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.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

scholarly journals Bending–torsional-coupled vibrations and buckling characteristics of single and double composite Timoshenko beams

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983445
Author(s):  
Ma’en S Sari ◽  
Wael G Al-Kouz ◽  
Rafat Al-Waked
Keyword(s):  
Slenderness Ratio ◽  
Equations Of Motion ◽  
Mode Shapes ◽  
Timoshenko Beams ◽  
Engineering Structures ◽  
Axial Forces ◽  
Double Beam ◽  
Tensile Forces ◽  
Torsional Coupling ◽  
The Stability

The stability and free vibration analyses of single and double composite Timoshenko beams have been investigated. The closed-section beams are subjected to constant axially compressive or tensile forces. The double beams are assumed to be connected by a layer of elastic translational and rotational springs. The coupled governing partial differential equations of motion are discretized, and the resulted eigenvalue problem is solved numerically by applying the Chebyshev spectral collocation method. The effects of the elastic layer parameters, the axial forces, the slenderness ratio, the bending–torsional coupling, and the boundary conditions on the critical buckling loads, mode shapes, and natural transverse frequencies have been studied. A parametric study was performed, and the obtained results revealed different features, which hopefully can be useful for single- and double-beam-like engineering structures.

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.

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 Vibrations of Viscoelastic Timoshenko Beams

1976 ◽  
Vol 98 (3) ◽  
pp. 820-826 ◽  
Author(s):  
C. C. Huang ◽  
T. C. Huang
Keyword(s):  
Boundary Conditions ◽  
Laplace Transform ◽  
Attenuation Factor ◽  
Equations Of Motion ◽  
Bending Moment ◽  
Expansion Method ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Mode Shapes ◽  
Timoshenko Beams

In a previous paper, the correspondence principle has been applied to derive the differential equations of motion of viscoelastic Timoshenko beams with or without external viscous damping. To study free vibrations these equations are solved by Laplace transform and boundary conditions are applied to obtain the attenuation factor and the frequency of the damped free vibrations and mode shapes. The present paper continues to analyze this subject and deals with the responses in deflection, bending slope, bending moment and shear for forced vibrations. Laplace transform and appropriate boundary conditions have been applied. Examples are given and results are plotted. The solution of forced vibrations of elastic Timoshenko beams obtained as a result of reduction from viscoelastic case and by eigenfunction expansion method concludes the paper.

Forced Vibration of Mistuned Bladed Discs in Last Stage LP Steam Turbine

2016 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Artur Maurin ◽  
Leszek Kubitz ◽  
Ryszard Szczepanik
Keyword(s):  
Steam Turbine ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Lower Stress ◽  
Free And Forced Vibrations ◽  
Specific Order ◽  
Last Stage ◽  
Forced Vibration Analysis ◽  
Blade Geometry

During the exploitation of a commercial LP steam turbine, self-excitation occurred in the last stage of slender blades, inducing high vibration amplitudes. These problems were solved by changing the geometry of certain blades (feathering) and arranging them in a specific order (alternating mistuning). This paper presents free and forced vibrations of various mistuned steam turbine bladed discs. The natural frequencies and mode shapes of the steam turbine bladed discs were calculated using FEM models. Two different approaches to mistuning were applied: either the blade geometry or the Young’s Modulus were changed. Next, the results were compared. This showed that blade geometry mistuning gave the best results for long blades in the case of higher mistuning. The forced vibration analysis showed that the maximal blade stress location differed, depending on the kind of mistuning. The application feathering and alternating mistuning showed lower stress levels than the tip-timing measured standard mistuning pattern.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Discs

2003 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Nonlinear Structure ◽  
Sector Model ◽  
Symmetry Properties ◽  
Symmetric Structures

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disc using a periodic sector model without any loss of accuracy in calculations and modelling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disc forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disc model: (i) using sector finite element matrices; (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disc with shrouds have demonstrated the high efficiency of the method.

Forced Vibration Analysis of Spinning Disks Subjected to Transverse Loads

2015 ◽  
Vol 15 (03) ◽  
pp. 1450049 ◽  
Author(s):  
Hamed Norouzi ◽  
Davood Younesian
Keyword(s):  
Coordinate System ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Rotating Disk ◽  
Transverse Load ◽  
Solution Technique ◽  
Rotating Speed ◽  
Stationary Coordinate System ◽  
Forced Vibration Analysis ◽  
The Galerkin Method

Forced vibration of a rotating disk subjected to a stationary transverse load is studied in this paper. Time and frequency responses are obtained and effects of the rotating speed on the natural frequencies are evaluated. Finite element method (FEM) is employed as the solution technique and natural frequencies are obtained for different speeds. Forced vibration is then considered and disk responses are determined using the Galerkin method. The solution is determined in two different coordinate systems. In the first one, the disk is assumed to be rotating in an inertial coordinate system, while in the second coordinate system, a rotating peripheral force is applied on a stationary disk. The objective here in this paper is to compare the two modeling scenarios and is to find limiting range of the rotational speed for employing the stationary coordinate system.

Sign in / Sign up

Export Citation Format

Share Document