scholarly journals The approximate calculation of the natural frequencies of a Stockbridge type vibration damper and analysis of natural frequencies' sensitivity to the structural parameters

2021 ◽  
Vol 12 (2) ◽  
pp. 863-873
Author(s):  
Qing Yin ◽  
Jianli Zhao ◽  
Yong Liu ◽  
Yisheng Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Approximate Calculation ◽  
Natural Frequencies ◽  
Second Order ◽  
Design Parameters ◽  
Gyration Radius ◽  
Vibration Damper ◽  
First Order ◽  
Highly Sensitive ◽  
Eccentric Distance

Abstract. Vibration damper is widely used in overhead transmission lines to alleviate aeolian vibration. Its natural frequencies are important parameters for a vibration damper. In this paper, the approximate calculation formulas of natural frequencies of the one-side subsystem of a Stockbridge type vibration damper were derived and the design sensitivity analysis of the natural frequencies was studied using partial differential equations with respect to each concerned parameter including the length of the steel strand, the mass of the counterweight, the eccentric distance, and the radius of gyration of the counterweight. Through a case study that considered a variation of up to ±30 % in the values of the design parameters, the exact calculation and approximate calculation results of the natural frequencies were analysed, and the sensitivity of the vibration damper's natural frequencies to the design parameters was studied. The results show that, within the range of the parameters used in this study, the approximately calculated first-order frequency is lower than the exact values, whereas the approximately calculated second-order frequency is larger than the exact values. The sensitivity analysis indicates that the first-order frequency is highly sensitive to the steel strand's length, whereas it is moderately sensitive to the counterweight's mass and slightly sensitive to the eccentric distance and the gyration radius of the counterweight; the second-order frequency is highly sensitive to the steel strand's length and the gyration radius of the counterweight, moderately sensitive to the counterweight's mass, and slightly sensitive to the eccentric distance. It will provide theoretical guidance and approximate analysis method in engineering for the design of the vibration damper.

scholarly journals Natural Frequency Sensitivity Analysis of Fire-Fighting Jet System with Adaptive Gun Head

Processes ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 808 ◽  
Author(s):  
Xiaoming Yuan ◽  
Xuan Zhu ◽  
Chu Wang ◽  
Lijie Zhang ◽  
Yong Zhu
Keyword(s):  
Sensitivity Analysis ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Fire Fighting ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Design Parameters ◽  
Parameter Method ◽  
First Order ◽  
Typical Design

The gun head is the end effector of the fire-fighting jet system. Compared with a traditional fixed gun head, an adaptive gun head has the advantages of having an adjustable nozzle opening, a wide applicable flow range, and a high fire-extinguishing efficiency. Thus, the adaptive gun head can extinguish large fires quickly and efficiently. The fire-fighting jet system with an adaptive gun head has fluid-structure interaction and discrete-continuous coupling characteristics, and the influence of key design parameters on its natural frequencies needs to be determined by a sensitivity analysis. In this paper, the dynamic model and equations of the jet system were established based on the lumped parameter method, and the sensitivity calculation formulas of the natural frequency of the jet system to typical design parameters were derived. Natural frequencies and mode shapes of the jet system were determined based on a mode analysis. The variation law of the sensitivity of the natural frequency of the jet system to typical design parameters was revealed by the sensitivity analysis. The results show that the fluid mass inside the spray core within a certain initial gas content is the most important factor affecting the natural frequency of the jet system. There was only a 0.51% error between the value of the first-order natural frequency of the jet system determined by the modal experiment and the theoretical one, showing that good agreement with the first-order natural frequency of the jet system was found. This paper provides a theoretical basis for the dynamic optimization design of the adaptive gun head of the fire water monitor.

