Investigation of Effective Bending and Shear Stiffness of Thin-Walled Girders Related to Ship Hull Vibration Analysis

1989 ◽  
Vol 33 (04) ◽  
pp. 298-309
Author(s):  
Ivo Senjanovic ◽  
Ying Fan
Keyword(s):  
Finite Element ◽  
Frequency Domain ◽  
Vibration Analysis ◽  
Ship Hull ◽  
Moment Of Inertia ◽  
Cross Sectional ◽  
Simply Supported ◽  
Thin Walled ◽  
Beam Parameters ◽  
Shear Area

Application of beam theory in flexural vibration analysis of thin-walled girders is extended for the high-frequency domain by introducing the concept of effective values of beam parameters, that is, cross-sectional moment of inertia, shear area, mass, and mass moment of inertia. Formulation of these parameters is based on equivalence of deformation energy and inertia work, respectively, for a considered structure and its beam model, resulting in the same values of their natural frequencies. For illustration, the natural vertical vibration of a simply supported pontoon has been considered, where it was possible to obtain the analytical solution due to sinusoidal mode shapes. The effective values of cross-sectional moment of inertia and shear area show significant variation in frequency domain. Transfer of effective values of beam parameters, determined for simply supported structure, in the case of other boundary conditions is suggested, based on equal mode wavelengths, and checked for the free pontoon. The results show very low discrepancies compared with a three-dimensional finite-element model solution, so this procedure may be applied generally, as well as to the problem of ship hull vibration. In conclusion, the possibility of calculating the values of effective parameters for multicell ship cross sections, utilizing the theory of folded structure and the finite-element method, is pointed out.

scholarly journals Nonlinear Pounding Analysis of Multispan and Simply Supported Beam Bridges Subjected to Strong Ground Motions

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Hong-Yu Jia ◽  
Xian-Lin Lan ◽  
Nan Luo ◽  
Jian Yang ◽  
Shi-Xiong Zheng ◽  
...  
Keyword(s):  
Finite Element ◽  
Parameter Analysis ◽  
Cross Sectional ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Finite Element Software ◽  
Impact Element ◽  
Bearing Stiffness ◽  
The Impact ◽  
Gap Width

To investigate the nonlinear impact effect of multispan simply supported beam bridges under strong earthquakes, firstly, the dynamic motion equation, the algorithm of its solution, and some pounding modelling methods are presented and the finite element model of a considered multispan simply supported railway beam bridge is established in the nonlinear finite element software of SAP2000 in which the primary nonlinear characteristics of the bearing and the impact element are considered herein. Secondly, the natural vibration characteristic of the considered railway bridge is analyzed to prepare for the subsequent parameter analysis. Finally, the influence of three nonlinear parameters, i.e., stiffness of impact element, separation gap width of expansion joint, and bearing stiffness, on impact responses of bridge structures is studied. The results show that the first several modes of multispan simply supported beam bridges are mainly longitudinal and vertical vibrations. Under longitudinal seismic excitations, the large longitudinal displacement response is induced possibly and results in the collision or even unseating of superstructures at the expansion joints and abutments. The influence of separation gap width between adjacent decks on the pounding effect of bridges is greater than that of collision stiffness originated from the pounding modelling element. The impact force and pounding number run up to the maximum conditional on the collision stiffness of 9.9 × 109 (N/m) and the separation gap width of 0.14 (m). The bearing stiffness affects significantly the displacement of the pier top and the cross-sectional internal force at the bottom of piers but has little effect on the collision force and number.

Free Vibration Analysis of Circular FGM Plate Having Variable Thickness Under Axisymmetric Condition by Finite Element Method

2005 ◽  
Author(s):  
M. Nikkhah-Bahrami ◽  
Abazar Shamekhi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Thickness Variation ◽  
Simply Supported ◽  
Element Method

This study presents the free vibration analysis of circular plate having variable thickness made of functionally-graded material. The boundary conditions of the plate is either simply supported or clamped. Dynamic equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander’s non-linear strain-displacement relation for thin plates. The finite element method is used to determine the natural frequencies. The results obtained show good agreement with known analytical data. The effects of thickness variation and Poisson’s ratio are investigated by calculating the natural frequencies. These effects are found not to be the same for simply supported and clamped plates.

