Optimal Design of a Scroll Case with Natural Frequency Constraints

2011 ◽  
Vol 94-96 ◽  
pp. 1719-1722
Author(s):  
Xin Li Bai ◽  
Gui Rong Liu ◽  
Song An Zhang
Keyword(s):  
Optimal Design ◽  
Natural Frequency ◽  
Analytical Method ◽  
Mass Matrix ◽  
Program System ◽  
Structural Dynamic ◽  
Frequency Constraints ◽  
Frequency Sensitivity ◽  
Scroll Case ◽  
Calculation Results

In this paper, sensitivity formula with analytical method is derived for calculating structural natural frequency, and the partial derivative of plate element stiffness matrix and mass matrix with respect to design variables are gained respectively. Computer programs for computing frequency sensitivity with analytical method are developed. And combining it with large finite element structural analysis software ADINA, the optimal design software based on genetic algorithms, a structural dynamic optimization program system is constituted for computing structural natural frequency sensitivity with analytical method. Finally, the program system is applied to the optimal design of a turbine scroll case of a hydropower station (taking into account the natural frequency constraints). Calculation results show that analytical method presented in the paper is of higher computational precision, good stability, convenient to use, and can be popularized. Calculation results obtained the approval of client and used in real engineering.

scholarly journals Analytical Method for Geometric Nonlinear Problems Based on Offshore Derricks

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 610
Author(s):  
Chunbao Li ◽  
Hui Cao ◽  
Mengxin Han ◽  
Pengju Qin ◽  
Xiaohui Liu
Keyword(s):  
Analytical Method ◽  
Bending Moment ◽  
Nonlinear Problems ◽  
Weather Conditions ◽  
Order Effect ◽  
Practical Calculation ◽  
Geometrically Nonlinear ◽  
Uniform Load ◽  
Safety Research ◽  
Calculation Results

The marine derrick sometimes operates under extreme weather conditions, especially wind; therefore, the buckling analysis of the components in the derrick is one of the critical contents of engineering safety research. This paper aimed to study the local stability of marine derrick and propose an analytical method for geometrically nonlinear problems. The rod in the derrick is simplified as a compression rod with simply supported ends, which is subjected to transverse uniform load. Considering the second-order effect, the differential equations were used to establish the deflection, rotation angle, and bending moment equations of the derrick rod under the lateral uniform load. This method was defined as a geometrically nonlinear analytical method. Moreover, the deflection deformation and stability of the derrick members were analyzed, and the practical calculation formula was obtained. The Ansys analysis results were compared with the calculation results in this paper.

Speed Dependency of Coupled Rotor-Blade Torsional Natural Frequencies

2013 ◽  
Author(s):  
Ulrich Ehehalt ◽  
Balazs Becs ◽  
Xiaoping Zhou ◽  
Stefan Güllenstern
Keyword(s):  
Natural Frequency ◽  
Rotor Blade ◽  
Natural Frequencies ◽  
Low Pressure ◽  
Campbell Diagram ◽  
Calculation Results ◽  
Measured Speed ◽  
High Level ◽  
Blade Model ◽  
Proper Analysis

The natural frequencies of blades depend on the rotational speed of the rotor train as the stiffness changes with centrifugal loading. In the case of low pressure turbines with shrunk-on-disc design the coupled rotor-blade torsional natural frequencies can also show this property. For proper analysis of the speed dependency, a complete rotor-blade model which takes the elasticity of the blades into account is required. In this paper the torsional natural frequencies calculated with a complete rotor-blade model are compared with those calculated with a model in which blade elasticity is not included. The analysis clearly demonstrates that calculations without blade elasticity lead to different natural frequencies. By modeling the complete rotor and taking blade elasticity into account, it is demonstrated that the torsional natural frequencies of a complete rotor-blade model can also become speed dependent. As a consequence, a distinction between the natural frequencies at nominal speed and natural frequency at critical speeds becomes necessary. In the following, measured torsional natural frequencies at different rotating speeds of an individual low pressure rotor are presented. A comparison of the measured speed dependency of the torsional natural frequency with calculation results thereby taking the blade elasticity into account is conducted. The analysis shows that the measured speed dependency can be predicted with a high level of accuracy and can become important for modes which are dominated by the blades of the last stages. As a consequence of this analysis, a clear distinction between natural frequency at nominal and at critical speed has to be made for certain rotor and blade designs. It is shown that the use of the Campbell diagram is highly beneficial for designing rotor trains with large blades with regard to their torsional vibration behavior.

