Energy Approach for Determine Frequency and Amplitude of Vibration of Piping With Closed Side Branches

2015 ◽  
Author(s):  
Igor Orynyak ◽  
Iaroslav Dubyk ◽  
Anatolii Batura
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Calculation Method ◽  
Acoustic Vibration ◽  
Energy Functional ◽  
Energy Approach ◽  
Calculation Algorithm ◽  
Local Excitation ◽  
Resonance Frequencies ◽  
System Energy

This article suggests calculation method for frequency and amplitude of acoustic vibration in piping with closed side branches, caused by gaseous running flow. The calculation algorithm consists of following steps: i) local excitation system is defined; ii) different combinations of boundary conditions are formed; iii) for fixed pair of boundary conditions ratio of stored in system energy and radiated from boundaries energy is written; iv) for every frequency energy functional is maximized to find boundary conditions; v) resonance frequencies are determined from plotting a curve of maximal energy ratio vs. frequency. Energy approach was further developed to analyze amplitude of vibration. For amplitude determine balance between injected energy (which depends on the Strouhal number and is defined from experimental data for laboratory geometries), and radiated from boundaries energy is written.

Stochastic model of nonideal mixer. Boundary conditions in batch system

1984 ◽  
Vol 49 (2) ◽  
pp. 490-505
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Jiří Vlček
Keyword(s):  
Experimental Data ◽  
Stochastic Model ◽  
Boundary Conditions ◽  
Closed System ◽  
Batch System ◽  
Ideal Mixer

The earlier proposed general approach for description of the non-ideal mixer is coupled with corresponding boundary conditions for the closed system. Some simplifications in this procedure result in relations which are in agreement with experimental data.

Experimental and Theoretical Nonlinear Dynamic Response of Intact and Cracked Bone-Like Specimens With Various Boundary Conditions

2007 ◽  
Vol 129 (5) ◽  
pp. 541-549 ◽  
Author(s):  
Erick Ogam ◽  
Armand Wirgin ◽  
Z. E. A. Fellah ◽  
Yongzhi Xu
Keyword(s):  
Boundary Conditions ◽  
Duffing Oscillator ◽  
Contact Friction ◽  
Nonlinear Dynamic Response ◽  
Various Boundary Conditions ◽  
Vibration Data ◽  
Element Simulation ◽  
Resonance Frequencies ◽  
Vibration Experiment ◽  
Freely Suspended

The potentiality of employing nonlinear vibrations as a method for the detection of osteoporosis in human bones is assessed. We show that if the boundary conditions (BC), relative to the connection of the specimen to its surroundings, are not taken into account, the method is apparently unable to differentiate between defects (whose detection is the purpose of the method) and nonrelevant features (related to the boundary conditions). A simple nonlinear vibration experiment is described which employs piezoelectric transducers (PZT) and two idealized long bones in the form of nominally-identical drinking glasses, one intact, but in friction contact with a support, and the second cracked, but freely-suspended in air. The nonlinear dynamics of these specimens is described by the Duffing oscillator model. The nonlinear parameters recovered from vibration data coupled to the linear phenomena of mode splitting and shifting of resonance frequencies, show that, despite the similar soft spring behavior of the two dynamic systems, a crack is distinguishable from a contact friction BC. The frequency response of the intact glass with contact friction BC is modeled using a direct steady state finite element simulation with contact friction.

Natural Frequencies of Parallelogrammic Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method

1992 ◽  
Author(s):  
L. T. Lee ◽  
W. F. Pon
Keyword(s):  
Boundary Conditions ◽  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Energy Functional ◽  
Comprehensive Treatment ◽  
Energy Functionals ◽  
Simply Supported ◽  
Cartesian Coordinate

Abstract Natural frequencies of parallelogrammic plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generalted by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. The strain energy functional and kinetic energy functionals are transformed from Cartesian coordinate system to a skew coordinate system. The natural frequencies obtained by using the orthogonal polynomial functions are compared with those obtained by other methods with all four edges clamped boundary conditions and greet agreements are found between them. The natural frequencies for parallelogrammic plates with other boundary conditions, such as four edges simply supported, clamped-free and simply supported-free, are also obtained. This method is considered as a better and accurate comprehensive treatment for this type of problems.

