Dynamics of the Water-Pipeline-Soil Interaction

1982 ◽  
Vol 104 (4) ◽  
pp. 307-312 ◽  
Author(s):  
K. Karal ◽  
S. A. Halvorsen
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Particle Motion ◽  
Flexural Rigidity ◽  
Time Histories ◽  
Normal Water ◽  
Concrete Coating ◽  
Water Pipeline ◽  
The Mathematical Model ◽  
Oriented Approach

A design engineer-oriented approach to determining the pipeline dynamic response to ocean forces accounting for complex environmental and pipeline conditions is presented. The described analysis yields time histories of pipeline motion and steel pipe stresses induced by water motion. Sinusoidal variation of normal water particle motion in time and along the pipeline, waves, flexural rigidity of pipe, damaged concrete coating, among other effects, are accounted for in the mathematical model.

scholarly journals Large Deflection Model for Multiple, Inline, Interacting Cantilever Beams

2020 ◽  
Vol 88 (4) ◽  
Author(s):  
Austin Bebee ◽  
Christopher J. Stubbs ◽  
Daniel J. Robertson
Keyword(s):  
Mathematical Model ◽  
Flexural Rigidity ◽  
Cantilever Beams ◽  
Model Concept ◽  
Math Model ◽  
Rigid Body Model ◽  
High Throughput Phenotyping ◽  
Stalk Lodging ◽  
The Mathematical Model

Abstract Numerous natural and synthetic systems can be modeled as clusters of interacting cantilever beams. However, a closed-form mathematical model capable of representing the mechanics of multiple interacting cantilever beams undergoing large deflections has yet to be presented. In this work, a pioneering mathematical model of the force–deflection response of multiple, inline, interacting (i.e., contacting) cantilever beams is presented. The math model enables the determination of the force–deflection response of a system of interacting cantilever beams and is predicated upon the “Pseudo Rigid Body Model” concept. The model was validated through data triangulation experiments which included both physical and computational studies. An analysis of the mathematical model indicates it is most accurate with deflections less than 50 deg. In the future, the model may be used in high throughput phenotyping applications for investigating stalk lodging and estimating the flexural rigidity of crop stems. The model can also be used to gain intuition and aid in the design of synthetic systems composed of multiple cantilever beams.

Mathematical Model and Analytical Solution for the Vibration of Inclined Fluid-Transporting Submarine Pipelines

2019 ◽  
Vol 161 (A4) ◽  
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Integral Transform ◽  
Internal Flow ◽  
Equation System ◽  
Theoretical Understanding ◽  
Wake Oscillator ◽  
Lock In ◽  
Irregular Topography ◽  
The Mathematical Model

Due to the complexity of submarine environments, the nature of the dynamic response of free-spanning submarine pipelines, particularly inclined pipelines, is unclear. This paper aims to theoretically analyze the vibration behaviors of inclined fluid-transporting free-spanning submarine pipelines in the deepwater area. The mathematical model for the vibration of inclined fluid-transporting pipelines is established considering the influence of gravity on vibration response, and a non-linear wake oscillator is employed to model the vortex shedding behind the pipeline free span. The partial differential equation system is solved through the generalized integral transform technique (GITT), which is an analytical or semi-analytical method. Parametric analysis are carried out to investigate the effects of the inclination on the dynamic response of fluid-transporting pipelines. It is found that the inclination of the free-spanning pipeline will radically alter the natural frequency of the structure, and consequently the VIV lock-in region. In addition, the slope of the seabed will cause a more significant internal flow effect. The thorough theoretical understanding of inclined fluid-transporting pipelines helps increase the design accuracy for pipelines installed on a seabed with a highly irregular topography.

Study on Dynamic Characteristics and Dynamic Response of Woodworking Four-Side Planer

2011 ◽  
Vol 291-294 ◽  
pp. 1970-1976
Author(s):  
Shao Qun Zhang ◽  
Jun Hua ◽  
Wei Xu
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Natural Frequency ◽  
Dynamic Characteristics ◽  
Feed Rate ◽  
Reference Data ◽  
Damping Ratio ◽  
Vibration Test ◽  
Vibration Magnitude ◽  
The Mathematical Model

Through woodworking four-side planer vibration test, this article studiesits dynamic characteristics and dynamic response to identify the vibration magnitudes law of each feed roll shafts of the four-side feed beam; then finds the natural frequency and damping ratio of the feed beam and lathe bed; obtains the mathematical model of feed roll shaft vibration magnitude changing with the feed rate U under different process thicknesses. The analysis of feeding quantity and the rationality of lathe bed from the perspective of vibration design supplies the designs and operation staff with reference data.