Optimal Capacitors Placement of Distribution Systems Using 2nd Order Power Loss Sensitivity Analysis and Hierarchical Clustering

2014 ◽  
Vol 986-987 ◽  
pp. 377-382 ◽  
Author(s):  
Hui Min Gao ◽  
Jian Min Zhang ◽  
Chen Xi Wu
Keyword(s):  
Sensitivity Analysis ◽  
Hierarchical Clustering ◽  
Distribution System ◽  
Power Flow ◽  
Distribution Systems ◽  
Reactive Power ◽  
Digital Simulation ◽  
Second Order ◽  
First Order ◽  
The Impact

Heuristic methods by first order sensitivity analysis are often used to determine location of capacitors of distribution power system. The selected nodes by first order sensitivity analysis often have virtual high by first order sensitivities, which could not obtain the optimal results. This paper presents an effective method to optimally determine the location and capacities of capacitors of distribution systems, based on an innovative approach by the second order sensitivity analysis and hierarchical clustering. The approach determines the location by the second order sensitivity analysis. Comparing with the traditional method, the new method considers the nonlinear factor of power flow equation and the impact of the latter selected compensation nodes on the previously selected compensation location. This method is tested on a 28-bus distribution system. Digital simulation results show that the reactive power optimization plan with the proposed method is more economic while maintaining the same level of effectiveness.

First- and Second-Order Design Sensitivity Analysis Scheme Based on Trefftz Method

1999 ◽  
Vol 121 (1) ◽  
pp. 84-91 ◽  
Author(s):  
E. Kita ◽  
Y. Kataoka ◽  
N. Kamiya
Keyword(s):  
Sensitivity Analysis ◽  
Design Sensitivity ◽  
Second Order ◽  
Design Sensitivity Analysis ◽  
Design Parameters ◽  
Trefftz Method ◽  
Analysis Scheme ◽  
Complete Functions ◽  
Approximate Expressions ◽  
Physical Quantities

This paper presents a new scheme for the first- and second-order design sensitivity analysis of the two-dimensional elastic problem by using Trefftz method. In the Trefftz method, the physical quantities are approximated by superposition of regular T-complete functions. Therefore, direct differentiation of the approximate expressions with respect to design parameters leads to the regular expressions of the sensitivities. The present schemes are applied to some examples in order to confirm the validity.

Probabilistic Optimal Design Using Second Moment Criteria

1988 ◽  
Vol 110 (3) ◽  
pp. 324-329 ◽  
Author(s):  
A. D. Belegundu
Keyword(s):  
Finite Element Method ◽  
Sensitivity Analysis ◽  
Optimal Design ◽  
Design Sensitivity ◽  
Design Criterion ◽  
Second Order ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Programming Technique ◽  
Second Moment

Probability-based optimal design of structures is presented. The emphasis here is to develop a practical approach to optimal design given random design parameters. The method is applicable to structures which are modeled using the finite element method. The Hasofer-Lind (H-L) second-moment design criterion is used to formulate the general design problem. A method for calculating the sensitivity coefficients is presented, which involves second-order design sensitivity analysis. The importance of second order derivatives is established. A nonlinear programming technique is used to solve the problem. Numerical results are presented, where stiffness parameters are treated as random variables.

Second Order Wave Loads on TLP-TAD Multi-Body System

2017 ◽  
Author(s):  
Miguel A. M. Ramirez ◽  
Antonio Carlos Fernandes
Keyword(s):  
Wave Amplitude ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Direct Method ◽  
Second Order ◽  
Order Effects ◽  
Wave Loads ◽  
Body System ◽  
First Order ◽  
Multi Body

The motions of floating moored structures are affected by first order wave loads which are proportional to the wave amplitude and associated with the wave frequency. On the other hand, second order wave loads are proportional to the square of the wave amplitude and related to the sum or difference of a pair of frequencies of the irregular sea. Although the second order loads are usually smaller compared to the first order loads, these loads can excite resonance motions in frequencies that the system has very low damping. Therefore, second order wave loads have particular importance in the design of mooring systems. The multi-body system composed by Tension Leg Platform (TLP) and Tender Assisted Drilling (TAD) is particularly susceptible to the second order effects, due to the very low natural frequencies of their horizontal modes and the very high natural frequencies of the vertical modes of the TLP. This work presents a numerical study of second order wave loads on the TLP-TAD multi-body system. An extensive hydrodynamic analysis focus on the hydrodynamic interactions between the floaters and how these effects modify the second order loads on the platforms was performed. The second order quadratic transform functions (QTFs) were evaluated using the indirect and the direct method. Moreover, the importance of the free surface integral was checked. Finally, the accuracy of Newman approximation for the low-frequency QTF was evaluated.

