Vibration Modes of Centrifugally Stiffened Beams

1982 ◽  
Vol 49 (1) ◽  
pp. 197-202 ◽  
Author(s):  
A. D. Wright ◽  
C. E. Smith ◽  
R. W. Thresher ◽  
J. L. C. Wang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Cantilever Beam ◽  
Mass Distribution ◽  
Flexural Rigidity ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Finite Element Code ◽  
Rotating Beams ◽  
Tip Mass

The method of Frobenius is used to solve for the exact frequencies and mode shapes for rotating beams in which both the flexural rigidity and the mass distribution vary linearly. Results are tabulated for a variety of situations including uniform and tapered beams, with root offset and tip mass, and for both hinged root and fixed root boundary conditions. The results obtained for the case of the uniform cantilever beam are compared with other solutions, and the results of a conventional finite-element code.

Rotating Beams and Nonrotating Beams With Shared Eigenpair

2009 ◽  
Vol 76 (5) ◽  
Author(s):  
Ananth Kumar ◽  
Ranjan Ganguli
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cantilever Beam ◽  
Mass Distribution ◽  
Mode Shapes ◽  
Flexural Stiffness ◽  
Rotating Beam ◽  
Element Analysis ◽  
Rotating Beams ◽  
The Finite Element Analysis

In this paper, we look for rotating beams whose eigenpair (frequency and mode-shape) is the same as that of uniform nonrotating beams for a particular mode. It is found that, for any given mode, there exist flexural stiffness functions (FSFs) for which the jth mode eigenpair of a rotating beam, with uniform mass distribution, is identical to that of a corresponding nonrotating uniform beam with the same length and mass distribution. By putting the derived FSF in the finite element analysis of a rotating cantilever beam, the frequencies and mode-shapes of a nonrotating cantilever beam are obtained. For the first mode, a physically feasible equivalent rotating beam exists, but for higher modes, the flexural stiffness has internal singularities. Strategies for addressing the singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams.

Damping Frame Vibrations Using Anechoic Stubs: Analysis Using an Exact Wave-based Approach

2020 ◽  
pp. 1-21
Author(s):  
Hangyuan Lv ◽  
Michael Leamy
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Forced Vibration ◽  
Mode Shapes ◽  
Frame Structures ◽  
Vibration Modes ◽  
Timoshenko Beams ◽  
Modal Damping ◽  
Reflection Matrix ◽  
Resonance Response

Abstract This paper explores the addition of small stubs with anechoic terminations (termed herein ‘anechoic stubs’) as means for damping and/or removing vibration modes from planar frame structures. Due to the difficulties associated with representing anechoic boundary conditions in more traditional analysis approaches (e.g., analytical, finite element, finite difference, finite volume, etc.), the paper employs and further develops an exact wave-based approach, incorporating Timoshenko beams, in which ideal and non-ideal anechoic terminations are simply represented by a reflection matrix. Several numerically-evaluated examples are presented documenting novel effects anechoic stubs have on the vibration modes of a two-story frame, such as eliminated, inserted and exchanged mode shapes. Modal damping ratios are also computed as a function of the location and number of anechoic stubs, illustrating optimal locations and optimal reflection ratios as a function of mode number. Forced vibration studies are then carried-out, demonstrating reduced, eliminated, and inserted resonance response.

Anechoic Stubs As a Means for Damping Frame Vibrations: Analysis Using an Exact Wave-Based Approach

2020 ◽  
Author(s):  
Hangyuan Lv ◽  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Forced Vibration ◽  
Mode Shapes ◽  
Frame Structures ◽  
Vibration Modes ◽  
Timoshenko Beams ◽  
Modal Damping ◽  
Reflection Matrix ◽  
Resonance Response

Abstract This paper explores the addition of small stubs with anechoic terminations (termed herein ‘anechoic stubs’) as means for damping and/or removing vibration modes from planar frame structures. Due to the difficulties associated with representing anechoic boundary conditions in more traditional analysis approaches (e.g., analytical, finite element, finite difference, finite volume, etc.), the paper employs an exact wave-based approach, incorporating Timoshenko beams, in which an anechoic boundary is simply represented by a zero reflection matrix. Several numerically-evaluated examples are presented documenting novel effects anechoic stubs have on the vibration modes of a two-story frame, such as eliminated, inserted and exchanged mode shapes. Modal damping ratios are also computed as a function of the location and number of anechoic stubs, illustrating optimal locations as a function of mode number. Forced vibration studies are then carried-out, demonstrating reduced, eliminated, and inserted resonance response.

