Charles Pezerat

Periodic assembly of multicoupled beams: Wave propagation and natural modes

The present work is concerned with the vibrations of a discrete multi‐coupled periodic system. It lies within a larger study on the vibroacoustic behaviour of a heat exchanger. These structures are usually made of a succession of huge number of identical parallel fins (around 600 per meter) connected by tubes conveying the coolant fluid. By now their behaviour can not be calculated using FE model. As a first step, the periodicity principles are applied on a simpler structure, i.e.. an assembly of identical beams linked by several damped springs. The basic unit is symmetric and composed of one flexural beam with several springs on each side. Using the Floquet‐Blochs theorem and the works of Denys Mead (receptance matrix), it is possible to completely describe the whole structure behaviour (natural modes, response) only from the vibroacoustic knowledge of the basic unit. This has be done analytically and the results were confirmed by a (very time consuming) FE model calculation. The study of the basic unit can also give valuable information on the physical phenomena governing the transmission from one unit to the next, and then the propagation in the whole structure.

Prediction of multiple sources exciting a cylinder filled by a heavy fluid using an inverse method

In this paper, a finite circular cylindrical shell filled with fluid and subjected to multiple excitations (mechanical and acoustical) is studied. The exact solution for vibration is based on the Donnell thin shell theory and the frequency equation of the coupled vibration problem is obtained by taking account of the effect of the inner fluid. In the direct problem, displacements are obtained by the modal method when the cylinder is assumed to be simply supported. The proposed predicting method is based on finite difference principle which makes it possible to express the derivatives of the equation of motion in term of displacements in order to calculate the distribution resulting from excitations. Simulations show that there exists a condition under which deformations can be neglected but it is found that this assumption would cause error in the results when exciting the cylinder below the ring frequency. In order to evaluate the effect of the fluid, some results of the cylindrical shell filled with fluid are compared with those of the shell in vacuo. Other numerical results are finally presented using exact and inexact displacements and a regularisation procedure based on the filtering of the wavenumber domain is used to minimise the effect of errors. This technique gives good results and makes the problem stable when the displacements are contaminated by noise resulting from measurement.