scholarly journals AN INNOVATE METHOD OF THERMOGRAVIMETRIC DATA ANALYSIS

2021 ◽  
Vol 64 (3) ◽  
pp. 24-32
Author(s):  
Mihail V. Mal’ko ◽  
Sergej V. Vasilevich ◽  
Andrey V. Mitrofanov ◽  
Vadim E. Mizonov
Keyword(s):  
Experimental Data ◽  
Thermal Decomposition ◽  
Thermogravimetric Analysis ◽  
Kinetic Parameters ◽  
Calculation Method ◽  
Kinetic Calculation ◽  
Pyrolysis Mechanism ◽  
Total Mass Loss ◽  
Thermogravimetric Data ◽  
Heavy Tar

The objective of the study is to examine the Coats-Redfern approximation and to propose an innovative kinetic calculation method for the complex process of the heavy tar thermal decomposition under non-isothermal process. The thermal decomposition process was examined using the thermogravimetric analysis. There are several kinetic models proposed to analyze pyrolysis mechanism in terms of the formal reaction. In this manner, the kinetic parameters of the pyrolysis process can be evaluated based on total mass loss (thermogravimetric analysis –TGA). The TGA procedures can be conducted with isothermal or non-isothermal conditions, but the experimental data obtained according to this procedure have to be transformed into appropriate correlation. The obtained results have shown that the reaction takes place within temperature range of 540 K to 700 K and the inductive period of the process is about 224 min. Kinetic parameters were estimated with using of the conventional Coats-Redfern method. A new kinetic calculation method has been designed to provide a less laboriousness of identifications procedures compared with Coats-Redfern approximation and to take into account an induction time of the process. As the outcome of this study, it was shown that the kinetic parameters estimated with using of the proposed model-fitted method gives the more appropriate correlation in comparison with the conventional Coats-Redfern method. The proposed method uses the Coats-Redfern algorithm for evaluation of the reaction mechanism, but the value of the constant rate is defined directly from experimental data on the conversion rate.

scholarly journals DEVELOPMENT AND TESTING OF ALGORITHM FOR CALCULATION OF OPERATING PARAMETERS OF TRAWLING SYSTEMS

2019 ◽  
Vol 198 ◽  
pp. 221-229 ◽  
Author(s):  
E. A. Zakharov ◽  
O. N. Kruchinin ◽  
D. L. Shabelsky
Keyword(s):  
Experimental Data ◽  
Visual Basic ◽  
Educational Process ◽  
Resistance Force ◽  
Operating Parameters ◽  
Calculation Algorithm ◽  
Model Application ◽  
Bottom Trawling ◽  
Good Convergence ◽  
Expansion Force

Numerical model of trawling system is developed on the base of equilibrium principle, using F.I. Baranov’s scheme of its power and geometric parameters interdependence. The model application to bottom trawling takes into account the effect of bottom grounds on the resistance force and expansion force of the trawling system. Algorithm is proposed for calculation of operating parameters of bottom and midwater trawls, with an operation to minimize the error of iteration. The model and the calculation algorithm were tested in MS Office Excel environment, using Visual Basic programming, and showed good convergence of the calculated and experimental data that indicates reliability of the model. This algorithm and the program for calculation of operating parameters could be used for trawl designing, in accounting surveys to determine the trawl opening, and in educational process for training the industrial fishery scholars.

