the plate. The results show that tip-rub has the characteristics of multiple frequency vibrations, and high frequency vibrations are significant. On the contrary, thermal shock shows the low frequency vibrations. The thermal shock makes the rubbing plate gradually change into low frequency vibrations. Because rub-induced vibrations are more complicated than those caused by thermal shock, tip-rub is easier to result in the destruction of the blade. The increasing friction coefficient intensifies vibrations of the rubbing plate. Minimizing friction coefficients can be an effective way to reduce rub-induced damage through reducing the surface roughness between the blade tip and the inner surface of the casing.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

Influence of Materials on the Performance Limits of Microactuators

2007 ◽  
Vol 1052 ◽  
Author(s):  
Prasanna Srinivasan ◽  
S. Mark Spearing
Keyword(s):  
Thin Films ◽  
Shape Memory ◽  
High Performance ◽  
Low Frequency ◽  
Beam Theory ◽  
Performance Limits ◽  
Low Frequencies ◽  
Thermal Actuators ◽  
Work Volume ◽  
Selection Of

AbstractThe selection of actuators at the micro-scale requires an understanding of the performance limits of different actuation mechanisms governed by the optimal selection of materials. This paper presents the results of analyses for elastic bi-material actuators based on simple beam theory and lumped parameter thermal models. Comparisons are made among commonly employed actuation schemes (electro-thermal, piezoelectric and shape memory) at micro scales and promising candidate materials are identified. Polymeric films on Si subjected to electro-thermal heating are optimal candidates for high displacement, low frequency devices while ferroelectric thin films of Pb-based ceramics on Si/ DLC are optimal for high force, high frequency devices. The ability to achieve ∼10 kHz at scales < 100μm make electro-thermal actuators competitive with piezoelectric actuators considering the low work/volume obtained in piezoelectric actuation (∼ 10−8J.m−3.mV−2). Although shape memory alloy (SMA) actuators such as Ni-Ti on Si deliver larger work (∼ 1 J.m−3K−2) than electro-thermal actuators at relatively low frequencies (∼ 1 kHz), the critical scale associated with the cessation of the shape memory effect forms the bounding limit for the actuator design. The built-in compressive stress levels (∼ 1GPa) in thin films of Si and DLC could be exploited for realizing a high performance actuator by electro-thermal buckling.

scholarly journals Ship Radiated Noise Recognition Using Resonance-Based Sparse Signal Decomposition

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jiaquan Yan ◽  
Haixin Sun ◽  
En Cheng ◽  
Xiaoyan Kuai ◽  
Xiaoliang Zhang
Keyword(s):  
Feature Extraction ◽  
Low Frequency ◽  
Signal Decomposition ◽  
Sparse Signal ◽  
Support Vector ◽  
Analysis Method ◽  
Radiated Noise ◽  
High Resonance ◽  
Residual Component ◽  
Sparse Signal Decomposition

Under the complex oceanic environment, robust and effective feature extraction is the key issue of ship radiated noise recognition. Since traditional feature extraction methods are susceptible to the inevitable environmental noise, the type of vessels, and the speed of ships, the recognition accuracy will degrade significantly. Hence, we propose a robust time-frequency analysis method which combines resonance-based sparse signal decomposition (RSSD) and Hilbert marginal spectrum (HMS) analysis. First, the observed signals are decomposed into high resonance component, low resonance component, and residual component by RSSD, which is a nonlinear signal analysis method based not on frequency or scale but on resonance. High resonance component is multiple simultaneous sustained oscillations, low resonance component is nonoscillatory transients, and residual component is white Gaussian noises. According to the low-frequency periodic oscillatory characteristic of ship radiated noise, high resonance component is the purified ship radiated noise. RSSD is suited to noise suppression for low-frequency oscillation signals. Second, HMS of high resonance component is extracted by Hilbert-Huang transform (HHT) as the feature vector. Finally, support vector machine (SVM) is adopted as a classifier. Real audio recordings are employed in the experiments under different signal-to-noise ratios (SNRs). The experimental results indicate that the proposed method has a better recognition performance than the traditional method under different SNRs.

