Initial Investigation of Energy Finite Element Validation on High‐Frequency Flexural Vibration of Stiffened Thin Orthotropic Plates

Abstract

Energy finite element analysis (EFEA) has unique advantages in solving high-frequency dynamic responses of orthotropic structures, due to its ability to obtain detailed local response information. In order to accurately predict high-frequency vibration response of the stiffened orthotropic plate, EFEA theory on the propagation of bending wave in the orthotropic structure and the energy transfer coefficient which express the energy transfer at the stiffener was investigated. Based on the EFEA theory presented, high-frequency dynamic responses of a stiffened orthotropic plates were predicted. Furthermore, tests were done for the same problem, and differences between prediction and test were discussed. Finally, the future works were pointed out.

Analytical model of high-frequency energy flow response for a beam with free layer damping

“…The last two terms of equation 10are near-field solutions describing the evanescent waves, which are dissipated rapidly more than one wavelength away from the boundaries and driving points. 26 Departing from x = 0, as represented in Figure 3, the displacement ratio of the right travelling wave Ae Àjk f x to the evanescent wave Ce Àk f x is dependent on e k f1 + k f2 ð Þ x , as shown in equation (14). If the reference for the waves moving to the left is taken at x = x 0 , the displacement ratio of the left travelling wave Be jk f x to the evanescent wave De k f x is dependent on e k f1 + k f2 ð…”

“…where B 0 and D 0 are constants related to waves departing from x = x 0 by B 0 = Be jk f x 0 and D 0 = De k f x 0 . For a beam with high frequency vibration, the nearfield solutions are much less than far-field solutions from equations (14) and (15) due to k f1 + k f2 ð Þ x ) 1 and k f1 + k f2 ð Þx À x 0 ð Þ)1 away from the boundaries and driving points. The former are usually neglected while the latter are useful for the energy flow analysis.…”

“…6 The governing equations of EFA were developed for structural components such as rods, 7–9 beams, 7,8 membranes, 10 and plates. 11,12 To predict the vibrational response of the coupled structures, the energy flow coupling relationships were derived at various joints of these structures like beam-plate, 13,14 plate-plate, 15,16 shell-shell, 17 and structure-to fluid, 18–20 and acoustic 21,22 field coupling. For structures in thermal environment, the energy density governing equation of beams with thermal effects was derived by Zhang et al, 23 whose work was afterwards extended by Wang et al 24 to plates in non-uniform thermal environment.…”

Prediction of the Transient Local Energy by Energy Finite Element Analysis

“…Some complex theories, such as the Timoshenko beam [20], the Mindlin plate [21,22], and the Rayleigh-Love and Rayleigh-Bishop rod theories [23], have also been adopted by EFEA. It has also been applied to some built-up structures, such as composite structures [24], beams with stepped thickness and variable cross-sections [25], and stiffened plates [26][27][28][29]. An energy flow analysis model for free-layer damped treated panels has recently been developed [30].…”