A Calculation Method to Investigate the Effects of Geometric Parameters and Operational Conditions on the Static Characteristics of Aerostatic Spherical Bearings

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Hailong Cui ◽  
Huan Xia ◽  
Dajiang Lei ◽  
Xinjiang Zhang ◽  
Zhengyi Jiang
Keyword(s):  
Experimental Data ◽  
Calculation Method ◽  
Reynolds Equation ◽  
Geometric Parameters ◽  
Static Characteristics ◽  
Optimal Parameters ◽  
Film Pressure ◽  
Operational Conditions ◽  
Pressure Distributions ◽  
Calculation Results

In this paper, a calculation method based on matlab partial differential equations (PDE) tool is proposed to investigate the static characteristics of aerostatic spherical bearings. The Reynolds equation of aerostatic spherical bearings is transformed into a standard elliptic equation. The effects of geometric parameters and operational conditions on the film pressure, bearing film force, and stiffness are studied. The axial and radial eccentricities result in different film pressure distributions; the bearing film force and stiffness are significantly influenced by geometric parameters and operational conditions. The relative optimal parameters are confirmed based on the calculation results. A comparison between the numerical and experimental results is also presented. The highest relative error between the numerical results and the experimental data is 11.3%; the calculation results show good agreements with the experimental data, thus verifying the accuracy of the calculation method used in this paper.

Acoustic Vibration and Mechanical In Vivo Analysis of the Hip Joint After a Total Hip Arthroplasty

2007 ◽  
Author(s):  
D. A. Glaser ◽  
R. D. Komistek ◽  
H. E. Cates ◽  
M. Mahfouz
Keyword(s):  
Femoral Head ◽  
Total Hip Replacement ◽  
Hip Joint ◽  
Hip Replacement ◽  
Acoustic Vibration ◽  
Valuable Insight ◽  
Acetabular Cup ◽  
Total Hip ◽  
Resonance Frequencies

The major complications following total hip replacement (THA) are implant loosening, dislocation, instability, fracture and infection. It is hypothesized that vibration, in the range of the resonance frequencies, may cause pain, bone degeneration and fracture. A further understanding of the physical response resulting from impact during femoral head sliding may lead to valuable insight pertaining to THA failure. Therefore, the first objective of this present study was to determine if frequencies propagating through the hip joint near resonant frequencies may lead to wear or loosening of the components. Recently, studies found that femoral head sliding, often referred to as hip separation, between the acetabulum cup and the femoral head does occur, which may also play a role in complications observed with THA today, but a the effects of hip separation and the causes of its occurrence has not been studied as jet. Therefore, the second objective of this study was to determine if a sound sensor, externally attached, could be used to correlate impact loading sounds from femoral head sliding in the acetabular cup. Additional objective of this study was to develop a mathematical model that better simulates the in vivo loading conditions of total hip replacement patients using in vivo fluoroscopic and ground reaction data as input.

scholarly journals Plastic limit bearing calculation of blasting-roof in deep hole mining and its applications

2019 ◽  
Vol 6 (7) ◽  
pp. 190074
Author(s):  
Wei Wang ◽  
Zhouquan Luo ◽  
Yaguang Qin ◽  
Jun Xiang
Keyword(s):  
Boundary Conditions ◽  
Calculation Method ◽  
Virtual Work ◽  
Theoretical Calculations ◽  
Limit State ◽  
Mechanical Analysis ◽  
Deep Hole ◽  
Plastic Limit ◽  
Analysis Model ◽  
Various Boundary Conditions

A plastic bearing calculation method for a blasting-roof is proposed to solve the problem of determining the blasting-roof thickness in deep hole mining. A mechanical analysis model for the plastic bearing was built for the typical boundary conditions of blasting-roofs. The external and internal work of the blasting-roof are equal under the plastic limit state through calculation. The limit bearing formulae of blasting-roofs under various boundary conditions were derived based on the principle of virtual work. A Vertical Crater Retreat stope was taken as the object, and the safe blasting-roof thickness was determined to be 6 m using the derived formula (considering the safety coefficient). A numerical model of stope was constructed using the Surpac-Flac3D technique, while the blasting-roof stability was simulated under different thicknesses. Variations in the simulated indexes (stress and plastic zone volume) prove that the theoretical calculations are reliable. The plastic bearing calculation method can provide a new method to determine the blasting-roof thickness in deep hole mining.

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