Output Only Modal Analysis of a Nonuniform Beam Experiment by Using Decomposition Methods

2011 ◽  
Author(s):  
Rickey A. Caldwell ◽  
Brian F. Feeny
Keyword(s):  
Natural Frequencies ◽  
Normal Modes ◽  
Decomposition Methods ◽  
Analytical Approximation ◽  
Orthogonal Decomposition ◽  
Modal Assurance Criterion ◽  
Beam Experiment ◽  
Saw Blade ◽  
Output Only ◽  
Nonuniform Beam

This work explores the application of reduced-order mass-weighted proper orthogonal decomposition (RMPOD), state variable modal decomposition (SVMD), and smooth orthogonal decomposition (SOD) for extracting approximations of linear normal modes (LNMs) of a free vibrating thin lightly damped nonuniform beam experiment. The application of these decomposition methods involves organizing sensed outputs into ensemble matrices. The ensemble matrices are utilized to create correlation matrices, which are used in solving an eigenvalue problem. This is realized experimentally by sensing a thin nonuniform cantilevered beam, a saw blade, with eleven equally spaced accelerometers, during free vibration. The first mode was filtered out since its frequency was below the threshold of reliable accelerometers performance. RMPOD was able to extract the second, third, and fourth mode as implied by modal assurance criterion (MAC) in a comparison with an analytical approximation of the nonuniform Euler-Bernoulli beam modes. SVMD was able to extract an approximation to the LNMs and natural frequencies for the second, third, and fourth modes. SOD was able to extract the second, third, and fourth modes and natural frequencies successfully.

Output-Only Modal Identification of a Nonuniform Beam by Using Decomposition Methods

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Rickey A. Caldwell ◽  
Brian F. Feeny
Keyword(s):  
Decomposition Methods ◽  
Analytical Approximation ◽  
Orthogonal Decomposition ◽  
Modal Identification ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Accelerometer Data ◽  
Pass Filter ◽  
Modal Damping ◽  
Output Only

Reduced-order mass weighted proper orthogonal decomposition (RMPOD), smooth orthogonal decomposition (SOD), and state variable modal decomposition (SVMD) are used to extract modal parameters from a nonuniform experimental beam. The beam was sensed by accelerometers. Accelerometer signals were integrated and passed through a high-pass filter to obtain velocities and displacements, all of which were used to build the necessary ensembles for the decomposition matrices. Each of these decomposition methods was used to extract mode shapes and modal coordinates. RMPOD can directly quantify modal energy, while SOD and SVMD directly produce estimates of modal frequencies. The extracted mode shapes and modal frequencies were compared to an analytical approximation of these quantities, and to frequencies estimated by applying the fast Fourier transform to accelerometer data. SVMD is also applied to estimate modal damping, which was compared to the estimate by logarithmic decrement applied to modal coordinate signals, with varying degrees of success. This paper shows that these decomposition methods are capable of extracting lower modal parameters of an actual experimental beam.

Vibration analysis of an aviation engine turbine shaft shield

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Stanisław Noga ◽  
Kaja Maciejowska ◽  
Tomasz Rogalski
Keyword(s):  
Natural Frequencies ◽  
Dynamic Properties ◽  
Normal Modes ◽  
Measuring System ◽  
Mode Shapes ◽  
Modal Assurance Criterion ◽  
Natural Form ◽  
Content Type ◽  
Turbine Shaft ◽  
The Impact

Purpose This paper aims to deal with the problem of vibration in an aircraft engine turbine shaft shield. The physical model of the system under study is inspired by the PZL-10W aviation jet engine shaft shield and is a structure of the profile circular arc. The main goal of the presented research is to develop a modal model of the discussed object. Another task is to determine the impact of the shaft shield damage on the change of dynamic parameters (the values of the natural frequencies and changing of the shape of the corresponding natural forms) of the discussed object. Finally, the task is connected with the calculation of the excitation speeds of the discussed shaft shield’s respective natural frequencies. Design/methodology/approach To realize the main goal finite element method simulation and experimental investigation were conducted. The quality of the achieved models is determined based on the relative error of natural frequencies and the similarity to normal modes established on the basis of the modal assurance criterion (MAC) indicator. The Campbell diagram was used to calculate the excitation speeds of the discussed shaft shield’s respective natural frequencies. Findings The obtained results indicate the changes in the dynamic properties of the shaft shield as a result of its cracking. On the basis of the adopted measurement (MAC indicator), the level of similarity was established between the numerical simulation results and the measurement results for the undamaged shield. Verification of the different mode shapes using the CrossMAC tool is an effective method, which allows comparing of the shape of the natural form and may be helpful in the process of adjusting modal models to the results of experimental tests. Practical implications It is important to note that as a result of using commercial software (ANSYS program) and a commercial measuring system (Bruel and Kjaer), the presented analysis can be attractive for design engineers dealing with the dynamics of aviation systems. Originality/value The paper presents the authors’ original approach to the dynamic analysis of the aviation engine turbine shaft shield, which can be useful for engineers dealing with the issue of vibration in shaft shield systems.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

