A Practical Estimation of Frequency Response Functions for System Decoupling Indirectly Using a Variable Cross Section Rod

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Jun Wang ◽  
Tian-Ya Meng ◽  
Ming-Yu Li ◽  
Teik C. Lim ◽  
Wen-Xuan Kuang
Keyword(s):  
Frequency Response ◽  
Cross Section ◽  
Low Frequency ◽  
Coupled System ◽  
Variable Cross Section ◽  
Probe Method ◽  
Variable Cross ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Spatial Limitation

It is of high importance to be able to decouple a system to obtain the dynamic characteristics of its substructures; however, the necessary frequency response functions (FRFs) of the coupling interface are usually challenging to measure due to the limited accessible space and complex geometries. In this paper, a measurement technique in the decoupling process of a coupled system is proposed in order to obtain the FRFs at coupling interface. Specifically, a variable cross section rod is adopted to transmit the dynamic behavior of coupling interface. The proposed technique has three advantages: (a) the thick end with large cross section can provide enough area for applying excitation force like using impact hammer and/or setting up sensors; (b) the slender end with small cross section can break through the spatial limitation more easily; and (c) the convenience that no additional experimental setup is required but just using an available variable cross section rod. Vibrational equation of the variable cross section probe method is derived and then combined with the existing decoupling theories. Finally, the proposed probe method and the new decoupling theory combining probe theory are validated through numerical simulations (FEM) and laboratory experiments, respectively. The results show its great practicability in decoupling process especially in low frequency range.

Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 2: Application

1998 ◽  
Vol 120 (2) ◽  
pp. 509-516 ◽  
Author(s):  
J. A. Morgan ◽  
C. Pierre ◽  
G. M. Hulbert
Keyword(s):  
Frequency Response ◽  
Coupled System ◽  
Companion Paper ◽  
Component Mode Synthesis ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Measured Frequency Response ◽  
Coupled Beams ◽  
The Individual

This paper demonstrates how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.

Frequency Based Subsystem Identification Using Hybrid Primal-Dual Formulation

2011 ◽  
Author(s):  
Walter D’Ambrogio ◽  
Annalisa Fregolent
Keyword(s):  
Frequency Response ◽  
Dynamic Balance ◽  
Coupled System ◽  
Response Functions ◽  
Structural System ◽  
Frequency Response Functions ◽  
Dual Formulation ◽  
System A ◽  
Primal Dual

The paper considers the identification of a structural subsystem, starting from the Frequency Response Functions of the assembled system, and from information about the remaining part of the structural system (residual subsystem), i.e. the so called decoupling problem. A possible approach is direct decoupling, which consists in adding to the coupled system a fictitious subsystem which is the negative of the residual subsystem. Starting from the 3-field formulation (dynamic balance, compatibility and equilibrium at the interface), the problem can be solved in a primal or in a dual manner. Compatibility and equilibrium can be required either at coupling DoFs only, or at additional internal DoFs of the residual subsystem. Furthermore DoFs used to enforce equilibrium might be not the same as DoFs used for compatibility: this generates the so called non collocated approach. In this paper, a hybrid primal-dual formulation is applied in combination with collocated and non collocated interface.

Use of experimental dynamic substructuring to predict the low frequency structural dynamics under different boundary conditions

2017 ◽  
Vol 23 (11) ◽  
pp. 1444-1455
Author(s):  
Walter D’Ambrogio ◽  
Annalisa Fregolent
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Low Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Different Boundary Conditions ◽  
Rigid Body Modes

Flexible structural components can be attached to the rest of the structure using different types of joints. For instance, this is the case of solar panels or array antennas for space applications that are joined to the body of the satellite. To predict the dynamic behaviour of such structures under different boundary conditions, such as additional constraints or appended structures, it is possible to start from the frequency response functions in free-free conditions. In this situation, any structure exhibits rigid body modes at zero frequency. To experimentally simulate free-free boundary conditions, flexible supports such as soft springs are typically used: with such arrangement, rigid body modes occur at low non-zero frequencies. Since a flexible structure exhibits the first flexible modes at very low frequencies, rigid body modes and flexible modes become coupled: therefore, experimental frequency response function measurements provide incorrect information about the low frequency dynamics of the free-free structure. To overcome this problem, substructure decoupling can be used, that allows us to identify the dynamics of a substructure (i.e. the free-free structure) after measuring the frequency response functions on the complete structure (i.e. the structure plus the supports) and from a dynamic model of the residual substructure (i.e. the supporting structure). Subsequently, the effect of additional boundary conditions can be predicted using a frequency response function condensation technique. The procedure is tested on a reduced scale model of a space solar panel.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

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