Bending, longitudinal and torsional wave transmission on Euler-Bernoulli and Timoshenko beams with high propagation losses

Abstract

Advanced Statistical Energy Analysis (ASEA) is used to predict vibration transmission across coupled beams which support multiple wave types up to high frequencies where Timoshenko theory is valid. Bending-longitudinal and bending-torsional models are considered for an L-junction and rectangular beam frame. Comparisons are made with measurements, Finite Element Methods (FEM) and Statistical Energy Analysis (SEA). When beams support at least two local modes for each wave type in a frequency band and the modal overlap factor is at least 0.1, measurements and FEM have relatively smooth curves. Agreement between measurements, FEM, and ASEA demonstrates that ASEA is able to predict high propagation losses which are not accounted for with SEA. These propagation losses tend to become more important at high frequencies with relatively high internal loss factors and can occur when there is more than one wave type. At such high frequencies, Timoshenko theory, rather than Euler-Bernoulli theory, is often required. Timoshenko theory is incorporated in ASEA and SEA using wave theory transmission coefficients derived assuming Euler-Bernoulli theory, but using Timoshenko group velocity when calculating coupling loss factors. The changeover between theories is appropriate above the frequency where there is a 26% difference between Euler-Bernoulli and Timoshenko group velocities.

Experimental and numerical validation of Advanced Statistical Energy Analysis to incorporate tunneling mechanisms for vibration transmission across a grillage of beams

“…Previous work by the authors [1] used Advanced Statistical Energy Analysis (ASEA) [2] to model a rectangular beam framework which was shown to be able to predict the high propagation losses at high frequencies. This paper extends the assessment of ASEA to determine whether vibration transmission can be predicted across a finite, periodic structure where there is significant indirect coupling, i.e.…”

“…The transmission coefficients are determined using wave theory based on semi-infinite Euler-Bernoulli beams for a bending and longitudinal wave model (BL model), and a bending and torsional wave model (BT model). The wave theory for L-junctions is given in previous work [1]; hence, only the derivations for T-junctions are given in the appendices of this paper.…”

“…This paper considers whether ASEA incorporating multiple wave types can predict vibration transmission across a finite, periodic framework of beams, when this framework is (a) "perfectly periodic" (identical material properties and geometry) and (b) "imperfectly periodic" with uncertainty in the Young's modulus of the beams. In previous work [1], seven identical L-junctions were built from Perspex beams and tested. These gave nominally identical results in terms of the modal fluctuations.…”

Numerical study of acoustic transmission across heavily damped plate using hybrid Ray-Tracing-SEA method

“…This approach was validated against FEM on periodic box-like structures which were highly damped to simulate concrete walls and floors in buildings. Wang and Hopkins 18 subsequently validated ASEA using ray tracing for multiple wave types on beams with relatively high propagation losses. With the development of material technology, the internal loss factors of well-designed passive damping treatment could reach as high as 0.21 to 0.53.…”

“…Figure18. Energy ratio (contribution from direct field or first order reflection field to the total energy transmitted through each segment) against length with ILF = 0.015 and ILF = 0.060 (edge AB).…”