Sensitivity Analysis of a Flexible Marine Riser Using Sobol’s Method

2017 ◽  
Author(s):  
Firooz Bakhtiari-Nejad ◽  
Arastou Azimi ◽  
Robert G. Parker
Keyword(s):  
Sensitivity Analysis ◽  
Structural Parameters ◽  
Unit Length ◽  
Mode Shapes ◽  
External Diameter ◽  
Marine Riser ◽  
Assumed Mode Method ◽  
Flexible System ◽  
Mode Method ◽  
Sobol’S Method

In this research, sensitivity analysis of upper and lower end angles in addition to the midpoint displacement of the flexible marine riser with respect to structural parameters such as: uniform mass per unit length, external diameter and the tension of the riser are conducted. Harsh environmental circumstances of ocean flow in addition to exerted tension on top of risers may lead to irreparable damages, so it is important to have a parametric study of dynamic response before it is controlled. The “Sobol” method is applied here as a reliable statistical method to sensitivity analysis of a flexible system. Motion equation of the system is developed based on Hamilton’s principle. The riser is modeled as a distributed parameter system. Moreover, simulations are carried out based on Assumed Mode Method (AMM) to solve PDE of the riser through mode shapes and generalized coordinates. Finally, the results of sensitivity analysis are presented.

Parameter Sensitivity Analysis of Rotating Beams in Frequency Domain

2009 ◽  
Author(s):  
Masoud Ansari ◽  
Ebrahim Esmailzadeh ◽  
Nader Jalili
Keyword(s):  
Sensitivity Analysis ◽  
Closed Form ◽  
Characteristic Equation ◽  
Frequency Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Tip Mass ◽  
Assumed Mode

Many mechanical rotating systems can be modeled as a cantilever beam attached to a rotating substrate. Vibratory beam gyroscopes are good examples of such systems. They consist of a rotating beam with a tip mass, attached to a rotating base. Due to the base rotation, the governing partial differential equations of the system are coupled, and hence, the system undergoes coupled torsional-bending vibrations. The coupling effect complicates the frequency analysis of the system, especially in determining the system characteristic equation. Many investigators have chosen to use the assumed mode method in their analysis of such systems instead of extracting the exact mode shapes of the system. In spite of all these difficulties, this paper addresses the exact frequency analysis of such systems and presents a closed-form frequency characteristic equation and evaluates the accurate values of the natural frequencies. The application of the proposed method is not limited to the system at hand, as it can be utilized for analyzing general systems with coupled governing equations of motion. Having analyzed a closed-form frequency equation has two valuable advantages: a) it can serve as the basis for the subsequent time-domain analysis; and b) it can be very essential in developing control strategies. In this study a thorough sensitivity analysis is performed to determine the effects of different parameters on the natural frequencies of the coupled vibrating system. The proposed method reveals some interesting findings in the systems which were difficult, if not impossible, to be revealed by the assumed mode method commonly utilized in many research work reported recently in literature.

Complex Modal Analysis of a Non-Modally Damped Continuous Beam

2013 ◽  
Author(s):  
Xing Xing ◽  
Brian F. Feeny
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Separation Of Variables ◽  
Mode Shapes ◽  
Modal Assurance Criterion ◽  
Assumed Mode Method ◽  
State Variable ◽  
Mode Method ◽  
Cantilevered Beam ◽  
Assumed Mode

This work represents an investigation of the complex modes of continuous vibration systems with nonmodal damping. As an example, a cantilevered beam with damping at the free end is studied. Traditional separation of variables for this problem leads to a differential eigenvalue problem which requires a numerical solution. In this paper, assumed modes are applied to discretize the eigenvalue problem in state-variable form, to then obtain estimates of the frequencies and modes. The finite-element method (FEM) is also utilized to get the mass, stiffness, and damping matrices and further to solve a state-variable eigenproblem. A comparison between the assumed-mode and finite-element eigenvalues and modal vectors shows that the methods produce consistent results. The comparison of the modes was done visually and also by using the modal assurance criterion (MAC) on the modal vectors. The assumed-mode method is then used to study the effects of the damping coefficient on mode shapes and modal damping.

