Random Response of Multi-Segment Beam May Exceed Response of Homogeneous Counterparts by Order of Magnitude

2020 ◽  
Vol 20 (13) ◽  
pp. 2041006
Author(s):  
T. Fang ◽  
I. Elishakoff ◽  
C. Jiang
Keyword(s):  
Random Vibration ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Mode Shapes ◽  
Random Response ◽  
Euler Beam ◽  
Mode Method ◽  
Order Of Magnitude ◽  
Engineering Significance ◽  
Normal Mode Method

This paper investigates the dynamic properties of an inhomogeneous, Bernoulli–Euler multi-segment beam composed of different materials. To the best of knowledge of the authors, the problem of random vibrations of beams composing of different chunks of the beams, namely, strong and weak parts, has not been studied in the literature. In this paper, exact solution of the natural frequencies and associated mode shapes of the multi-segment Bernoulli–Euler beam are obtained using Krylov–Duncan functions, followed by free, forced, and random vibration analyses using the normal mode method. Special emphasis is placed on two special configurations of multi-segment beam, namely, the ‘rigid-soft-rigid beam’ (RSR beam) and ‘soft-rigid-soft beam’ (SRS beam) as simplest manifestations of the multi-chunked structures. Some remarkable properties exhibited by the dynamic response of multi-segment beam are demonstrated through this work, which may be of considerable engineering significance, and could not have been anticipated in advance, especially quantitatively.

scholarly journals Identification of Mistuning Characteristics of Bladed Disks From Free Response Data

1998 ◽  
Author(s):  
Marc P. Mignolet ◽  
Alejandro Rivas-Guerra
Keyword(s):  
Dynamic Models ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Structural Parameters ◽  
Identification Problem ◽  
Forced Response ◽  
Mode Shapes ◽  
Likelihood Principle ◽  
Bladed Disks ◽  
Block Test

The focus of the present investigation is on the estimation of the dynamic properties, i.e. masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. Two distinct approaches will be investigated to resolve the shortfall of data. The first one relies on the imposition of as many constraints as needed to insure a unique solution to this identification problem. Specifically, the mode shapes and modal masses of the blades are set to their design/tuned counterparts while the modal stiffnesses are varied from blade-to-blade to match the measured natural frequencies. The second approach, based on the maximum likelihood principle, yields estimates of all the structural parameters of the blades through the minimization of a specified “cost function”. The accuracy of these two techniques in predicting the forced response of mistuned bladed disks will be assessed on simple dynamic models of the blades.

Dynamic Characteristics of Tsing Ma Suspension Bridge

1996 ◽  
Vol 1541 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Siu Kui Au ◽  
Neil Mickleborough ◽  
Paul N. Roschke
Keyword(s):  
Analytical Solutions ◽  
Bridge Deck ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Suspension Bridge ◽  
Mode Shapes ◽  
Out Of Plane ◽  
Quantitative Results ◽  
Suspension Cable ◽  
Bending Modes

Numerical simulation was carried out to determine the dynamic properties of the Tsing Ma Suspension Bridge. Both the structure as a whole and individual subcomponents were modeled. Classical analytical solutions for simplified models from the available literature were compared with the results obtained from a finite-element code. Quantitative results for static deflection, natural frequencies, and mode shapes were compared with analytical solutions from linear theory. Out-of-plane modes were shown to be dominant. For in-plane antisymmetric and symmetric bending modes, in which the suspension cable and bridge deck vibrate in the same direction, the natural frequency of the main span of the bridge is determined to be approximately equal to the square root of the sum of the squares of the frequencies of the cable and bridge deck.

Buckling Loads and Natural Frequencies of Drill Bits and Fluted Cutters

1984 ◽  
Vol 106 (3) ◽  
pp. 196-204 ◽  
Author(s):  
E. B. Magrab ◽  
D. E. Gilsinn
Keyword(s):  
Natural Frequencies ◽  
Twist Angle ◽  
Axial Loading ◽  
Basis Functions ◽  
Mode Shapes ◽  
Euler Beam ◽  
Buckling Loads ◽  
Drill Bits ◽  
Out Of Plane ◽  
Beam Type

The buckling loads, natural frequencies and mode shapes of twist-drill bits and certain fluted cutters under a variety of combinations of twist angle, cross-section geometry, and axial loading have been obtained. The drill bit is modelled as a twisted Euler beam under axial loading that is clamped at both ends. The governing system of differential equations is solved by the Galerkin procedure. Explicit forms for the basis functions used to generate the Galerkin coefficients are presented in general form in an appendix. They may be used for obtaining numerical results for that class of problems which use the Rayleigh-Ritz-Galerkin methods with beam-type functions as the basis functions. The representative set of modes obtained exhibit a complex out-of-plane twisting-type motion that suggests a possible explanation for the out-of-roundness of certain drilled holes.

