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.

scholarly journals Finite Element Vibration Analysis of Laminated Composite Folded Plate Structures

1999 ◽  
Vol 6 (5-6) ◽  
pp. 273-283 ◽  
Author(s):  
A. Guha Niyogi ◽  
M.K. Laha ◽  
P.K. Sinha
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Plate Structures ◽  
Drilling Degree Of Freedom ◽  
Vibration Responses ◽  
Forced Vibration Analysis

A nine-noded Lagrangian plate bending finite element that incorporates first-order transverse shear deformation and rotary inertia is used to predict the free and forced vibration response of laminated composite folded plate structures. A 6 × 6 transformation matrix is derived to transform the system element matrices before assembly. The usual five degrees-of-freedom per node is appended with an additional drilling degree of freedom in order to fit the transformation. The present finite element results show good agreement with the available semi-analytical solutions and finite element results. Parametric studies are conducted for free and forced vibration analysis for laminated folded plates, with reference to crank angle, fibre angle and stacking sequence. The natural frequencies and mode shapes, and forced vibration responses furnished here may serve as a benchmark for future investigations.

scholarly journals Forced Vibration of Delaminated Timoshenko Beams under the Action of Moving Oscillatory Mass

2013 ◽  
Vol 20 (1) ◽  
pp. 79-96 ◽  
Author(s):  
M.H. Kargarnovin ◽  
M.T. Ahmadian ◽  
R.A. Jafari-Talookolaei
Keyword(s):  
Dynamic Response ◽  
Forced Vibration ◽  
Equations Of Motion ◽  
Mode Shapes ◽  
Solution Technique ◽  
Timoshenko Beams ◽  
Modal Expansion ◽  
Forced Vibration Analysis ◽  
First Time ◽  
Moving Oscillator

This paper presents the dynamic response of a delaminated composite beam under the action of a moving oscillating mass. In this analysis the Poisson's effect is considered for the first time. Moreover, the effects of rotary inertia and shear deformation are incorporated. In our modeling linear springs are used between delaminated surfaces to simulate the dynamic interaction between sub-beams. To solve the governing differential equations of motion using modal expansion series, eigen-solution technique is used to obtain the natural frequencies and their corresponding mode shapes necessary for forced vibration analysis. The obtained results for the free and forced vibrations of beams are verified against reported similar results in the literatures. Moreover, the maximum dynamic response of such beam is compared with an intact beam. The effects of different parameters such as the velocity of oscillating mass, different ply configuration and the delamination length, its depth and spanwise location on the dynamic response of the beam are studied. In addition, the effects of delamination parameters on the oscillator critical speed are investigated. Furthermore, different conditions under which the detachment of moving oscillator from the beam will initiate are investigated.

Analysis of Nonlinear Modal Damping due to Friction at Blade Roots Using High-Fidelity Modelling

2018 ◽  
Author(s):  
Junjie Chen ◽  
Chaoping Zang ◽  
Biao Zhou ◽  
E. P. Petrov
Keyword(s):  
Finite Element ◽  
Direct Calculation ◽  
Surface Friction ◽  
Mode Shapes ◽  
Finite Element Models ◽  
High Fidelity ◽  
Three Dimension ◽  
Blade Vibration ◽  
Modal Damping ◽  
Energy Dissipated

In this paper, a methodology is developed for analysis of modal damping in root joints of bladed discs using large finite element models and detailed description of friction contacts at contact interfaces of the joints. The methods allows the analysis of: (i) a single blade vibration and (ii) a bladed-disc assembly for any family of modes (lower and higher modes) calculating the modal damping factors for different levels of vibrations. Three-dimension solid finite element models are used in the calculations. The analysis is performed in time domain through the transient dynamics analysis. The methodology allows the use of widely available finite element packages and based on the direct calculation of the energy dissipated at root joints due to micro-slip over the multitude of contact elements modelling the surface-to-surface friction contact interactions. The numerical studies of the dependency of modal damping factors on the vibration amplitudes are performed for simplified and realistic bladed disc models for different blade mode shapes, engine-order excitation numbers and nodal diameter numbers using high-fidelity models.

Analysis of Free and Forced Ship Vibrations Using Finite Element Method

2010 ◽  
Author(s):  
Adil Yucel ◽  
Alaeddin Arpaci
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Ship Hull ◽  
Mode Shapes ◽  
Ship Structures ◽  
Hull Structure ◽  
Forced Vibration Analysis ◽  
Ship Vibration

With the increase of ship size and speed, shipboard vibration becomes a great concern in the design and construction of the vessels. Excessive ship vibration is to be avoided for passenger comfort and crew habitability. In addition to undesired effects on humans, excessive ship vibration may result in the fatigue failure of local structural members or malfunction of machinery and equipment. The propeller induces fluctuating pressures on the surface of the hull, which induce vibration in the hull structure. These pressure pulses acting on the ship hull surface above the propeller as the predominant factor for vibrations of ship structures are taken as excitation forces for forced vibration analysis. Ship structures are complex and may be analyzed after idealization of the structure. Several simplifying assumptions are made in the finite element idealization of the hull structure. In this study, a three-dimensional finite element model representing the entire ship hull, including the deckhouse and machinery propulsion system, has been developed using a solid modeling software for local and global vibration analyses. Vibration analysis has been studied under two conditions which are free-free (dry) and in-water (wet). Wet analysis has been implemented using acoustic elements. The total damping associated with overall ship hull structure vibration has been considered as a combination of the several damping components. As the result of global ship free vibration analysis, global natural frequencies and mode shapes have been determined. Besides, responses of local ship structures have been determined as the result of propeller induced forced vibration analysis.