Free Vibration Analysis of Rectangular Plates With Multiple Rectangular Openings and Arbitrary Edge Constraints

2014 ◽  
Author(s):  
Dae-Seung Cho ◽  
Nikola Vladimir ◽  
Tae-Muk Choi
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Relevant Literature ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Ocean Engineering ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Assumed Mode

Free vibration analysis of plates with openings represents an important issue in naval architecture and ocean engineering applications. Namely, they are often primary design members of complex structures and knowledge about their dynamic behavior becomes a prerogative for the proper structural design. This paper deals with application of assumed mode method to free vibration analysis of rectangular plates with multiple rectangular openings at arbitrary defined locations. Developed method can be applied to both thin and thick plates as well as to classical and non-classical edge constraints. In the assumed mode method natural frequencies and mode shapes of a corresponding plate are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange’s equations of motion. The developed procedure actually represents an extension of a method for the natural vibration analysis of rectangular plates without openings, which has been recently presented in the relevant literature. The effect of an opening is taken into account in a simple and intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with single and multiple rectangular openings with various thicknesses and different combinations of boundary conditions. Also, the influence of the rectangular opening area on the plate dynamic response is analyzed. The comparisons of the results with those obtained using the finite element method (FEM) is also provided, and very good agreement is achieved. Finally, related conclusions are drawn and recommendations for future investigations are presented.

scholarly journals Free Vibration Analysis of Piezoelectric Cylindrical Nanoshell: Nonlocal and Surface Elasticity Effects

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Surface Elasticity ◽  
Free Vibration Analysis ◽  
Nonlocal Theory ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Assumed Mode Method ◽  
Mode Method

Vibration analysis of piezoelectric cylindrical nanoshell subjected to visco-Pasternak medium with arbitrary boundary conditions is investigated. In these analysis simultaneous effects of the nonlocal, surface elasticity and the different material scale parameter are considered. To this end, Eringen nonlocal theory and Gurtin–Murdoch surface/interface theory considering Donnell's shell theory are used. The governing equations and boundary conditions are derived using Hamilton’s principle and the assumed mode method combined with Euler–Lagrange method is used for discretizing the equations of motion. The viscoelastic nanoshell medium is modeled as Visco-Pasternak foundation. A variety of new vibration results including frequencies and mode shapes for piezoelectric cylindrical nano-shell with non-classical restraints as well as different material parameters are presented. The convergence, accuracy and reliability of the current formulation are validated by comparisons with existing experimental and numerical results. Also, the effects of nonlocality, surface energy, nanoshell radius, circumferential wavenumber, nanoshell damping coefficient, and foundation damping are accurately studied on frequencies and mode shapes of piezoelectric cylindrical nanoshell.

Dynamic Characteristic Analysis of a Rotor-Bearing System Using Global Assumed Mode Method With Different Polynomial Function

2011 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
C. H. Kang ◽  
C. Y. Liao
Keyword(s):  
High Speed ◽  
Polynomial Function ◽  
Mode Shapes ◽  
Characteristic Analysis ◽  
Assumed Mode Method ◽  
Higher Order Modes ◽  
Rotor Bearing ◽  
Mode Method ◽  
Assumed Mode ◽  
Bearing System

In this study, the dynamic analysis of a domestic high speed rotor bearing system in turbo machines by using global assumed mode with different polynomial is investigated. This system consists of rotating multi flexible shaft, rigid disks and stiffness bearing effects. The analysis includes the whirl speeds, critical speeds, and mode shapes. The Global Assumed Modes Method (GAMM) and Finite Element Method (FEM) are employed to model the rotor-bearing system, and the accuracy of the results is discussed. With the application of GAMM, similarity transformation of different types of polynomials and interval has been investigated. The results show that using different polynomial function in GAMM have similar results, and which are also be agreed with the FEM. The results also show that the number of polynomial can be increased as the interval of the assumed mode function is altered. Consequently, the convergence of higher order modes will be more accurate.

Investigation and Comparison of Possible Boundary Conditions and System Vibration Modes in Two-Link Flexible Manipulators

2001 ◽  
Author(s):  
Joono Cheong ◽  
Youngil Youm ◽  
Wan Kyun Chung
Keyword(s):  
Boundary Conditions ◽  
Mode Shapes ◽  
Natural Mode ◽  
Vibration Modes ◽  
Flexible Robot ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Robot Systems ◽  
Comparative Concept ◽  
System Vibration

Abstract In the slewing multi-link flexible robot systems, the natural frequencies and mode shapes have been determined using the assumed component mode method with clamped-joint condition, in which the system modes is reconstructed by the series of assumed modes of each link. This method, however, requires large number of assumed modes to accurately describe the system and even more, sometimes, the results are erroneous. The direct analytic solution of entire system vibration mode which is a comparative concept of assumed mode method can accurately account for the entire vibration with a few number of significant modes. This paper deals with system vibration modes of two-link flexible robot and their appropriate boundary conditions. There are four possible set of boundary conditions, that is, clamped-clamped, clamped-spring, spring-clamped, spring-spring, according to joint servo condition, and we compare mode shapes and modal frequencies of each case by numerical and experimental results. We also provide important characteristics of natural mode when imposed certain kind of boundary conditions.

