Numerical vibroacoustic analysis of plates with constrained-layer damping patches

Abstract

A numerical vibroacoustic model that can manage multilayered plates locally covered with damping patches is presented. All the layers can have an on-axis orthotropic viscoelastic behavior. Continuity of displacements and transverse shear stresses at each interface is enforced, which permits to write the entire displacement field in function of the displacements of the--common--first layer, leading to a two-dimensional plate model. The problem is then discretized by Rayleigh-Ritz's method using a trigonometric basis that includes both sine and cosine functions in order to treat various boundary conditions. The excitation can be of mechanical kind (concentrated or distributed forces) or of acoustic kind (plane wave of any incidence, diffuse field, etc.). The model permits to compute different vibroacoustic indicators: the mean square velocity of the plate, the radiation efficiency, and the transmission loss. Comparisons between the present model and numerical results from literature or finite element computations show that the model gives good results in both mechanical and acoustical aspects. Then, a comparison of the effects of different distributions of patches is presented. The role of the surface covering rate is first discussed, followed by a study involving different geometries for the same surface covering rate.

Radiation efficiency of damped plates

“…Consequently, the infinite plate radiates no sound below the critical frequency. 11 If the plate is damped, the amplitude of the flexural waves is decaying with increasing distance from the excitation point. The amplitudes of the propagating flexural waves are no longer equal, as illustrated in Fig.…”

“…This phenomenon is often stated to be due to that the damping treatment reduces the plate response significantly, while having less effect on the radiated sound. 11 This phenomenon, however, has not been well explained so far.…”

A multilayer anisotropic plate model with warping functions for the study of vibrations reformulated from Woodcock's work

“…These above 14 equalities show that only 69 − 14 = 55 strain energy coefficients are independent, which is the number previously announced after the examination of symmetries of tensors done in section 2.4 starting from formula (19). The presence of minus sign in the blocs corresponding to B and E blocs is not easy to understand because it is due to two sign differences between the two formulations: −w ,αβ are used here instead of w ,αβ in Woodcock's work, and γ α3 are used here instead of ϕ α = −γ α3 (hence ϕ α,β = −γ α3,β ) in Woodcock's work.…”

“…This model has been developed in a slightly different way: the middle plane of the first layer is the reference plane. This is particularly useful, although not essential, to study plates damped with patches [19,20]. In this last case, the number of layers can vary from a point to another and the definition of a middle plane is difficult to establish.…”

Novel Approach to The Design of Sound Insulating Composites by Means of a Non-linearly Extrapolated Master Curve

“…In order to compensate the error introduced by the diffused sound field condition and the neglected boundary conditions, we choose to model our system by means of a technique capable of carrying out a high regular frequency analysis and discretizing the geometrical testing environment. FEM models typically can't be used to model high regular frequency Vibroacoustic phenomena, as the low wavelength involved usually require an higher number of seeds for the correct discretization (ideally a number higher than [30]). As the high frequencies involved in this study involve a great number of modal contributions, we used a SEA approach.…”