Computational Efficiency of First and Second Order Sensitivity Analysis Methods for Dynamic Systems

1993 ◽  
Author(s):  
Qiushi Cao ◽  
Prakash Krishnaswami
Keyword(s):  
Sensitivity Analysis ◽  
Finite Difference ◽  
Dynamic Systems ◽  
Computational Efficiency ◽  
Computing Time ◽  
Design Sensitivity ◽  
Second Order ◽  
First Order ◽  
Comparison Results ◽  
Finite Difference Solution

Abstract First and second order design sensitivity information have become very popular in engineering design, due to the recent development of appropriate methodology and computer technology. This paper presents an empirical study of the computing effort required for computing first and second order design sensitivity information for constrained dynamic mechanical systems and compares the relative efficiency of analytical and finite difference method. Four typical examples have been solved, with the computing time being recorded in each case. The time comparison results indicate that it is generally much more efficient to produce first order design sensitivity information by a direct analytical method than by finite differencing. For second order design sensitivity analysis, the results indicate that a purely analytical solution is usually more efficient than a pure finite difference solution. However, a hybrid scheme appears to be very competitive in terms of computational efficiency.

A Study on Flange Lathe of Double-Tool Holder Based on Optimization Design Method of FE

2011 ◽  
Vol 48-49 ◽  
pp. 118-122
Author(s):  
Fu Qiang Ying ◽  
Yi Wang ◽  
Ling Dong Wu ◽  
Liang Yi Li
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Design ◽  
Natural Frequencies ◽  
Design Method ◽  
Dynamic Performance ◽  
The Other ◽  
Design Parameters ◽  
Fe Model ◽  
Tool Holder ◽  
Dynamic Performances

With the optimization design method of FE,the FE model of vertical flange lathe beam of double-tool holder was established,the sensitivity analysis of dynamic performance for the machine tool was performed based on presented modal analysis and probability analysis.The influence rules of the first four natural frequencies affected by the design parameters of the lathe beam were confirmed and the weaknesses of it were indicated as well.Then, the structure of the lathe beam was optimized.As a result ,the dynamic performances of the lathe beam are improved and it offers the basis for the optimization design of the other lathe parts.

On Transverse Vibrations of Rectangular Plates of Unidirectional Parabolic Thickness Variation

2005 ◽  
Author(s):  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Natural Frequencies ◽  
Order Approximation ◽  
Second Order ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Partial Differential ◽  
First Order ◽  
Transverse Vibrations

This paper presents an approach for finding the solution of partial differential equation describing the motion of transverse vibrations of rectangular plates of unidirectional convex parabolic varying thickness. The partial differential equation consists of three operators: fourth-order spatial-dependent, second-order spatial-dependent, and second-order time-dependent. Using the method of multiple scales, the partial differential equation has been reduced to two simpler partial differential equations which can be analytically solved and which represent two levels of approximation. The first partial differential equation was a homogeneous equation and consisted of two operators, the fourth-order spatial-dependent and second-order time-dependent. Using the factorization method, so-called zero-order approximation of the exact solution has been found. The second partial differential equation was an inhomogeneous equation. Its solution, so-called first-order approximation of the exact solution has been found. This way the first-order approximations of the natural frequencies and mode shapes are found. Various boundary conditions can be considered. The influence of Poisson’s ratio on the natural frequencies and mode shapes could be further studied using the approximations reported here. This approach can be extended to nonlinear, and/or forced vibrations.

scholarly journals Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: II. Effects of Imprecisely Known Microscopic Scattering Cross Sections

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4114 ◽  
Author(s):  
Fang ◽  
Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Second Order ◽  
The Other ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
First Order ◽  
Scattering Cross ◽  
Analysis Methodology ◽  
Scattering Cross Sections

This work continues the presentation commenced in Part I of the second-order sensitivity analysis of nuclear data of a polyethylene-reflected plutonium (PERP) benchmark using the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM). This work reports the results of the computations of the first- and second-order sensitivities of this benchmark’s computed leakage response with respect to the benchmark’s 21600 parameters underlying the computed group-averaged isotopic scattering cross sections. The numerical results obtained for the 21600 first-order relative sensitivities indicate that the majority of these were small, the largest having relative values of O (10−2). Furthermore, the vast majority of the (21600)2 second-order sensitivities with respect to the scattering cross sections were much smaller than the corresponding first-order ones. Consequently, this work shows that the effects of variances in the scattering cross sections on the expected value, variance, and skewness of the response distribution were negligible in comparison to the corresponding effects stemming from uncertainties in the total cross sections, which were presented in Part I. On the other hand, it was found that 52 of the mixed second-order sensitivities of the leakage response with respect to the scattering and total microscopic cross sections had values that were significantly larger than the unmixed second-order sensitivities of the leakage response with respect to the group-averaged scattering microscopic cross sections. The first- and second-order mixed sensitivities of the PERP benchmark’s leakage response with respect to the scattering cross sections and the other benchmark parameters (fission cross sections, average number of neutrons per fission, fission spectrum, isotopic atomic number densities, and source parameters) have also been computed and will be reported in subsequent works.