The Simulation of Six Phase PMSM Taking Iron Loss into Account

2012 ◽  
Vol 433-440 ◽  
pp. 7535-7540
Author(s):  
Dong Xing ◽  
Xiao Ning Zhang ◽  
Yong Ling Fu ◽  
Hai Tao Qi
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Dynamic Response ◽  
Iron Loss ◽  
Field Oriented Control ◽  
Three Phase ◽  
Simulation Results ◽  
Set Up ◽  
The Mathematical Model ◽  
Fast Dynamic

This paper studies the mathematical model considering iron loss in the d-q axis of six phase permanent magnetic synchronous motor (PMSM), through the expansion of Field-Oriented Control (FOC) based on three phase PMSM, the simulation model of six phase PMSM under environment of simulink7.0 is set up, which has fast dynamic response, high steady-state precision, and has no problems about current balance compared to dual three phase PMSM. In order to get an accurate simulation results, this mathematical model takes iron loss into account. The simulation results show that iron loss have bad effects on the performance of PMSM especially affect the dynamic response, and to reduce the bad effects, the resistance of the motor core should be increased.

A Mathematical Model to Assess Occupant Compartment Intrusion on Rear Occupant Responses in Rear Crashes

2020 ◽  
Author(s):  
Gregory Stephens ◽  
David Michalski ◽  
Chantal S. Parenteau ◽  
Roger Burnett
Keyword(s):  
Mathematical Model ◽  
Test Data ◽  
Dynamic Effect ◽  
Crash Test ◽  
Acceleration Time Histories ◽  
Reconstructed Field ◽  
Time Histories ◽  
Biomechanical Responses ◽  
The Mathematical Model ◽  
Good Agreement

Abstract Rear occupant protection in rear crashes is a complex issue. Structural intrusion has been shown to be a significant factor in the injury mechanism of second-row children. In this study, a new model was developed to help quantify dynamic second-row intrusion, in terms of displacement, velocity, and acceleration, and assess its effect on rear occupant responses as a function of time. A mathematical model was developed using crash test data based on two reconstructed field accidents involving two different rear-ended vehicles with second-row children. The model also used the corresponding FMVSS 301R-type rear barrier tests of a similar vehicle. The crash test pulse data and videos from FMVSS 301R-type tests were analyzed to determine the timing and magnitude of second-row intrusion. Crash tests that had been conducted to simulate the field accidents were then used to validate the model. These tests included instrumented ATDs (Anthropometric Test Device) seated in the second-row area of the struck vehicles. The biomechanical responses were used to assess the validity of the mathematical model. Comparison between the mathematical model and the test data showed good agreement. For example, the model correctly showed that the dynamic second-row intrusion was greater than residual/static intrusion/displacement. The model also predicted accelerations that were in good agreement with the test data. Video analysis and head/chest acceleration time histories of the ATD’s indicated that intrusion occurred early and was an important factor in the occupant responses. Both the extent and velocity of dynamic intrusion also influenced the biomechanical responses. The model predicted head and chest accelerations that were greater than the overall vehicle accelerations due to localized structural intrusion. The mathematical model developed in this study is a first to assess the dynamic effect of second-row intrusion on rear occupant responses. Identifying factors that influence injury mechanisms are important when assessing the potential effectiveness of countermeasures.

Study on the Response of Flexible Joint Coupled With Unbalanced Rotor

2005 ◽  
Author(s):  
Zhen-Zhong Zhang ◽  
Cun-Sheng Zhao ◽  
Shi-Jian Zhu
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Dynamic Response ◽  
Periodic Coefficient ◽  
Steady Solution ◽  
Stability Conditions ◽  
Flexible Joint ◽  
Unbalanced Rotor ◽  
The Stability ◽  
The Mathematical Model

The dynamic response of the flexible joint with unbalanced rotor was analyzed. The mathematical model was investigated and simplified and the unbalanced system was found to be with periodic coefficient. The stability conditions of the periodic solution were simply derived from existing conclusions. And a method for an approximate steady solution was presented. The validity was confirmed by the simulation.

