scholarly journals Stability Analysis of Multispan Pipeline Embedded in Temperature-Dependent Matrix

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Nan Wu ◽  
Yongshou Liu ◽  
Guojun Tong ◽  
Jiayin Dai
Keyword(s):  
Natural Frequency ◽  
Critical Velocity ◽  
Critical Pressure ◽  
Dynamic Stiffness ◽  
Second Order ◽  
Temperature Dependent ◽  
Temperature Changes ◽  
First Order ◽  
The Stability ◽  
Increasing Temperature

In this paper, dynamic stiffness method is used to study the stability of multispan pipelines in temperature-dependent matrix. The effects of temperature changes and different span combinations on the natural frequency, critical velocity, and critical pressure of pipelines are discussed. The main conclusions are obtained and shown as follows. The increase of temperature will lead to the decrease of the first three order natural frequencies. The first two order critical velocities and critical pressure of the system will also decrease with increasing temperature. The change of span combination has no influence on the first-order critical velocity and first-order critical pressure of the system, but it has influence on the second order. The influence of the change of span combination on the first-order natural frequency is regular, but that on the second-order and third-order is not. The increase of the velocity will change the instability form of systems with different span combinations, while the change of the pressure inside the tube will not change the instability form of the system.

Stability analysis of a two-segment constructed nanotube embedded in an elastic matrix

2019 ◽  
Vol 26 (3-4) ◽  
pp. 241-252
Author(s):  
Guo-jun Tong ◽  
Yong-shou Liu ◽  
Qian Cheng ◽  
Jia-yin Dai
Keyword(s):  
Elastic Modulus ◽  
Natural Frequency ◽  
Critical Velocity ◽  
Dynamic Stiffness ◽  
Elastic Matrix ◽  
Length Ratio ◽  
Mass Ratio ◽  
Modulus Ratio ◽  
Elastic Coefficient ◽  
The Stability

In this paper, the dynamic stiffness method is used to study the stability of a two-segment constructed nanotube embedded in an elastic matrix. The influences of the length ratio, elastic modulus ratio, mass ratio, and elastic coefficient on the stability of the nanotube are investigated. It can be concluded that a change in the elastic coefficient, length ratio, and elastic modulus ratio has no effect on the form of instability of the two-segment constructed nanotube, but a change in the mass ratio has a significant influence on the form of instability of the nanotube. The elastic coefficient of the elastic matrix mainly affects the natural frequency and the critical velocity of the nanotube of the first mode. The change in the length ratio and elastic modulus ratio mainly affects the natural frequency and the critical velocity of the second mode. The mass change in the two materials mainly affects the natural frequency of the nanotube and has no effect on the critical velocity.

ORIENTATION OF SYMMETRIC BODIES FALLING IN A SECOND-ORDER LIQUID AT NONZERO REYNOLDS NUMBER

2002 ◽  
Vol 12 (11) ◽  
pp. 1653-1690 ◽  
Author(s):  
GIOVANNI P. GALDI ◽  
ASHWIN VAIDYA ◽  
MILAN POKORNÝ ◽  
DANIEL D. JOSEPH ◽  
JIMMY FENG
Keyword(s):  
Prolate Spheroid ◽  
Critical Value ◽  
Second Order ◽  
The Body ◽  
Body Of Revolution ◽  
Translational Velocity ◽  
Homogeneous Body ◽  
First Order ◽  
The Stability ◽  
Elasticity Number

We study the steady translational fall of a homogeneous body of revolution around an axis a, with fore-and-aft symmetry, in a second-order liquid at nonzero Reynolds (Re) and Weissenberg (We) numbers. We show that, at first order in these parameters, only two orientations are allowed, namely, those with a either parallel or perpendicular to the direction of the gravity g. In both cases the translational velocity is parallel to g. The stability of the orientations can be described in terms of a critical value E c for the elasticity number E = We/Re , where E c depends only on the geometric properties of the body, such as size or shape, and on the quantity (Ψ1 + Ψ2)/Ψ1, where Ψ1 and Ψ2 are the first and second normal stress coefficients. These results are then applied to the case when the body is a prolate spheroid. Our analysis shows, in particular, that there is no tilt-angle phenomenon at first order in Re and We.

scholarly journals Effects of Machine Tool Spindle Decay on the Stability Lobe Diagram: An Analytical-Experimental Study

2021 ◽  
Author(s):  
Omar Gaber ◽  
Seyed M. Hashemi
Keyword(s):  
Machine Tool ◽  
Natural Frequency ◽  
Dynamic Stiffness ◽  
Significant Shift ◽  
Stability Lobe Diagram ◽  
Element Analysis ◽  
Stability Lobe ◽  
Machine Tool Spindle ◽  
Linear Spring ◽  
The Stability