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 Guided Waves in Thin-Walled Structural Members

2001 ◽  
Vol 123 (3) ◽  
pp. 376-382 ◽  
Author(s):  
A. H. Shah ◽  
W. Zhuang ◽  
N. Popplewell ◽  
J. B. C. Rogers
Keyword(s):  
Finite Element ◽  
Guided Waves ◽  
Polynomial Interpolation ◽  
Axial Direction ◽  
Thin Plates ◽  
Infinite Length ◽  
Structural Members ◽  
Cross Sectional ◽  
Frequency Spectra ◽  
Thin Walled

A semi-analytical finite element (SAFE) formulation is proposed to study the wave propagation characteristics of thin-walled members with an infinite length in the longitudinal (axial) direction. Common structural members are considered as an assemblage of thin plates. The ratio of the thickness of the plate to the wavelength in the axial direction is assumed to be small so that the plane-stress assumption is valid. Employing a finite element modeling in the transverse direction circumvents difficulties associated with the cross-sectional profile of the member. The dynamic behavior is approximated by dividing the plates into several line (one-dimensional) segments and representing the generalized displacement distribution through the segment by polynomial interpolation functions. By applying Hamilton’s principle, the dispersion equation is obtained as a standard algebraic eigenvalue problem. The reasonably good accuracy of the method is demonstrated for the lowest modes by comparing, where feasible, the results with analytical solutions. To demonstrate the method’s versatility, frequency spectra are also presented for I and L shaped cross sections.

scholarly journals Assessment of Model Uncertainty in the Prediction of the Vibroacoustic Behavior of a Rectangular Plate by Means of Bayesian Inference

2021 ◽  
pp. 264-277
Author(s):  
Nikolai Kleinfeller ◽  
Christopher M. Gehb ◽  
Maximilian Schaeffner ◽  
Christian Adams ◽  
Tobias Melz
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Bayesian Inference ◽  
Boundary Conditions ◽  
Model Uncertainty ◽  
Prediction Error ◽  
Finite Element Models ◽  
Simply Supported ◽  
Thin Walled Structures ◽  
Thin Walled

AbstractDesigning the vibroacoustic properties of thin-walled structures is of particularly high practical relevance in the design of vehicle structures. The vibroacoustic properties of thin-walled structures, e.g., vehicle bodies, are usually designed using finite element models. Additional development effort, e.g., experimental tests, arises if the quality of the model predictions are limited due to inherent model uncertainty. Model uncertainty of finite element models usually occurs in the modeling process due to simplifications of the geometry or boundary conditions. The latter highly affect the vibroacoustic properties of a thin-walled structure. The stiffness of the boundary condition is often assumed to be infinite or zero in the finite element model, which can lead to a discrepancy between the measured and the calculated vibroacoustic behavior. This paper compares two different boundary condition assumptions for the finite element (FE) model of a simply supported rectangular plate in their capability to predict the vibroacoustic behavior. The two different boundary conditions are of increasing complexity in assuming the stiffness. In a first step, a probabilistic model parameter calibration via Bayesian inference for the boundary conditions related parameters for the two FE models is performed. For this purpose, a test stand for simply supported rectangular plates is set up and the experimental data is obtained by measuring the vibrations of the test specimen by means of scanning laser Doppler vibrometry. In a second step, the model uncertainty of the two finite element models is identified. For this purpose, the prediction error of the vibroacoustic behavior is calculated. The prediction error describes the discrepancy between the experimental and the numerical data. Based on the distribution of the prediction error, which is determined from the results of the probabilistic model calibration, the model uncertainty is assessed and the model, which most adequately predicts the vibroacoustic behavior, is identified.

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