scholarly journals Nonlinear free and forced vibration of Euler-Bernoulli beams resting on intermediate flexible supports

2018 ◽  
Vol 211 ◽  
pp. 02003
Author(s):  
Hatim Fakhreddine ◽  
Ahmed Adri ◽  
Saïd Rifai ◽  
Rhali Benamar
Keyword(s):  
Forced Vibration ◽  
Algebraic System ◽  
Displacement Function ◽  
Mode Shapes ◽  
Transverse Displacement ◽  
Bending Vibration ◽  
End Conditions ◽  
Flexible Supports ◽  
Elastic Restraints ◽  
Forced Vibration Analysis

This paper deals with the geometrically nonlinear free and forced vibration analysis of a multi-span Euler Bernoulli beam resting on arbitrary number N of flexible supports, denoted as BNIFS, with general end conditions. The generality of the approach is based on use of translational and rotational springs at both ends, allowing examination of all possible combinations of classical beam end conditions, as well as elastic restraints. First, the linear case is examined to obtain the mode shapes used as trial functions in the nonlinear analysis. The beam bending vibration equation is first written in each span. Then, the continuity requirements at each elastic support are stated, in addition to the beam end conditions. This leads to a homogeneous linear system whose determinant must vanish in order to allow nontrivial solutions to be obtained. Numerical results are given to illustrate the effects of the support stiffness and locations on the natural frequencies and mode shapes of the BNIFS. The nonlinear theory is then developed, based on the Hamilton’s principle and spectral analysis. The nonlinear beam transverse displacement function is defined as a linear combination of the linear modes calculated before. The problem is reduced to solution of a non-linear algebraic system using numerical or analytical methods. The nonlinear algebraic system is solved using an explicit method developed previously (second formulation) leading to the amplitude dependent nonlinear fundamental mode of the BNIFS.

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.

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.

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.

scholarly journals Geometrically nonlinear free and forced vibrations of Euler-Bernoulli multi-span beams

2018 ◽  
Vol 211 ◽  
pp. 02001 ◽  
Author(s):  
Hatim Fakhreddine ◽  
Ahmed Adri ◽  
Saïd Rifai ◽  
Rhali Benamar
Keyword(s):  
Algebraic System ◽  
Single Mode ◽  
Forced Vibrations ◽  
Nonlinear Frequency ◽  
Bending Vibration ◽  
End Conditions ◽  
Nonlinear Frequency Response ◽  
Simple Support ◽  
Beam Bending ◽  
Nonlinear Algebraic System

The objective of this paper is to establish the formulation of the problem of nonlinear transverse forced vibrations of uniform multi-span beams, with several intermediate simple supports and general end conditions, including use of translational and rotational springs at the ends. The beam bending vibration equation is first written at each span and then the continuity requirements at each simple support are stated, in addition to the beam end conditions. This leads to a homogeneous linear system whose determinant must vanish in order to allow nontrivial solutions to be obtained. The formulation is based on the application of Hamilton’s principle and spectral analysis to the problem of nonlinear forced vibrations occurring at large displacement amplitudes, leading to the solution of a nonlinear algebraic system using numerical or analytical methods. The nonlinear algebraic system has been solved here in the case of a four span beam in the free regime using an approximate method developed previously (second formulation) leading to the amplitude dependent fundamental nonlinear mode of the multi-span beam and to the corresponding backbone curves. Considering the nonlinear regime, under a uniformly distributed excitation harmonic force, the calculation of the corresponding generalised forces has led to the conclusion that the nonlinear response involves predominately the fourth mode. Consequently, an analysis has been performed in the neighbourhood of this mode, based on the single mode approach, to obtain the multi-span beam nonlinear frequency response functions for various excitation levels.

