A mathematical model to describe the dynamic response of a spruce tree to the wind

Trees ◽  
1998 ◽  
Vol 12 (6) ◽  
pp. 385 ◽  
Author(s):  
Tobias Kerzenmacher ◽  
Barry Gardiner
Keyword(s):  
Mathematical Model ◽  
Dynamic Response

Dynamic Response Modeling of Fluid-Solid Coupling for Wet Brake Disc

2013 ◽  
Vol 475-476 ◽  
pp. 1397-1401 ◽  
Author(s):  
Xun Jia Zheng ◽  
Tian Hong Luo ◽  
Ce Jia
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Three Dimensional ◽  
Brake Disc ◽  
Field Variation ◽  
Thermal Stress Field ◽  
Friction Plate ◽  
Transient Thermal ◽  
Response Modeling ◽  
Surface Temperature Field

Due to the poor conditions of wet brake cooling and the high temperature of the working characteristics, this paper intended to introduce the oil film vadose between the brake linings, considered the variation of volume of grooves on the friction plate, and then proposes the three-dimensional transient dynamic response of fluid-solid coupling mathematical model. By numerical analysis of the disc transient thermal stress field distribution on the friction plate, the friction surface temperature field variation is obtained. Finally, the results shows that the mathematical model is effective and feasible.

A Simple Mathematical Model of Metal Hydride Elements for Thermal Powered Plants

1993 ◽  
Vol 207 (2) ◽  
pp. 89-94 ◽  
Author(s):  
V M Liventsov ◽  
A V Kuznetsov
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Thermal Energy ◽  
Metal Hydride ◽  
Simple Mathematical Model ◽  
Model Calculations ◽  
Stationary Method ◽  
Different Types ◽  
Simplified Mathematical Model

This paper proposes a model for metal hydride elements which are used as hydrogen accumulators for different types of thermal powered systems. The quasi-stationary method has been used to obtain a simplified mathematical model. Calculations to predict the dynamic response of a thermal energy engine have been made.

Dynamics of the Head-Neck Complex in Response to the Trunk Horizontal Vibration: Modeling and Identification

2003 ◽  
Vol 125 (4) ◽  
pp. 533-539 ◽  
Author(s):  
Mohammad A. Fard ◽  
Tadashi Ishihara ◽  
Hikaru Inooka
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Fourth Order ◽  
Optimization Method ◽  
Horizontal Vibration ◽  
Domain Identification ◽  
Viscoelastic Parameters ◽  
Resonance Frequencies ◽  
Fourth Order Model ◽  
Head Neck

Although many studies exist concerning the influence of seat vibration on the head in the seated human body, the dynamic response of the head-neck complex (HNC) to the trunk vibration has not been well investigated. Little quantitative knowledge exists about viscoelastic parameters of the neck. In this study, the dynamics of the HNC is identified when it is exposed to the trunk horizontal (fore-and-aft) vibration. The frequency response functions between the HNC angular velocity and the trunk horizontal acceleration, corresponding to four volunteers, are obtained in the frequency range of 0.5 Hz to 10 Hz. A fourth-order mathematical model, derived by considering a double-inverted-pendulum model for the HNC, is designed to simulate the dynamic response of the HNC to the trunk horizontal vibration. The frequency domain identification method is used to determine the coefficients of the mathematical model of the HNC. Good agreement has been obtained between experimental and simulation results. This indicates that the system, similar to the designed fourth-order model, has mainly two resonance frequencies. The viscoelastic parameters of the neck, including the spring and damping coefficients, are then obtained by use of the optimization method.

scholarly journals A Mathematical Model for Forced Vibration of Pre-Stressed Piezoelectric Plate-Strip Resting On Rigid Foundation

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 419-431
Author(s):  
Ahmet Daşdemir
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Initial Stress ◽  
Piezoelectric Plate ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rigid Foundation ◽  
Time Harmonic ◽  
Governing System ◽  
Plate Strip

A mathematical model to investigate the dynamic response of a piezoelectric plate-strip with initial stress under the action of a time-harmonic force resting on a rigid foundation is presented within the scope of the three-dimensional linearized theory of electro-elasticity waves in initially stressed bodies (TLTEEWISB). The governing system of equations of motion is solved by employing the Finite Element Method (FEM). The numerical results illustrating the dependencies of different problem parameters are investigated. In particular, the influence of a change in the value of the initial stress parameter on the dynamic response of the plate-strip is discussed.