Forced Vibration Testing and Finite Element Modeling of a Nine-Story Reinforced Concrete Flat Plate-Wall Building

2015 ◽  
Vol 31 (2) ◽  
pp. 1069-1081 ◽  
Author(s):  
Ozan Cem Celik ◽  
Haluk Sucuoğlu ◽  
Ugurhan Akyuz
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Flat Plate ◽  
Forced Vibration ◽  
Structural Model ◽  
Dynamic Properties ◽  
Mode Shapes ◽  
Structural System ◽  
Vibration Testing ◽  
Forced Vibration Testing

Tunnel form buildings, owing to their higher construction speed and quality, lower cost, and superior earthquake resistance over that of conventional reinforced concrete buildings, have been widely used for mass housing, urban renewal, and post-earthquake reconstruction projects all over the world as well as in Turkey. However, there have been few dynamic tests performed on existing buildings with this structural system. This study investigates the dynamic structural properties of a typical nine-story reinforced concrete flat plate-wall building by forced vibration testing and develops its three-dimensional (3-D) linear elastic finite element structural model. The finite element model that uses the modulus of elasticity for concrete in ACI 318 predicts the natural vibration periods well. Mode shapes are also in good agreement with the test results. Door and window openings in the shear walls, and the basement with peripheral wall emerge as modeling considerations that have the most significant impact on structural system dynamic properties.

scholarly journals Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

2017 ◽  
Vol 2017 ◽  
pp. 1-26 ◽  
Author(s):  
Taehyun Kim ◽  
Ilwook Park ◽  
Usik Lee
Keyword(s):  
Modal Analysis ◽  
Timoshenko Beam ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Timoshenko Beams ◽  
Moving Loads ◽  
Analysis Method ◽  
Simply Supported

The modal analysis method (MAM) is very useful for obtaining the dynamic responses of a structure in analytical closed forms. In order to use the MAM, accurate information is needed on the natural frequencies, mode shapes, and orthogonality of the mode shapes a priori. A thorough literature survey reveals that the necessary information reported in the existing literature is sometimes very limited or incomplete, even for simple beam models such as Timoshenko beams. Thus, we present complete information on the natural frequencies, three types of mode shapes, and the orthogonality of the mode shapes for simply supported Timoshenko beams. Based on this information, we use the MAM to derive the forced vibration responses of a simply supported Timoshenko beam subjected to arbitrary initial conditions and to stationary or moving loads (a point transverse force and a point bending moment) in analytical closed form. We then conduct numerical studies to investigate the effects of each type of mode shape on the long-term dynamic responses (vibrations), the short-term dynamic responses (waves), and the deformed shapes of an example Timoshenko beam subjected to stationary or moving point loads.

Multistage Coupling of Eight Bladed Discs on a Solid Shaft

2010 ◽  
Author(s):  
Romuald Rza˛dkowski ◽  
Marcin Drewczynski
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Centrifugal Stiffening ◽  
Shaft Deflection ◽  
Forced Vibration Analysis

Considered here is the effect of multistage coupling on the dynamics of a rotor consisting of eight bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study, the global rotating mode shapes of flexible tuned bladed discs-shaft assemblies were calculated, taking into account rotational effects, such as centrifugal stiffening. The thus obtained natural frequencies of the blade, the shaft, the bladed disc, and the entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that the flexible modes of the tuned bladed discs affected by shaft motion were those with zero, one and two nodal diameters. In these modes shaft deflection was clearly visible. In forced vibration analysis a different EO excitation was applied for each stage. The importance of using models with different numbers of blades on each disc is apparent when compared with earlier results concerning discs with identical numbers of blades. Here the model of 8 discs with an equal number of blades on each disc is referred to as (Model 1), and the model of 8 discs with a different number of blades on each disc is referred to as (Model 2).

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.

Analytical and finite element solutions of free and forced vibration of unrestrained and braced thin-walled beams

2019 ◽  
Vol 26 (5-6) ◽  
pp. 255-276
Author(s):  
Wassim Jrad ◽  
Foudil Mohri ◽  
Guillaume Robin ◽  
El Mostafa Daya ◽  
Jihad Al-Hajjar
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Forced Vibration ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Vibration Modes ◽  
Coupled Modes ◽  
Steady State Method ◽  
Thin Walled ◽  
Benchmark Solutions

In this article, vibration of thin-walled beams with arbitrary open cross-section shape is investigated. Based on the beam element model accounting for warping and flexural–torsional coupling, analytical solutions for different boundary conditions are derived for higher free vibration modes in bending, torsion and flexural–torsional coupled modes. In the model, the effects of rotational inertial kinematic terms are considered. The finite element approach of the model is also investigated. Three-dimensional beams with seven degrees of freedom per node are adopted in the mesh process. Free vibration and forced vibration analyses are possible. In forced vibration, the behaviour of the beams is studied in the frequency domain using the steady-state method (modal analysis). Damping is considered using the Rayleigh model. The model is validated by comparing the results to benchmark solutions found in the literature and to other recent numerical and experimental results. Additional finite element simulations are performed by means of commercial softwares (Abaqus and Adina). In slender unrestrained beams, the vibration behaviour is predominated by torsion and lateral bending modes. In design, recourse to braces is a good compromise. This solution is discussed, and improvement of the vibration behaviour in the presence of intermediate braces is confirmed. Application of higher vibration modes in building and bridge design is outlined. The effects of the number and distribution of the intermediate braces to improve structural stability against vibration behaviour is outlined.

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