scholarly journals Overcoming Effects from Environmental Temperature on the Natural Frequencies of Cable-strut Structures

2020 ◽  
pp. 22-30
Author(s):  
Nasseradeen Ashwear ◽  
Haithem Elderrat ◽  
Mahmud A. Eljaarani
Keyword(s):  
Genetic Algorithm ◽  
Health Monitoring ◽  
Optimization Problem ◽  
Environmental Temperature ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Environmental Variable ◽  
Mode Shapes ◽  
Stress Vector ◽  
Temperature Changes

The changes in dynamic properties such as natural frequencies and mode shapes are used in vibration health monitoring as tools for assessing the structures health status. They are, however, also affected by environmental conditions like wind, humidity and temperature changes. Of particular importance is the change of the environmental temperature, and it is the most commonly considered environmental variable that influences the vibration health monitoring algorithms. This paper discusses how cable-strut structures can be designed such that their first natural frequency is less sensitive to the temperature changes. The optimization problem is solved by using a genetic algorithm. The level of pre-stress can be regulated to achieve the solution, particularly when a symmetric self-stress vector is chosen.

scholarly journals Rigid Finite Element Method in Modeling Composite Steel-Polymer Concrete Machine Tool Frames

Materials ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3151 ◽  
Author(s):  
Paweł Dunaj ◽  
Krzysztof Marchelek ◽  
Stefan Berczyński ◽  
Berkay Mizrak
Keyword(s):  
Finite Element ◽  
Machine Tool ◽  
Experimental Verification ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
High Accuracy ◽  
Mode Shapes ◽  
Polymer Concrete ◽  
Beam Model ◽  
Low Dimensional

At the stage of designing a special machine tool, it is necessary to analyze many variants of structural solutions of frames and load-bearing systems and to choose the best solution in terms of dynamic properties, in particular considering its resistance to chatter. For this reason, it is preferred to adopt a low-dimensional calculation model, which allows the user to reduce the necessary calculation time while maintaining a high accuracy. The paper presents the methodology of modeling the natural frequencies, mode shapes, and receptance functions of machine tool steel welded frames filled with strongly heterogenous polymer concrete, using low-dimensional models developed by the rigid finite elements method (RigFEM). In the presented study, a RigFEM model of a simple steel beam filled with polymer concrete and a frame composed of such beams were built. Then, the dynamic properties obtained on the basis of the developed RigFEM models were compared with the experimental results and the 1D and 3D finite element models (FEM) in terms of accuracy and dimensionality. As a result of the experimental verification, the full structural compliance of the RigFEM models (for beam and frame) was obtained, which was manifested by the agreement of the mode shapes. Additionally, experimental verification showed a high accuracy of the RigFEM models, obtaining for the beam model a relative error for natural frequencies of less than 4% and on average 2.2%, and for the frame model at a level not exceeding 11% and on average 5.5%. Comparing the RigFEM and FEM models, it was found that the RigFEM models have a slightly worse accuracy, with a dimensionality significantly reduced by 95% for the beam and 99.8% for the frame.

INVESTIGATION OF DYNAMIC PROPERTIES OF ELASTOMERIC BEARING COMPONENTS VIA MODAL ANALYSIS

2015 ◽  
Vol 76 (8) ◽  
Author(s):  
A. I. Yusuf ◽  
M. A. Norliyati ◽  
M. A. Yunus ◽  
M. N. Abdul Rani
Keyword(s):  
Modal Analysis ◽  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Seismic Loads ◽  
Ground Structure ◽  
Elastomeric Bearing ◽  
Earthquake Load

Elastomeric bearing is a significant device in structures such as in bridges and buildings. It is used to isolate the ground structure (substructure) and the above ground structure (superstructure) from seismic loads such as earthquake load. Understanding the dynamic behavior of the elastomeric bearing in terms of natural frequencies, mode shapes and damping are increasingly important especially in improving the design and the failure limit of the elastomeric bearing. Modal analysis is one of the methods used to determine the dynamic properties of any materials. Hence, the main objective of this research is to determine the dynamic properties of elastomeric bearing components in terms of natural frequencies, mode shapes, and damping via numerical and experimental modal analysis. This method had been successfully performed in investigating the dynamic behavior of rubber and steel shim plate.