Free and Forced Vibration Analysis of an Idealized Compliant Tower With Superstructure, due to Current Loads, Wave Excitation, and Earthquake Impulses

2014 ◽  
Author(s):  
Ankit ◽  
N. Datta
Keyword(s):  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Wave Excitation ◽  
Uniform Beam ◽  
Compliant Tower ◽  
Forced Vibration Analysis ◽  
Beam Mode

A compliant tower (CT) is modeled as a partially dry, partially tapered, damped Timoshenko beam with the superstructure modeled as an eccentric tip mass, and a non-classical damped boundary at the base. The foundation is modeled as a combination of a linear spring and a torsional spring, along with linear and torsional dampers. The mean empty space factor due to the truss type structure of the tower is included. The effect of shear deformation and rotary inertia are included in the vibration analysis; with the non-uniform beam mode-shapes being a weighted sum of the uniform beam mode-shapes. The weights are evaluated by the Rayleigh-Ritz method, using the first ten modes and verified using Finite Element Method (FEM). The superstructure adds to the kinetic energy without affecting the stiffness of the beam, thereby reducing the natural frequencies. The weight of the superstructure acts as an axial compressive load on the beam, reducing its frequencies further. Kelvin-Voigt model of structural damping is included. A part of the structure being underwater, the virtual added inertia is included to calculate the wet natural frequencies. The CT is first subjected to steady current loads of a given velocity profile. The static deflection and overturning moment is estimated for current loads. The CT is then studied for wave excitation at various seas states. Morrison’s equation and Pierson-Moskowitz Spectrum are used to derive the forces for different sea states. The forced vibration analysis of the structure is done via Rayleigh-Ritz method and verified using FEM. The maximum horizontal deflection and shear stress of the base of the superstructure, and the normal/shear stresses at the foundation are analyzed. Finally, the CT is subjected to earthquake excitation, modeled as an arbitrary horizontal impact excitation at the base. The above forced vibration analysis is repeated.

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).

Assessment of Serviceability of the Footbridge Across Opatovska Street

2016 ◽  
Vol 827 ◽  
pp. 263-266
Author(s):  
Vladimír Sana
Keyword(s):  
Theoretical Analysis ◽  
Modal Analysis ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Fe Model ◽  
Matlab Code ◽  
Forced Vibration Analysis

This paper is focused on the assessment of serviceability of the footbridge structure, which has been excited by pedestrians and vandals. The three dimensional FE model of the footbridge structure was created for the necessities of theoretical modal analysis. Computed mode shapes and natural frequencies were subsequently used for the forced vibration analysis as an input files into MATLAB code. Results obtained by the theoretical analysis were compared with the experimental results. At the end of this paper, the comfort criterion of crossing pedestrians has been evaluated.

Forced vibration analysis for dynamic coupling of finite-element spring-reduced suspension system

2008 ◽  
Vol 222 (3) ◽  
pp. 349-356 ◽  
Author(s):  
Jaeyoung Kang
Keyword(s):  
Forced Vibration ◽  
Vibration Analysis ◽  
Load Transfer ◽  
Contact Stiffness ◽  
Coupled System ◽  
Suspension System ◽  
Frequency Variation ◽  
Coil Spring ◽  
Bending Vibration ◽  
Forced Vibration Analysis

The current paper studies the dynamic behaviour of a coil spring in a vehicle suspension system. A portion of the coil spring is contacted with the top and bottom spring pads. The contact interface is modelled as a set of linear spring elements on the contact nodes of the coil spring. The eigensensitivity analysis is conducted to investigate the frequency variation of the stiffness-coupled system with respect to the contact stiffness variation. In the forced vibration analysis, the transfer function through the coil spring is obtained. The contribution of the coil spring modes to the load transfer is calculated by the modal contribution factor. It is shown that some of the longitudinal and bending vibration modes participate on the load transfer.

scholarly journals Modal analysis of a membrane structure with actuators

2021 ◽  
Vol 1209 (1) ◽  
pp. 012052
Author(s):  
L Stulerova ◽  
L Kapolka ◽  
S Kmet
Keyword(s):  
Stress State ◽  
Modal Analysis ◽  
Static Analysis ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Membrane Structure ◽  
Natural Vibration ◽  
Mode Shapes ◽  
Forced Vibration Analysis ◽  
Modal Vibration

Abstract The aim of this paper is the analysis of the modal vibration of the membrane structure. Membranes are defined as structures of the lightweight architecture and they are currently very popular. They have a long history and development, in which they have reached a stage where we can complement them with action elements, also called actuators. These elements can change their length and thus affect a stress state of a membrane, which allows more efficient use. In addition to a static analysis, it is necessary to subject structures to a dynamic analysis, in this case we deal with the natural vibration. This modal analysis deals with the first 5 mode shapes and their dependence on the change in the length of the actuators. This initial calculation will be followed by a forced vibration analysis in the future.

Sign in / Sign up

Export Citation Format

Share Document