Transverse Free Vibration Analysis of Buried Pipeline under Simply Supported Restraint

2012 ◽  
Vol 446-449 ◽  
pp. 2210-2213
Author(s):  
Ting Yue Hao
Keyword(s):  
Vibration Analysis ◽  
Vibration Mode ◽  
Free Vibration Analysis ◽  
Beam Model ◽  
Pipe Conveying Fluid ◽  
Buried Pipeline ◽  
Simply Supported ◽  
Pipe Model ◽  
Elastic Foundation Beam ◽  
Conveying Fluid

The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli in the paper. Considering the effect of fluid flow in the pipe and outer soil constraint, the transverse vibration differential equation of buried pipeline is derived by using of Hamilton principle. By utilization of the first three-order modal and the orthogoality of main vibration mode, the equation is deduced and transformed into state formulas. The typical numerical example is analyzed by Matlab software. It is found that the natural frequency of pipe conveying fluid usually decreases along with flow velocity improving and the effect of foundation on the pipe stability is apparent.

Axial Vibration Analysis of Buried Pipeline

2012 ◽  
Vol 518-523 ◽  
pp. 3757-3760
Author(s):  
Ting Yue Hao
Keyword(s):  
Differential Equation ◽  
Vibration Analysis ◽  
Vibration Mode ◽  
Beam Model ◽  
Viscoelastic Foundation ◽  
Buried Pipeline ◽  
Axial Vibration ◽  
Pipe Model ◽  
Foundation Model ◽  
Elastic Foundation Beam

The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli in the paper. The supported forms are fixed support and free support in the analysis of axial vibration. Kelvin viscoelastic foundation model is adopted and the dynamic model of soil spring is regarded as linearity. Applying the principle of Hamilton, the differential equation of axial vibration is deduced. By utilization of the first three-order modal and the orthogoality of main vibration mode, the equations of earthquake excitaiton are discreted and transformed into common form of dynamic equation. A typical numerical example is analyzed by using of the Matlab software.

Establishment of Mathematical Model of Buried Pipeline on Nonlinear Soil Dynamic Model

2012 ◽  
Vol 452-453 ◽  
pp. 334-338 ◽  
Author(s):  
Ting Yue Hao
Keyword(s):  
Dynamic Model ◽  
Vibration Mode ◽  
Beam Model ◽  
Viscoelastic Foundation ◽  
Buried Pipeline ◽  
Critical Flow Velocity ◽  
Pipe Model ◽  
Foundation Model ◽  
Soil Dynamic ◽  
Elastic Foundation Beam

The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli in the paper, the supported form of pin rocker bearing in the analysis of transverse vibration. Kelvin viscoelastic foundation model is adopted and the dynamic model of soil spring is regarded as nonlinearity. Applying the principle of Hamilton, the differential equation of vibration is deduced. By utilization of the first three-order modal and the orthogoality of main vibration mode, the equations are discreted and transformed into state formulas. The critical flow velocity is obtained using the Matlab software in a typical numerical example.

Transverse Vibration Analysis of Buried Pipeline under Fluid-Solid Coupling Interaction

2012 ◽  
Vol 472-475 ◽  
pp. 2810-2813 ◽  
Author(s):  
Ting Yue Hao
Keyword(s):  
Differential Equation ◽  
Elastic Foundation ◽  
Transverse Vibration ◽  
Vibration Analysis ◽  
Beam Model ◽  
Buried Pipeline ◽  
Coupling Interaction ◽  
Numerical Example ◽  
Pipe Model ◽  
Elastic Foundation Beam

The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli, the form of pin rocker bearing in the analysis of transverse vibration in the paper. According the principle of Hamilton, after a series of variation, exchanging the order of integral and integration by parts, the transverse vibration differential equation of pipe is obtained without fluid. Considering different boundary consitions, the solving process is carried out. By utlization of MALAB language, the numerical example is analyzed, considering fluid and foundation. Thus, the fluid-solid coupling interaction is not ignored in transverse vibration in the buried pipeline.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

scholarly journals Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory

2021 ◽  
pp. 1-11
Author(s):  
Param D. Gajbhiye ◽  
Vishisht Bhaiya ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Shear Mode ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Thickness Shear

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.

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