Dynamic response of a bi-axially pre-stressed bi-layered plate resting on a rigid foundation under a harmonic force

2019 ◽  
Vol 234 (3) ◽  
pp. 784-795
Author(s):  
Ahmet Daşdemir
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Three Dimensional ◽  
Dimensionless Frequency ◽  
Rigid Foundation ◽  
Layered Plate ◽  
Harmonic Force ◽  
Time Harmonic ◽  
Linearized Theory ◽  
Complete Contact

This study aims to investigate the forced vibrations caused by a time-harmonic force from a pre-stressed bi-layered plate resting on a rigid foundation under the action of a time-harmonic pointwise loading. Our investigation was conducted according to a piecewise homogeneous body model utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies. Throughout this study, we assumed that there is complete contact between the plate and the rigid foundation. The purpose of this study is threefold: the development of a mathematical model to investigate the dynamic response of the pre-stressed bi-layered plate, the analysis of the frequency response of the plate under consideration, and finally, demonstrating the relationship between the initial stress and the dimensionless frequency of the plate. We solved the mathematical model by employing the finite element method. We present our numerical results on the dynamic behavior of the plate. In particular, we have shown that an increase in the values of the aspect ratio of a plate under fixed thickness leads to a decrease in the normal stress resonance values.

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.

A Mathematical Model for Bone Remodeling

1999 ◽  
Author(s):  
Scott J. Hazelwood ◽  
R. Bruce Martin ◽  
Juan J. Rodrigo ◽  
Mark M. Rashid
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Dynamic Response ◽  
Finite Element Model ◽  
Bone Remodeling ◽  
Element Model ◽  
Oscillatory Behavior ◽  
Bone Diseases ◽  
Damage Repair ◽  
Sensitive Behavior

Abstract A bone remodeling algorithm based on disuse and damage repair was developed in this study. Important elements of the bone remodeling process, including the delay between resorption and formation of bone and the resulting porosity, were included in the algorithm. A study of the dynamic response of the algorithm indicated oscillatory behavior for disuse situations and critically sensitive behavior in overload situations beyond a threshold load. Application of the algorithm to a finite element model of the femur reproduced the observed internal structure. The model is being used in further studies to investigate remodeling around implant stems and bone diseases and their treatment.

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.

Mathematical Model of Cable Winding/Unwinding System

2017 ◽  
Vol 35 (1) ◽  
pp. 131-143 ◽  
Author(s):  
Lj. B. Kevac ◽  
M. M. Filipovic
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Experimental Analysis ◽  
Software Package ◽  
Mathematical Formulation ◽  
Theoretical Contribution ◽  
Cable Length ◽  
Simulation Results ◽  
Dynamic Variables

AbstractThe general form of mathematical model of cable winding/unwinding system is defined for several different constructions. The novelty of this mathematical model is detection and mathematical formulation of influence of new dynamic variables: winding/unwinding radius and cable length on dynamic response of cable winding/unwinding system. The validity of the obtained theoretical contribution has been illustrated through one case study by using a newly developed software package CWUSOFT which was generated in MATLAB. Theoretical and simulation results are confirmed through the experimental analysis of one novel construction of the cable winding/unwinding system.

Unified Power Quality Conditioner Using a Fuzzy Controller

2010 ◽  
Vol 11 (4) ◽  
Author(s):  
Chirag Patel ◽  
Ranjit Mahanty
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Power Quality ◽  
Set Theory ◽  
Fuzzy Controller ◽  
Pi Controller ◽  
Linguistic Variable ◽  
Unified Power Quality Conditioner ◽  
Three Phase ◽  
Power Quality Conditioner

The paper presents a three-phase unified power quality conditioner using a fuzzy controller. The fuzzy controller replaces the conventional PI controller in this work. The results obtained through the fuzzy controller are found superior to those obtained through conventional PI controller in terms of dynamic response. This is because of the fact that the fuzzy controller is based on a linguistic variable set theory and does not require a mathematical model of the system. Moreover, the tedious method of tuning the PI controller is not required in case of fuzzy controller. Simulations are carried out using MATLAB/Simulink to validate the theoretical findings.

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