scholarly journals On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
O. Barry ◽  
D. C. D. Oguamanam ◽  
J. W. Zu
Keyword(s):  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Approximate Methods ◽  
Orthogonality Relations ◽  
Mass Damper ◽  
Forced Vibration Analysis ◽  
Mass Spring

The exact natural frequencies, mode shapes, and the corresponding orthogonality relations are important in forced vibration analysis via modal expansion. In the present paper, a free vibration analysis is conducted to determine the exact natural frequencies and mode shapes of an axially loaded beam carrying several absorbers. An explicit expression is presented for the generalized orthogonality relations. These generalized orthogonality conditions are employed along with the assumed modes method to perform forced vibration analysis. The present approach is compared to other approximate methods in the literature with the classical orthogonality relations and different choice of mode shapes. The results indicate that the use of the generalized orthogonality relation with the exact mode shapes is required for a precise investigation of the dynamic response of a beam with mass-spring-mass-damper system.

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.

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 of Several Bladed Discs on the Shaft

2006 ◽  
Author(s):  
Romuald Rza¸dkowski ◽  
Marcin Drewczynski
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Coupling Effects ◽  
Centrifugal Stiffening ◽  
Shaft Deflection ◽  
Forced Vibration Analysis

The effect of multistage coupling on the dynamics of a rotor consisting of eight bladed discs on a solid shaft is considered. Free vibrations are examined using finite element representations of rotating single blades, bladed discs, and the complete rotor. In this study, the global rotating mode shapes of flexible tuned bladed discs-shaft assemblies are calculated. Rotational effects, such as centrifugal stiffening are accounted for. The calculated natural frequencies obtained from the blade, the shaft, the bladed disc, and the complete shaft with discs are carefully examined to discover resonance conditions and the coupling effects. It was found that the flexible modes of the tuned bladed discs affected by shaft motion are those with zero, one and two nodal diameters. In these modes the shaft deflection is clearly visible. Different EO excitation is applied for particular stages in forced vibration analysis.

Large Amplitude Forced Vibration Analysis of Stiffened Plates under Harmonic Excitation

2012 ◽  
pp. 26-61
Author(s):  
Anirban Mitra ◽  
Prasanta Sahoo ◽  
Kashinath Saha
Keyword(s):  
Free Vibration ◽  
Forced Vibration ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Mathematical Formulation ◽  
Free Vibration Analysis ◽  
Harmonic Excitation ◽  
Stiffened Plates ◽  
Backbone Curve ◽  
Forced Vibration Analysis

Large amplitude forced vibration behaviour of stiffened plates under harmonic excitation is studied numerically incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Large amplitude free vibration analysis of the same system is carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the set of governing equations for both forced and free vibration problems derived using Hamilton’s principle. Appropriate sets of coordinate functions are formed by following the two dimensional Gram-Schmidt orthogonalization procedure to satisfy the corresponding boundary conditions of the plate. The problem is solved by employing an iterative direct substitution method with an appropriate relaxation technique and when the system becomes computationally stiff, Broyden’s method is used. The results are furnished as frequency response curves along with the backbone curve in the dimensionless amplitude-frequency plane. Three dimensional operational deflection shape (ODS) plots and contour plots are provided in a few cases.

Modeling and Free Vibration Analysis of a Complex Cable-Stayed Bridge

2012 ◽  
Author(s):  
D. Q. Cao ◽  
M. T. Song ◽  
W. D. Zhu
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Longitudinal Vibrations ◽  
Simply Supported ◽  
Cable Stayed Bridge ◽  
Linear Partial Differential Equations ◽  
Localized Mode ◽  
Linearized Model

A complex cable-stayed bridge that consists of a simply-supported four-cable-stayed deck beam and two rigid towers is studied. The nonlinear and linear partial differential equations that govern the motions of the cables and segments of the deck beam, respectively, are derived, along with their boundary and matching conditions. The undamped natural frequencies and mode shapes of the linearized model of the cable-stayed bridge, which includes both the transverse and longitudinal vibrations of the cables, are determined. Numerical analysis of the natural frequencies and mode shapes of the cable-stayed bridge is conducted for a symmetrical case with regards to the sizes of the components of the bridge and the initial sags of the cables. The results show that there are very close natural frequencies and localized mode shapes.

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.

Free Vibration Analysis of an Inflated Toroidal Shell

2002 ◽  
Vol 124 (3) ◽  
pp. 387-396 ◽  
Author(s):  
Akhilesh K. Jha ◽  
Daniel J. Inman ◽  
Raymond H. Plaut
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Free Vibration Analysis ◽  
Longitudinal Direction ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Toroidal Shell

Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied.

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.

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