An Integral Representation Formulation of Some One-Dimensional Problems (original) (raw)
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Acoustical analysis of pipes with flow using invariant field functions
Journal of Sound and Vibration, 2003
Acoustic waves in pipes below first cut-on frequency are analyzed. Three invariant functions of the internal acoustic pressure field are evaluated. These functions allow for the determination of the following quantities: spatial mean RMS value of pressure spectrum, lower and upper bounds of the pressure spectrum for the entire pipe, pressure spectrum at an arbitrary position, speed of sound in the contained fluid and fluid flow velocity. Experimental identification of these quantities requires simultaneous pressure measurement in three points. Several measurements carried out on one air-filled and one water filled pipe have demonstrated the potential of pipe invariant functions for acoustical analysis.
Continuum Mechanics and Thermodynamics, 2010
The combined methodology of boundary integral equations and finite elements is formulated and applied to study the wave propagation phenomena in compound piping systems consisting of straight and curved pipe segments with compact elastic supports. This methodology replicates the concept of hierarchical boundary integral equations method proposed by L.I. Slepyan to model the time-harmonic wave propagation in wave guides, which have components of different dimensions. However, the formulation presented in this paper is tuned to match the finite element format and, therefore, it employs the dynamical stiffness matrix to describe wave guide properties of all components of the assembled structure. This matrix may readily be derived from the boundary integral equations, and such a derivation is superior over the conventional derivation from the transfer matrix. The proposed methodology is verified in several examples and applied for analysis of periodicity effects in compound piping systems of several alternative layouts.
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Journal of Sound and Vibration, 1981
A general algorithm is developed for estimating the beam type dynamic response of three dimensional multiplane pipe systems consisting of elbows and straight segments with smooth interface. The transfer matrix approach is adopted in modeling the elastodynamics of each duct with allowance for distributed loads. The formulation includes the acoustic coupling of a plane wave and elbow curvature. Secondary loads from plane wave distortion are considered from a modal solution of the Helmholtz equation in an equivalent rigid waveguide with square cross section. The effect of path imperfection is introduced as a perturbation from the hypothetical perfectly straight pipe. The one dimensional plane wave assumption is valid for frequencies below half the first cutoff frequency. Wave asymmetry from elbow curvature produces substantial increase in response level near and above cutoff .
A Note on an Analytic Solution for an Incompressible Fluid-Conveying Pipeline System
This paper presents an integral transform analytic solution to the equations governing a fluid-conveying pipeline segment where a gyroscopic or Coriolis force effect is taken into consideration. The mathematical model idealizes a segment of the pipeline as an elastic beam conveying an incompressible fluid. It is clearly shown that when such a system is supported at both ends and in a free motion, the Coriolis force dissipates no energy (or simply does not work) as it generates conjugate complex vibratory components for all flow velocities. It is demonstrated that the modal natural frequencies can be computed from the algebraic products of the complex frequency pairs. Clearly, the patterns of the characteristics of the system's natural frequencies are seen partly when the real and imaginary components are plotted, as widely seen in the literature. Nonetheless, results from this study revealed that a continuity profile exists to connect the subcritical, critical, and postcritical vibratory behaviours when the absolute values are plotted for any velocity. In the meantime, the efficacy and versatility of this method against the usual assumed spatial or temporal modal solutions are demonstrated by confirming the predictions and validity of results of earlier workers such as Paidoussis, Ziegler, and others where pre-and postdivergence behaviours are exhibited.
2019
This work involves the theoretical and experimental study of the vibroacoustic coupling occurring in a bent pipe line in the plane wave domain. In this type of piping line, resulting forces located in the elbows are generated by the internal sound pressure. The objective is then to estimate the internal pressure field as a function of the accelerations measured at each pipe bent. For this purpose, a modal extraction method of the structure is used in order to obtain the mode shapes and damping at each bend. Then, knowing these parameters, an inverse problem method is applied to estimate the pressure field, knowing the vibration field. An experimental validation of this prediction method demonstrated its robustness and simplicity of implementation, the industrial application of which concerns in particular the transport of gases inducing significant pressure gradients related to reciprocating compressor sources.
New Non-Linear Modelling for Vibration Analysis of a Straight Pipe Conveying Fluid
Journal of Sound and Vibration, 2002
A new non-linear model of a straight pipe conveying #uid is presented for vibration analysis when the pipe is "xed at both ends. Using the Euler}Bernoulli beam theory and the non-linear Lagrange strain theory, from the extended Hamilton's principle the coupled non-linear equations of motion for the longitudinal and transverse displacements are derived. These equations of motion are discretized by using the Galerkin method. After the discretized equations are linearized in the neighbourhood of the equilibrium position, the natural frequencies are computed from the linearized equations. On the other hand, the time histories for the displacements are also obtained by applying the generalized-time integration method to the non-linear discretized equations. The validity of the new modelling is provided by comparing results from the proposed non-linear equations with those from the equations proposed by PamK doussis.
Integral Method for Flow Induced Transverse Vibrations Analysis of Flexible Pipes
INCAS BULLETIN, 2020
This paper reviews some existing studies and numerical methods used for flow induced transverse vibrations analysis of flexible pipes. An integral method, based on the use of Green’s functions, already used for different straight beam dynamic analysis is adapted for the proposed subject. This approximate method leads to a matrix formulation and to an eigenvalue problem for free vibration analysis. The presented approach is able to estimate also the critical fluid velocities. Effects of boundary conditions and of elastic foundation characteristics, Coriolis terms and of other parameters on dynamic behavior of a pipe, can be included. Some numerical examples are also presented for comparisons with results obtained by FEM or with other data from literature. They show good agreement.
The Finite Element Technique for Modelling of Pipe System Vibroacoustical Characteristics
Procedia Engineering, 2017
In this paper, we consider two finite element techniques developed by the authors earlier for the solving differential equation systems of the complex configuration pipelines dynamics and compare calculation results with experimental data. One of the techniquies uses the new type of seven node finite elements for modeling vibroacoustical interaction between solid structures and oscillating fluid, another-two node finite elements. The proposed finite element techniques allow calculation of pipe vibroacoustical characteristics in the space-time domain. Because these techniques use the new element types, the computational coast is 3 orders less than for available finite element techniques, which use different element types for a fluid and a solid structure. The developed techniques are designed for a pipeline diameter much smaller than an acoustic wavelength in a fluid. The experimental research was conducted for the pipe system of the hydraulic test bench for generating pressure pulsation. The results of calculation by the proposed finite element techniques were confirmed by experimental data.