Forced Motions of Composite Conoidal Shell Roofs with Complicated Boundary Conditions

2010 ◽  
Vol 123-125 ◽  
pp. 89-92
Author(s):  
Kaustav Bakshi ◽  
Hari Sadhan Das ◽  
Dipankar Chakravorty
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Forced Vibration ◽  
Vibration Characteristics ◽  
Finite Element Code ◽  
Isoparametric Finite Element

An eight noded isoparametric finite element code is applied to study static bending, free and forced vibration characteristics of composite conoidal shell roofs with complicated boundary conditions which are often encountered in the industry.

Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

2003 ◽  
Vol 217 (2) ◽  
pp. 171-183 ◽  
Author(s):  
J-S Wu ◽  
H-M Chou ◽  
D-W Chen
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Normal Mode ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Mode Shapes

The dynamic characteristic of a uniform rectangular plate with four boundary conditions and carrying three kinds of multiple concentrated element (rigidly attached point masses, linear springs and elastically mounted point masses) was investigated. Firstly, the closed-form solutions for the natural frequencies and the corresponding normal mode shapes of a rectangular ‘bare’ (or ‘unconstrained’) plate (without any attachments) with the specified boundary conditions were determined analytically. Next, by using these natural frequencies and normal mode shapes incorporated with the expansion theory, the equation of motion of the ‘constrained’ plate (carrying the three kinds of multiple concentrated element) were derived. Finally, numerical methods were used to solve this equation of motion to give the natural frequencies and mode shapes of the ‘constrained’ plate. To confirm the reliability of previous free vibration analysis results, a finite element analysis was also conducted. It was found that the results obtained from the above-mentioned two approaches were in good agreement. Compared with the conventional finite element method (FEM), the approach employed in this paper has the advantages of saving computing time and achieving better accuracy, as can be seen from the existing literature.

Vibro-Acoustic Studies of Transmission Casing Structures

1998 ◽  
Author(s):  
D. Crimaldi ◽  
R. Singh
Keyword(s):  
Finite Element ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Material Properties ◽  
Acoustic Radiation ◽  
Real Life ◽  
Cover Plate ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Free Boundary Conditions

Abstract Automotive transmission casing plates of irregular shape, with complex boundary conditions and non-uniform material properties, are experimentally and computationally studied to acquire a fundamental understanding of their dynamic and acoustic radiation characteristics. A modified flat cover is designed which simplifies the geometry while providing uniform thickness and material properties. Both covers (“real-life” and “laboratory”) are studied with free and bolted boundary conditions. In particular, the free boundary conditions are useful because they eliminate the cover-housing interaction allowing for a more detailed analysis of the cover plate. Finite element models for both covers under the free boundary conditions are developed and refined. Predicted natural frequencies and mode shapes are in excellent agreement with measured modal data. Then the finite element models are coupled with boundary element models to predict acoustic radiation properties. Predictions match well with measured acoustic directivity at resonant frequencies.

Response variations of a cantilever beam–tip mass system with nonlinear and linearized boundary conditions

2018 ◽  
Vol 25 (3) ◽  
pp. 485-496 ◽  
Author(s):  
Vamsi C. Meesala ◽  
Muhammad R. Hajj
Keyword(s):  
Boundary Conditions ◽  
Cantilever Beam ◽  
Nonlinear Boundary ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Boundary Conditions ◽  
Distributed Parameter ◽  
Governing Equations ◽  
Mass System ◽  
Tip Mass

The distributed parameter governing equations of a cantilever beam with a tip mass subjected to principal parametric excitation are developed using a generalized Hamilton's principle. Using a Galerkin's discretization scheme, the discretized equation for the first mode is developed for simpler representation assuming linear and nonlinear boundary conditions. The discretized governing equation considering the nonlinear boundary conditions assumes a simpler form. We solve the distributed parameter and discretized equations separately using the method of multiple scales. Through comparison with the direct approach, we show that accounting for the nonlinear boundary conditions boundary conditions is important for accurate prediction in terms of type of bifurcation and response amplitude.