The Natural Frequencies of Free and Constrained Non-Uniform Beams

1960 ◽  
Vol 64 (599) ◽  
pp. 697-699 ◽  
Author(s):  
R. P. N. Jones ◽  
S. Mahalingam
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Normal Modes ◽  
Iteration Process ◽  
Conservative System ◽  
Basic System ◽  
Orthogonal Functions ◽  
Added Masses ◽  
The Given

The Rayleigh-Ritz method is well known as an approximate method of determining the natural frequencies of a conservative system, using a constrained deflection form. On the other hand, if a general deflection form (i.e. an unconstrained form) is used, the method provides a theoretically exact solution. An unconstrained form may be obtained by expressing the deflection as an expansion in terms of a suitable set of orthogonal functions, and in selecting such a set, it is convenient to use the known normal modes of a suitably chosen “ basic system.” The given system, whose vibration properties are to be determined, can then be regarded as a “ modified system,” which is derived from the basic system by a variation of mass and elasticity. A similar procedure has been applied to systems with a finite number of degrees of freedom. In the present note the method is applied to simple non-uniform beams, and to beams with added masses and constraints. A concise general solution is obtained, and an iteration process of obtaining a numerical solution is described.

scholarly journals COMPARISON OF SAW BLADE NATURAL FREQUENCIES AND CRITICAL SPEEDS USING CSAW AND FINITE ELEMENT ANALYSIS

2011 ◽  
Author(s):  
J. Poirier ◽  
P. Radziszewski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Saw Blade ◽  
Circular Saws ◽  
The Finite Element Model ◽  
Element Method

The natural frequencies of circular saws limit the operating speeds of the saws. Current industry methods of increasing natural frequency include pretensioning, where plastic deformation is induced into the saw. To better model the saw, the finite element model is compared to current software for steel saws; C-SAW, a software program that calculates frequencies for stiffened circular saws. Using C-SAW and the finite element method the results are compared and the finite element method is validated for steel saws.

Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions

1992 ◽  
Vol 59 (2S) ◽  
pp. S197-S204 ◽  
Author(s):  
Jean Wu-Zheng Zu ◽  
Ray P. S. Han
Keyword(s):  
Boundary Conditions ◽  
Mode Shape ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Single Mode ◽  
Mode Shapes ◽  
Simulation Studies ◽  
Classical Boundary ◽  
First Time

A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.

scholarly journals INFLUENCE OF A LIQUID ON THE NATURAL FREQUENCIES OF ALMOST CIRCULAR PLATES

2014 ◽  
Vol 06 (05) ◽  
pp. 1450052 ◽  
Author(s):  
MANUEL GASCÓN-PÉREZ ◽  
PABLO GARCÍA-FOGEDA
Keyword(s):  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Normal Modes ◽  
Virtual Mass ◽  
Circular Plates ◽  
Hankel Transformation ◽  
Fluid System ◽  
Surrounding Fluid ◽  
Good Agreement

In this work, the influence of the surrounding fluid on the dynamic characteristics of almost circular plates is investigated. First the natural frequencies and normal modes for the plates in vacuum are calculated by a perturbation procedure. The method is applied for the case of elliptical plates with a low value of eccentricity. The results are compared with other available methods for this type of plates with good agreement. Next, the effect of the fluid is considered. The normal modes of the plate in vacuum are used as a base to express the vibration mode of the coupled plate-fluid system. By applying the Hankel transformation the nondimensional added virtual mass 2 increment (NAVMI) are calculated for elliptical plates. Results of the NAVMI factors and the effect of the fluid on the natural frequencies are given and it is shown that when the eccentricity of the plate is reduced to zero (circular plate) the known results of the natural frequencies for circular plates surrounded by liquid are recovered.

Response Characteristics of Serially Connected Semisubmersibles

1999 ◽  
Vol 43 (04) ◽  
pp. 229-240
Author(s):  
H. R. Riggs ◽  
R. C. Ertekin
Keyword(s):  
Energy Loss ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Induced Response ◽  
Linear Wave ◽  
Response Characteristics ◽  
Response Modes ◽  
Wave Induced ◽  
The Impact ◽  
Large Aircraft

One design for a mobile offshore base is to link serially as many as five large semisubmersibles to form a platform long enough to support large aircraft. This paper investigates the linear, wave-induced response characteristics of serially-connected semisubmersibles. A major motivation of this study is to understand more completely the forces required to link semisubmersible modules. The impact of connector strategy and damping on the response, especially the connector forces, is investigated, and the response "modes" which contribute to the connector forces are evaluated in detail. It is shown that the response characteristics can be impacted significantly by the connection strategy, and that connector damping can be a significant source of energy loss when compared to radiation damping. The wet natural frequencies and normal modes are also determined and used to explain the response characteristics of different connection strategies. Although the analyses are based on a specific semisubmersible design, the results provide insight on how other systems of connected semisubmersibles would likely behave.

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