An analytical-experimental investigation of machine tool spindle decay and its effects of the system’s stability lobe diagram (SLD) is presented. A dynamic stiffness matrix (DSM)model for the vibration analysis of the OKADA VM500 machine spindle is developed and is validated against Finite Element Analysis (FEA).The model is then refined to incorporate flexibility of the system’s bearings, originally modeled as simply supported boundary conditions, where the bearings are modeled as linear spring elements.The system fundamental frequency obtained from the modal analysis carried on an experimental setup is then used to calibrate the DSM model by tuning the springs’ constants. The resulting natural frequency is also used to determine the 2D stability lobes diagram (SLD) for said spindle. Exploiting the presented approach and calibrated DSM model it is shown that a hypothetical 10% change in the natural frequency would result in a significant shift in the SLD of the spindle system, which should be taken into consideration to ensure chatter-free machining over the spindle’s life cycle.

scholarly journals Modal Interaction-Induced Parametric Resonance of Stayed Cable: A Combined Theoretical and Experimental Investigation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Qi-Chang Zhang ◽  
Su-Yu Cui ◽  
Zhi Fu ◽  
Jian-Xin Han
Keyword(s):  
Natural Frequency ◽  
Parametric Resonance ◽  
Bridge Deck ◽  
Primary Resonance ◽  
Second Order ◽  
Stay Cable ◽  
Modal Interaction ◽  
External Excitation ◽  
First Order ◽  
Principal Parametric Resonance

The cable-stayed bridge is widely used due to its strong spanning capacity and navigability. However, flexible cables parametrically resonated by external excitation may result in instability or even damage to the bridge. To prevent such undesirable resonance, this paper discusses an in-plane modal interaction-induced parametric resonance of the stayed cable excited by the bridge deck vibration via nonlinear dynamic analysis. Based on the nonlinear distributed model, two modal governing equations of the cable are established via the Galerkin method. A certain working condition, when the external excitation frequency is close to the second-order natural frequency of the stay cable while nearly twice the first-order natural frequency, is theoretically and experimentally investigated. Specifically, the frequency response equations are obtained by the multiscale method, and the stability of solutions is examined through the Routh Hurwitz criterion. Theoretical and experimental results show that bridge deck vibration can induce not only the primary and superharmonic resonance of the cable but also the principal parametric resonance. Parametric resonance-induced bifurcations are also observed in the system. Particularly, the energy exchange from second-order primary resonance to first-order principal parametric resonance is found, which can induce the parametric resonance with the response amplitude one to three times higher than that of the primary resonance. This paper also validates the superiority of the present modal interaction model over the traditional single-mode model in practical engineering applications.

The Von Neumann-Mullins Theory of Grain Growth – Valid or Not?!

2004 ◽  
Vol 467-470 ◽  
pp. 1111-1116 ◽  
Author(s):  
Lasar S. Shvindlerman ◽  
Günter Gottstein ◽  
Anthony D. Rollett
Keyword(s):  
Relative Rate ◽  
Second Order ◽  
Rate Of Change ◽  
Recent Analysis ◽  
Order Problem ◽  
Von Neumann ◽  
First Order ◽  
Dimensional Network ◽  
The Stability ◽  
Grain Topology

We present a new analysis of the relative rate of growth or shrinkage of grains in a two-dimensional network, based on the classical Von Neumann-Mullins (VN-M) analysis. We find that an analysis of the stability of the grain shape during shrinkage or growth shows that any change in the regular 2D grain leads to changes in the shape. We also re-examine a recent analysis that claims to have invalidated the VN-M relationship, but find that it is still valid, and that the cited analysis, in fact, confused a second order correction with a first order problem, partly because their derivation was in error. The erroneous magnitude of the discrepancy led them to use unphysical issues to explain the discrepancy. The way in which the curvature is distributed along the perimeter of a grain only gives rise only to second order corrections to the rate of change of area as a function of grain topology (number of sides).

The Optimization of a Middle-Sized Passenger Car Steering Wheel Vibration at Idle Speed

2011 ◽  
Vol 291-294 ◽  
pp. 1937-1940
Author(s):  
Lang Su ◽  
Hong Zhou ◽  
Lin Sen Zhu
Keyword(s):  
Natural Frequency ◽  
Second Order ◽  
Steering Wheel ◽  
Passenger Car ◽  
Idle Speed ◽  
First Order ◽  
Vibration Problem ◽  
Column System ◽  
Wheel Vibration

In this paper, based on the study of steering wheel vibration problem of a middle-sized passenger car under idle condition, the reason is found out with the help of testing and analyzing, and the result shows that it is its first-order natural frequency, which is too close to the engine’s second-order frequency under idle condition that causes resonance. Through the optimization of the steering column system the problem is solved, and a satisfying result is obtained.