Identification of Mistuning Characteristics of Bladed Disks From Free Response Data — Part II

1999 ◽  
Author(s):  
Marc P. Mignolet ◽  
Jason P. Delor ◽  
Alejandro Rivas-Guerra
Keyword(s):  
Dynamic Models ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Structural Parameters ◽  
Identification Problem ◽  
Forced Response ◽  
Mode Shapes ◽  
Likelihood Principle ◽  
Bladed Disks ◽  
Block Test

The focus of the present investigation is on the estimation of the dynamic properties, i.e. masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. Three distinct approaches will be investigated to resolve the shortfall of data. The first one relies on the imposition of as many constraints as needed to insure a unique solution to this identification problem. Specifically, the mode shapes and modal masses of the blades are set to their design/tuned counterparts while the modal stiffnesses are varied from blade-to-blade to match the measured natural frequencies. The second approach, based on the maximum likelihood principle, yields estimates of all the structural parameters of the blades through the minimization of a specified “cost function”. Finally, the third approach provides a bridge between the first two methods being based on the second but yielding a mistuning model similar to that of the first approach. The accuracy of these three techniques in predicting the forced response of mistuned bladed disks will be assessed on simple dynamic models of the blades.

scholarly journals Dynamic testing of a modern concrete bridge

1979 ◽  
Vol 6 (3) ◽  
pp. 447-455 ◽  
Author(s):  
J. H. Rainer ◽  
G. Pernica
Keyword(s):  
Natural Frequencies ◽  
Dynamic Testing ◽  
Dynamic Properties ◽  
Mode Shapes ◽  
Total Width ◽  
Concrete Bridge ◽  
Reinforced Concrete Bridge ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Good Agreement

A posttensioned reinforced concrete bridge, slated for demolition, was tested to obtain its dynamic properties. The 10 year old bridge consisted of a continuous flat slab deck of variable thickness having a total width of 103 ft (31.39 m) and spans of 28 ft 6 in. (8.69 m), 71 ft 0 in. (21.64 m), and 42 ft 6 in. (12.95 m). The entire bridge was skewed 10°50′ and the deck was slightly curved in plan.The mode shapes, natural frequencies, and damping ratios for the lowest five natural modes of vibration were determined using sinusoidal forcing functions from an electrohydraulic shaker. These modes, located at 5.7, 6.4, 8.7, 12.0, and 17.4 Hz, were found to be highly dependent on the lateral properties of the bridge deck. Damping ratios were determined from the widths of resonance peaks. The modal properties from the steady state excitation were compared with those obtained from measurements of traffic-induced vibrations and good agreement was found between the two methods.

Dynamic Properties of a Heliostat Structure Determined by Numerical and Experimental Modal Analysis

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
J. Felipe Vásquez-Arango ◽  
Reiner Buck ◽  
Robert Pitz-Paal
Keyword(s):  
Modal Analysis ◽  
Vortex Shedding ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Simple Approach ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Fe Model ◽  
Damping Coefficients ◽  
Operating Points

An experimental and numerical modal analysis was performed on an 8 m2 T-shaped heliostat structure at different elevation angles. The experimental results were used to validate a finite element (FE) model by comparing natural frequencies and mode shapes. The agreement between experiments and simulations is good in all operating points investigated. In addition, damping coefficients were determined experimentally for each mode, in order to provide all necessary information for the development of a dynamic model. Furthermore, potentially critical operating conditions caused by vortex shedding were identified using a simple approach.

scholarly journals Finite Element Modeling of the Dynamic Properties of Composite Steel–Polymer Concrete Beams

Materials ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1630
Author(s):  
Paweł Dunaj ◽  
Stefan Berczyński ◽  
Marcin Chodźko ◽  
Beata Niesterowicz
Keyword(s):  
Finite Element ◽  
Frequency Response ◽  
Natural Frequencies ◽  
Concrete Beams ◽  
Dynamic Properties ◽  
Mode Shapes ◽  
Polymer Concrete ◽  
Response Functions ◽  
Full Agreement ◽  
High Agreement

This paper presents a method for modeling the dynamic properties of steel–polymer concrete beams, the basic structural components of machine tools, assembly lines, vibratory machines, and other structures subjected to time-varying loads during operation. The presented method of modeling steel–polymer concrete beams was developed using the finite element method. Three models of beams differing in cross-sectional dimensions showed high agreement with experimental data: relative error in the case of natural frequencies did not exceed 5% (2.2% on average), the models were characterized by the full agreement of mode shapes and high agreement of frequency response functions with the results of experimental tests. Additionally, the developed beam models supported the reliable description of complex structures, as demonstrated on a spatial frame, obtaining a relative error for natural frequencies of less than 3% (on average 1.7%). Full agreement with the mode shapes and high agreement with the frequency response functions were achieved in the analyzed frequency range.

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