scholarly journals An asymptotic higher-order theory for rectangular beams

2018 ◽  
Vol 474 (2214) ◽  
pp. 20180001 ◽  
Author(s):  
E. Nolde ◽  
A. V. Pichugin ◽  
J. Kaplunov
Keyword(s):  
Governing Equation ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Low Frequency ◽  
Beam Theory ◽  
Correct Choice ◽  
Order Theory ◽  
Beam Equation ◽  
Dimensional Problem ◽  
Aspect Ratios

A direct asymptotic integration of the full three-dimensional problem of elasticity is employed to derive a consistent governing equation for a beam with the rectangular cross section. The governing equation is consistent in the sense that it has the same long-wave low-frequency behaviour as the exact solution of the original three-dimensional problem. Performance of the new beam equation is illustrated by comparing its predictions against the results of direct finite-element computations. Limiting behaviours for beams with large (and small) aspect ratios, which can be established using classical plate theories, are recovered from the new governing equation to illustrate its consistency and also to illustrate the importance of using plate theories with the correctly refined boundary conditions. The implications for the correct choice of the shear correction factor in Timoshenko's beam theory are also discussed.

Equivalent-Beam Theory of the Self-Anchored Suspension Bridge

2011 ◽  
Vol 255-260 ◽  
pp. 801-805
Author(s):  
Biao Wei ◽  
Qing Yuan Zeng ◽  
Wei An Liu
Keyword(s):  
Mechanical Properties ◽  
Theoretical Analysis ◽  
Structural Response ◽  
Beam Theory ◽  
Suspension Bridge ◽  
The Self ◽  
Analysis Method ◽  
The Future

Taking one typical two-tower three-span self-anchored suspension bridge as an example, structural response has been characterized in detailed followed by its own construction steps. Meanwhile, the structure’s mechanics properties have been mathematically formulated through theoretical analysis method. Finally, the formulation has been further expressed by using a simplified beam subjected to external equivalent forces, and then the equivalent-beam theory of the self-anchored suspension bridge has been well established thereafter. As been demonstrated, the equivalent-beam theory can be easily and clearly applied to determine the vertical mechanical properties of the self-anchored suspension bridge, and could be utilized to guide the self-anchored suspension bridge deign in the future.

scholarly journals Transverse Free Vibration of Axially Moving Stepped Beam with Different Length and Tip Mass

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Guoliang Ma ◽  
Minglong Xu ◽  
Liqun Chen ◽  
Zengyong An
Keyword(s):  
Free Vibration ◽  
Beam Theory ◽  
Bending Moment ◽  
Frequency Equation ◽  
Eigenvalue Equation ◽  
Stepped Beam ◽  
Complex Modal Analysis ◽  
Axially Moving ◽  
Semianalytical Method ◽  
Tip Mass

Axially moving stepped beam (AMSB) with different length and tip mass is represented by adopting Euler-Bernoulli beam theory, and its characteristics and displacements of transverse free vibration are calculated by using semianalytical method. Firstly, the governing equation of the transverse free vibration is established based on Hamilton’s principle. The equation is cast into eigenvalue equation through the complex modal analysis. Then, a scheme is proposed to derive the continuous condition accordingly as the displacement, rotation, bending moment, and shear force are all equal at the connections of any two segments. Another scheme is to derive frequency equation from the given boundary conditions which contain a tip mass in the last segment. Finally, the natural frequency and modal function are calculated by using numerical method according to the eigenvalue equation and frequency equation. Due to the introduction of modal truncation, displacement and, the free vibration solution can be obtained by adopting modal superposition after Hilbert transform. The numerical examples illustrate that length, velocity, mass, and geometry affect characteristics and displacements significantly; the series of methods are effective and accurate to investigate the vibration of the AMSB with different length and tip mass after comparing several results.

Sign in / Sign up

Export Citation Format

Share Document