Experimental and numerical analysis of vibration frequency in sandwich composites with different radii of curvature

2017 ◽  
Vol 21 (8) ◽  
pp. 2870-2886
Author(s):  
Melis Yurddaskal ◽  
Buket Okutan Baba
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Experimental Studies ◽  
Sandwich Panels ◽  
Mode Shapes ◽  
Sandwich Composite ◽  
Radius Of Curvature ◽  
Finite Element Software

In this study, free vibration responses of sandwich composite panels with different radius of curvature were presented numerically. The studies were carried out on square flat and curved sandwich panels made of E-glass/epoxy face sheets and polyvinyl chloride foam with three different radii of curvature. Experimental studies were used to verify the numerical results. Vibration tests were performed on flat and curved sandwich panels under free–free boundary conditions. The experimental data were then compared with finite element simulation, which was conducted by ANSYS finite element software and it was shown that the numerical analysis results agree well with the experimental ones. Effect of the curvature on natural frequencies under different boundary conditions (all edge free, simply supported, and fully clamped) was investigated numerically. Results indicated that the natural frequencies and corresponding mode shapes were affected by boundary conditions and curvature of the panel. For all boundary conditions, the variation of curvature had smaller effect on the natural frequency of the first mode than those of the other modes.

Investigation of the incremental and deformation theories of plasticity on the elastoplastic postbuckling of plates

2020 ◽  
Vol 234 (7) ◽  
pp. 1017-1031
Author(s):  
HM Soltani ◽  
M Kharazi
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Deformation Theory ◽  
Finite Element Code ◽  
Postbuckling Behavior ◽  
Incremental Theory ◽  
Aspect Ratios ◽  
Theory Of Plasticity ◽  
The Difference

This article investigates the elastoplastic response of buckling and postbuckling behavior of plates under uniaxial and biaxial end-shortening considering incremental theory and deformation theory of plasticity. According to elastoplastic buckling and postbuckling behavior of plates, the finite element code considering geometrically and material nonlinearities is developed based on incremental theory and deformation theory of plasticity. The results show that boundary conditions, loading ratios, and aspect ratios of a plate have a significant effect on the discrepancy between incremental theory and deformation theory. Moreover, differences in estimating the buckling point using incremental theory and deformation theory are less than 10%, while in a number of plates at the last loading steps, postbuckling paths determined by incremental theory and deformation theory are diverted from each other. Also the difference between these two theories in the postbuckling region is more noticeable by increasing the thickness of plates.

Exact Vibration Solution for Exponentially Tapered Cantilever With Tip Mass

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
C.Y. Wang ◽  
C. M. Wang
Keyword(s):  
Numerical Methods ◽  
Free Vibration ◽  
Cantilever Beam ◽  
Technical Note ◽  
Mode Shapes ◽  
Constant Thickness ◽  
Vibration Frequencies ◽  
Tapered Cantilever Beam ◽  
Tip Mass ◽  
First Time

This technical note is concerned with the free vibration problem of a cantilever beam with constant thickness and exponentially decaying width. Existing analytical results for such a vibration beam problem are found to be incomplete because lower frequencies could not be obtained. Presented herein is the exact characteristic equation for generating the complete vibration frequencies for the considered vibrating beam problem. Also the note treated for the first time such a tapered cantilever beam with a tip mass. The exact solutions (frequencies and mode shapes) are important to engineers designing such tapered beams and the results serve as benchmarks for assessing the validity, convergence and accuracy of numerical methods and solutions.

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