scholarly journals Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: I. Effects of Imprecisely Known Microscopic Total and Capture Cross Sections

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4219 ◽  
Author(s):  
Cacuci ◽  
Fang ◽  
Favorite
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Neutron Transport ◽  
Expected Value ◽  
Second Order ◽  
Numerical Results ◽  
Reactor Physics ◽  
Adjoint Sensitivity ◽  
Total Cross Sections ◽  
First Order

The subcritical polyethylene-reflected plutonium (PERP) metal fundamental physics benchmark, which is included in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook, has been selected to serve as a paradigm illustrative reactor physics system for the application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) that was developed by Cacuci. The 2nd-ASAM enables the exhaustive deterministic computation of the exact values of the 1st-order and 2nd-order sensitivities of a system response to the parameters underlying the respective system. The PERP benchmark is numerically modeled in this work by using the deterministic multigroup neutron transport equation discretized in the spatial and angular independent variables. Thus, the numerical model of the PERP benchmark developed includes the following imprecisely known uncertain parameters: 180 group-averaged total microscopic cross sections, 21,600 group-averaged scattering microscopic cross sections, 120 fission process parameters, 60 fission spectrum parameters, 10 parameters describing the experiment’s nuclear sources, and six isotopic number densities. Thus, the numerical simulation model for the PERP benchmark comprises 21,976 uncertain parameters, which implies that, for any response of interest, there are a total of 21,976 first-order sensitivities and 482,944,576 second-order sensitivities with respect to the model parameters. Computing these sensitivities exactly represents the largest sensitivity analysis endeavor ever carried out in the field of reactor physics. Only 241,483,276 are distinct from each other, and some of these turned out to be zero due to the symmetry of the 2nd-order sensitivities. The numerical results for all of these sensitivities, together with discussions of their major impacts, will be presented in a sequence of publications in the Special Issue of Energies dedicated to “Sensitivity Analysis, Uncertainty Quantification and Predictive Modeling of Nuclear Energy Systems”. This work is the first in this sequence, presenting formulas of general use for neutron transport problems, along with the numerical results that were produced by these formulas for the 180 first-order and 32,400 second-order sensitivities of the PERP leakage response with respect to the neutron transport model’s group-averaged isotopic total cross sections. For comparison, this work also presents formulas of general use and numerical results for the 180 first-order and 32,400 second-order sensitivities of the PERP leakage response with respect to the neutron transport model’s group-averaged isotopic capture cross sections. It has been widely believed hitherto that, for reactor physics systems modeled by the neutron transport or diffusion equations, the second-order sensitivities are all much smaller than the first-order ones. However, contrary to this widely held belief, the numerical results that were obtained in this work prove, for the first time ever, that many of the 2nd-order sensitivities are much larger than the corresponding 1st-order ones, so their effects can become much larger than the corresponding effects stemming from the 1st-order sensitivities. For example, the 2nd-order sensitivities of the PERP leakage response cause the expected value of this response to be significantly larger than the corresponding computed value. The importance of the 2nd-order sensitivities increases as the relative standard deviations for the cross sections increase. For the extreme case of fully correlated cross sections, for example, neglecting the 2nd-order sensitivities would cause an error as large as 2000% in the expected value of the leakage response and up to 6000% in the variance of the leakage response. The significant effects of the mixed 2nd-order sensitivities underscore the need for reliable values for the correlations that might exist among the total cross sections, which are unavailable at this time. The 2nd-order sensitivities with respect to the total cross sections also cause the response distribution to be skewed towards positive values relative to the expected value. Hence, neglecting the 2nd-order sensitivities could potentially cause very large non-conservative errors by under-reporting of the response variance and expected value.

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