Stability of a Beddington–DeAngelis type predator–prey model with trichotomous noises

2016 ◽  
Vol 30 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Yanfei Jin ◽  
Siyong Niu
Keyword(s):  
Correlation Time ◽  
Gaussian White Noise ◽  
Second Order ◽  
Predator Prey ◽  
First Order ◽  
Predator Prey Model ◽  
Order Solution ◽  
Prey Model ◽  
The Stability ◽  
The Moment

The stability analysis of a Beddington–DeAngelis (B–D) type predator–prey model driven by symmetric trichotomous noises is presented in this paper. Using the Shapiro–Loginov formula, the first-order and second-order solution moments of the system are obtained. The moment stability conditions of the B–D predator–prey model are given by using Routh–Hurwitz criterion. It is found that the stabilities of the first-order and second-order solution moments depend on the noise intensities and correlation time of noise. The first-order and second-order moments are stable when the correlation time of noise is increased. That is, the trichotomous noise plays a constructive role in stabilizing the solution moment with regard to Gaussian white noise. Finally, some numerical results are performed to support the theoretical analyses.

scholarly journals Design and Thermal Stability Analysis of Swing Micro-Mirror Structure for Gravitational Wave Observatory in Space

Machines ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 104
Author(s):  
Kunyao Zheng ◽  
Mingming Xu
Keyword(s):  
Thermal Stability ◽  
Gravitational Wave ◽  
Natural Frequency ◽  
Solution Method ◽  
Element Analysis ◽  
Temperature Changes ◽  
First Order ◽  
Angle Deviation ◽  
Thermal Stability Of ◽  
Mirror Structure

A kind of swing micro-mirror structure with high stability for gravitational wave observatory in space is proposed in this paper. As the key interface instrument in the gravitational wave observatory, the swing micro-mirror structure plays a very important role. Firstly, the 3D model of the mechanism is designed and established. Then, the solution method of the index of stability, pointing jitter, is researched. After that, the thermal stability and the first-order natural frequency of the mechanism are researched via finite element analysis. The first-order natural frequency of the mechanism is 247.55 Hz, which can meet the requirements of the design. It can be seen from the results of the simulation, the amplitude spectral density of the mirror angle deviation is 3.975 nrad/√Hz when the range of temperature variation is 0.1 °C, which is able to meet the requirements of the design. The thermal stability has a closed relationship with the structural stability around the X-axis. In addition, this article also studies the thermal stability of the mechanism in the case of temperature changes in different directions. It is found that the thermal stability of the mechanism around the Y-axis would be significantly affected by the temperature changes along the Y-axis.

scholarly journals Temperature-dependence of neuronal performance in the motion pathway of the blowfly calliphora erythrocephala

1999 ◽  
Vol 202 (22) ◽  
pp. 3161-3170 ◽  
Author(s):  
A. Warzecha ◽  
W. Horstmann ◽  
M. Egelhaaf
Keyword(s):  
Visual Motion ◽  
Neuronal Response ◽  
Mean Amplitude ◽  
Operating Conditions ◽  
Transient Temperature ◽  
Temperature Dependent ◽  
Calliphora Erythrocephala ◽  
Temperature Changes ◽  
Increasing Temperature ◽  
Relevant Range

Raising the head temperature within a behaviourally relevant range has strong effects on the performance of an identified neuron, the H1 neuron, in the visual motion pathway of blowflies. The effect is seen as an increase in the mean amplitude of the responses to motion under both transient and steady-state conditions, a considerable decrease in the response latency and an improvement in the reliability of the responses to motion. These temperature-dependent effects are independent of whether the animal is exposed to transient temperature changes or is maintained continuously at the same temperature for its entire life. The changes in the neuronal response properties with temperature may be of immediate functional significance for the animal under its normal operating conditions. In particular, the decrease in latency and the improvement in the reliability with increasing temperature may be relevant for the fly when executing its extremely virtuosic flight manoeuvres.

scholarly journals Effects of Machine Tool Spindle Decay on the Stability Lobe Diagram: An Analytical-Experimental Study

2021 ◽  
Author(s):  
Omar Gaber ◽  
Seyed M. Hashemi
Keyword(s):  
Machine Tool ◽  
Natural Frequency ◽  
Dynamic Stiffness ◽  
Significant Shift ◽  
Stability Lobe Diagram ◽  
Element Analysis ◽  
Stability Lobe ◽  
Machine Tool Spindle ◽  
Linear Spring ◽  
The Stability

An analytical-experimental investigation of machine tool spindle decay and its effects of the system’s stability lobe diagram (SLD) is presented. A dynamic stiffness matrix (DSM)model for the vibration analysis of the OKADA VM500 machine spindle is developed and is validated against Finite Element Analysis (FEA).The model is then refined to incorporate flexibility of the system’s bearings, originally modeled as simply supported boundary conditions, where the bearings are modeled as linear spring elements.The system fundamental frequency obtained from the modal analysis carried on an experimental setup is then used to calibrate the DSM model by tuning the springs’ constants. The resulting natural frequency is also used to determine the 2D stability lobes diagram (SLD) for said spindle. Exploiting the presented approach and calibrated DSM model it is shown that a hypothetical 10% change in the natural frequency would result in a significant shift in the SLD of the spindle system, which should be taken into consideration to ensure chatter-free machining over the spindle’s life cycle.

Sign in / Sign up

Export Citation Format

Share Document