An Analytical Method of Analyzing the Heat Conduction for the Unequal Cross-Section Straight Fin

2013 ◽  
Vol 365-366 ◽  
pp. 1211-1216
Author(s):  
Fan Zhang ◽  
Peng Yun Song
Keyword(s):  
Heat Conduction ◽  
Cross Section ◽  
Analytical Method ◽  
Thermal Analyses ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
Calculation Results ◽  
The Cross ◽  
Analytical Expressions

The cross-section area of straight fin is often considered to be equal in the thermal analyses of straight fin, but sometimes it is unequalin actual situation. Taking a straight fin with two unequal cross-sectional areas as an example,an analytical method of heat conduction for unequal section straight fin is presented. The analytical expressions of temperature field and heat dissipating capacity about the fin,which has a smaller cross-section area near the fin base and a larger one, is obtained respectively. The calculation results of the unequal cross-section are fully consistent with the equal area one, so the method is proved right. The results show that the larger the cross section areanear the base,the better is the heat transfer, and the temperature at the base with larger cross-section area is lower than that with smaller cross-section area when the amount of heat is fixed.

scholarly journals KARAKTERISTIK DINAMIKA STRUKTUR SATELIT MIKRO LAPAN-TUBSAT

2010 ◽  
Vol 3 (2) ◽  
Author(s):  
Robertus Heru Trihajanto ◽  
Sugiarmadji HPS
Keyword(s):  
Resonance Frequency ◽  
Dynamic Characteristic ◽  
Natural Frequency ◽  
Normal Modes ◽  
Longitudinal Direction ◽  
Mode Shapes ◽  
Al Alloy ◽  
Fem Modeling ◽  
Lateral Direction ◽  
Structural Dynamic

The TUBSAT-LAPAN micro satellite is planned to be launched using PSLV rocket. The design constraints of the mechanical system of the satellite are able to accomodate structural requirment for PSLV, which are first resonance frequency in the rocket longitudinal axis 90 Hz and first resonance frequency in the lateral axis 45 Hz. Therefore, the structural dynamic characteristic data of the satellite is important to be evaluated, such as natural frequency and mode shapes of the satellite structures, The normal modes analysis made is done usingh Finite Element Methods commercial software NASTRAN. To simplify the FEM modeling the satellite components inside the compartmens is replaced by a dummy load simulating their contribution to satellite mass, centerof gravity and inertia, which was made by the same material as the satellite's structure, i.e. Al-Alloy 2024T351. Meanwhile, the FEM modeling for both the UHF antena used the Stainless Steel materials as the real antena. The analysis results show that the lowest local natural frequency of the satellite occurs on the UHF antena. The first natural frequency of the antena structures in lateral direction is 52,29 Hz. The first natural frequency of the satellite in lateral direction 151.47 Hz completing the satellite integration, vibration test was done to the satellite. The test shows that the first global frequency is 72-75 Hz in the lateral direction and 148 Hz in longitudinal direction. Structural dynamic characteristic of TUBSAT_LAPAN micro satellite in free flying condition are also analyzed using no-constraint condition to check the safe separation clearance scenario. The results show that the first natural frequencies for satellite structures (combination) become very small, less than 0.00032 Hz. But, the lowest of the first natural frequency for UHF antena structures is almost constant, 52.30 Hz in lateral direction.

The Research of Calculation Method on Vertical Natural Frequency of the New Full-Prefabricated Floor

2016 ◽  
Vol 846 ◽  
pp. 506-511
Author(s):  
Chong Fang Sun ◽  
Shu Ting Liang ◽  
Xiao Jun Zhu
Keyword(s):  
Numerical Simulation ◽  
Natural Frequency ◽  
Calculation Method ◽  
Variable Stiffness ◽  
Series Method ◽  
Numerical Simulation Result ◽  
Stiffness Method ◽  
Calculation Results ◽  
New Type ◽  
Test Result

New-type floor is composed of three kinds of slabs joined together through fittings. It is a kind of anisotropic two-way slab. In order to study the calculation method of natural frequency, series method, variable thickness method and variable stiffness method are adopted to calculate the natural frequency. The calculation results of three methods are compared with test result and numerical simulation result. The conclusion is that the calculation result of the variable stiffness method is the closest to the real natural frequency of new-type floor.

Study on Dynamic Characteristics and Parameter Sensitivity of Three Spans Prestressed Continuous Beam

2013 ◽  
Vol 351-352 ◽  
pp. 386-391
Author(s):  
Lu Ning Shi ◽  
Hao Xiang He ◽  
Wei Ming Yan ◽  
Yan Jiang Chen ◽  
Da Zhang
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Frequency Equation ◽  
Dynamic Parameters ◽  
Continuous Beam ◽  
Analytical Expression ◽  
Beam Dynamic ◽  
Frequency Sensitivity ◽  
The Impact ◽  
Good Agreement

Established the three spans prestressed continuous beam dynamic equation, obtained analytical expression of frequency equation. To solve the frequency equation for natural frequency, and compared with the finite element numerical analysis results, the frequency both with analytical expression and with finite element are in good agreement. The formula can be obtained accurately the dynamic parameters of three spans prestressed continuous beam such as frequency. At the same time, the paper also studied the natural frequency sensitivity analysis of three spans prestressed continuous beam, and focuses on the impact on the frequency with effective prestress and prestressed eccentricity.

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