scholarly journals Comparing sensitivity analysis methods to advance lumped watershed model identification and evaluation

2007 ◽  
Vol 11 (2) ◽  
pp. 793-817 ◽  
Author(s):  
Y. Tang ◽  
P. Reed ◽  
T. Wagener ◽  
K. van Werkhoven
Keyword(s):  
Sensitivity Analysis ◽  
Model Identification ◽  
Local Analysis ◽  
Time Interval ◽  
Watershed Model ◽  
Soil Moisture Accounting ◽  
Analysis Methods ◽  
Accounting Model ◽  
Sobol’S Method ◽  
Comparative Results

Abstract. This study seeks to identify sensitivity tools that will advance our understanding of lumped hydrologic models for the purposes of model improvement, calibration efficiency and improved measurement schemes. Four sensitivity analysis methods were tested: (1) local analysis using parameter estimation software (PEST), (2) regional sensitivity analysis (RSA), (3) analysis of variance (ANOVA), and (4) Sobol's method. The methods' relative efficiencies and effectiveness have been analyzed and compared. These four sensitivity methods were applied to the lumped Sacramento soil moisture accounting model (SAC-SMA) coupled with SNOW-17. Results from this study characterize model sensitivities for two medium sized watersheds within the Juniata River Basin in Pennsylvania, USA. Comparative results for the 4 sensitivity methods are presented for a 3-year time series with 1 h, 6 h, and 24 h time intervals. The results of this study show that model parameter sensitivities are heavily impacted by the choice of analysis method as well as the model time interval. Differences between the two adjacent watersheds also suggest strong influences of local physical characteristics on the sensitivity methods' results. This study also contributes a comprehensive assessment of the repeatability, robustness, efficiency, and ease-of-implementation of the four sensitivity methods. Overall ANOVA and Sobol's method were shown to be superior to RSA and PEST. Relative to one another, ANOVA has reduced computational requirements and Sobol's method yielded more robust sensitivity rankings.

A Method to Improve the Modal Convergence for Structures With External Forcing

1987 ◽  
Vol 54 (4) ◽  
pp. 904-909 ◽  
Author(s):  
Keqin Gu ◽  
Benson H. Tongue
Keyword(s):  
Spatial Distribution ◽  
Free Vibration ◽  
Convergence Rate ◽  
Traditional Approach ◽  
Vibration Modes ◽  
External Forcing ◽  
Slow Convergence ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Assumed Mode

The traditional approach of using free vibration modes in the assumed mode method often leads to an extremely slow convergence rate, especially when discete interactive forces are involved. By introducing a number of forced modes, significant improvements can be achieved. These forced modes are intrinsic to the structure and the spatial distribution of forces. The motion of the structure can be described exactly by these forced modes and a few free vibration modes provided that certain conditions are satisfied. The forced modes can be viewed as an extension of static modes. The development of a forced mode formulation is outlined and a numerical example is presented.

scholarly journals Sensitivity Analysis of the Influence of Structural Parameters on Dynamic Behaviour of Highly Redundant Cable-Stayed Bridges

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
B. Asgari ◽  
S. A. Osman ◽  
A. Adnan
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Finite Element Model ◽  
Model Updating ◽  
Structural Parameters ◽  
Element Model ◽  
Structural Behavior ◽  
Model Tuning ◽  
The Finite Element Model ◽  
Cable Stayed Bridges

The model tuning through sensitivity analysis is a prominent procedure to assess the structural behavior and dynamic characteristics of cable-stayed bridges. Most of the previous sensitivity-based model tuning methods are automatic iterative processes; however, the results of recent studies show that the most reasonable results are achievable by applying the manual methods to update the analytical model of cable-stayed bridges. This paper presents a model updating algorithm for highly redundant cable-stayed bridges that can be used as an iterative manual procedure. The updating parameters are selected through the sensitivity analysis which helps to better understand the structural behavior of the bridge. The finite element model of Tatara Bridge is considered for the numerical studies. The results of the simulations indicate the efficiency and applicability of the presented manual tuning method for updating the finite element model of cable-stayed bridges. The new aspects regarding effective material and structural parameters and model tuning procedure presented in this paper will be useful for analyzing and model updating of cable-stayed bridges.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1993 ◽  
Author(s):  
Mohan D. Rao ◽  
Krishna M. Gorrepati
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

Abstract This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

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