Aeolian vibration of a single conductor with a Stockbridge damper

2012 ◽  
Vol 227 (5) ◽  
pp. 935-945 ◽  
Author(s):  
Oumar Barry ◽  
Donatus CD Oguamanam ◽  
Der Chyan Lin
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Forced Vibration ◽  
Flexural Rigidity ◽  
Excitation Frequency ◽  
Finite Element Code ◽  
Vibrational Response ◽  
Aeolian Vibration ◽  
The Mathematical Model ◽  
Stockbridge Damper

The planar vibrational response of a single conductor with an attached Stockbridge damper is investigated. The mathematical model accounts for the two-way coupling between the conductor and the damper, the flexural rigidity of both the damper and the conductor, and the mass of the two counterweights of the damper. Hence, the dynamic behaviors of the damper and conductor are simultaneously assessed. Both free and forced vibration analyses are implemented via the use of a finite element code developed in MATLAB. The results of the force vibration analyses show that the effectiveness of Stockbridge dampers depends on their location, mass, and excitation frequency.

Dynamic Response Control of Asymmetric Systems with Load Interference

2014 ◽  
Vol 926-930 ◽  
pp. 1326-1329
Author(s):  
Le Zeng ◽  
Jian Ping Tan ◽  
Jun Yang
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Dynamic Response ◽  
Dynamic Property ◽  
Servo System ◽  
Hydraulic Press ◽  
Reverse Direction ◽  
Response Control ◽  
The Mathematical Model

The article based on the valve driving servo system of 125MN hydraulic press extruder, aimed at solving the unconformity of the dynamic property in electromechanical integration equipment or control system. It analyzed the mathematical model of the system, the influencing parameter and the regularity related to the asymmetric characteristics, when the cylinder moving forward and reverse direction. According the application in industry field, it adopts the methods by adjusting the ratio of the proportion parameters to remove the asymmetric characteristics in different direction and different loads.

Dynamic Response of Two-Disk Systems With Friction and Misalignment

1998 ◽  
Author(s):  
Ahmed Anabtawi ◽  
Kambiz Farhang
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Contact Stiffness ◽  
Stick Slip ◽  
Torsional Response ◽  
Damping Characteristics ◽  
Disk Friction ◽  
Stiffness And Damping ◽  
The Mathematical Model ◽  
Friction Induced Vibration

Abstract Friction induced vibration and noise pose one of the most challenging problems. The complexity of the friction system arises due to the nonlinear nature of friction phenomena and that of contact stiffness and damping. This paper presents a mathematical model for studying the dynamic response of two-disk friction system in the presence of misalignment. The contact stiffness and damping characteristics of the system are represented in the axial as well as the torsional directions. In addition, the axial and torsional responses of the system are coupled by assuming dependency between the torsional response and the normal force between the two disks. Using the mathematical model, various scenarios are examined to study the effect of misalignment. These include cases of symmetric and asymmetric actuation forces as well as forces applied at unequal actuation times. The results suggest that asymmetry in actuation forces has negligible effect on stick-slip behavior of the system.

scholarly journals Modeling and Design of the Automatic Pressure Regulating Valve in the Foam Firefighting System

Processes ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 1616
Author(s):  
Zhijun Yang ◽  
Hongjun Chen ◽  
Lifang He ◽  
Xikun Wang
Keyword(s):  
Mathematical Model ◽  
Equilibrium State ◽  
Static Characteristics ◽  
Automatic Pressure ◽  
Precision Level ◽  
Water Pipeline ◽  
The Stability ◽  
The Mathematical Model ◽  
Geometrical Dimensions ◽  
Novel Design

This paper presents a novel design of the automatic pressure balancing valve, used in the in-line balanced pressure (ILBP) proportioner for the foam firefighting system, at a required percentage of solution. Featured in a four-chamber configuration with a double-acting diaphragm actuator, it can automatically maintain the foam concentrate pressure with the pressure in the supply water pipeline, within a precision level of 0.02 MPa (or 1.3%), under the design operating condition. The static characteristics at the equilibrium state have been discussed in terms of poppet displacement with reference to the geometrical dimensions and operating pressures of the valve. The dynamic response of the valve during the startup has been examined through building the mathematical model of the forces on the valve and solving it numerically using MATLAB. The results show that the response time of the valve is always less than 0.01 s, which fully satisfies the stability and hysteresis requirement. The prototype has been tested in the laboratory, which agrees well with the numerical results. It was then successfully put into production, forming the first series of ILBP foam pump firefighting system in China.

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