The effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates

Abstract

The boundary conditions of a vibrating plate are known to have an influence on its sound radiation for frequencies below the critical frequency. To investigate this effect in a systematic way, the average radiation efficiency and radiated power are calculated for a rectangular plate set in an infinite baffle using a modal summation approach. Whereas analytical expressions exist for simply supported boundary conditions, a numerical approach is required for other cases. Nine combinations of boundary conditions are considered, consisting of simply supported, clamped and free edges on different plate edges. The structural vibration is approximated by using independent beam functions in orthogonal directions allowing simple approximate formulae for mode shapes and natural frequencies.This assumption is checked against a finite element model and shown to give reliable results. It is shown that a free plate has the lowest radiation efficiency and a clamped plate the highest for most frequencies between the fundamental panel natural frequency and the critical frequency. Other combinations of boundary condition give intermediate results according to the level of constraint introduced. The differences depend on frequency: excluding the extreme case of a fully free plate all the other boundary conditions give results within a range of 8 dB in the middle part of the shortcircuiting region, decreasing towards the critical frequency. At low frequency the differences can be even greater, in some cases up to 20 dB. These conclusions are shown to hold for a range of plate thicknesses and dimensions.Keywords: plate vibration, baffled plates, radiation efficiency, radiation ratio, boundary condition. IntroductionIn many engineering applications it is important to be able to estimate the noise radiated by a vibrating structure during its design stage. In most cases the structures under consideration, whether industrial machinery, vehicles or civil structures such as bridges, can be subdivided into smaller components; thin vibrating panels, strips and beams are often important components that are 3 responsible for noise radiation. To evaluate the noise produced a common procedure is to evaluate the vibration velocity levels of each component and to estimate their acoustic power levels through their dimensions and radiation efficiency. It is particularly useful to study the radiation efficiency of the elementary components in order to be able to characterise the acoustic performance of the structure they form.The radiation efficiency of an object at a given frequency or frequency band can be defined as the radiated sound power rad W , normalized by the radiating area S, the air density  , the speed of sound c and the space-averaged mean square vibration velocity The denominator in eq. (1) represents the power that would be radiated by a surface area S, vibrating as a rigid piston to produce plane waves, with a mean square velocity equal to the surface-averaged mean-square velocity of the actual object. Furthermore, if the me...

The acoustic radiation impedance of a rectangular panel

“…Squicciarini et al [23] have shown that real part of the normalized radiation impedance (radiation efficiency) of a point excited panel mounted in an infinite baffle depends on the edge conditions. In particular they have shown that when m > 1 a freely supported panel has lower radiation efficiency than a simply supported panel and that a clamped panel has higher radiation efficiency than a simply supported panel except at very low values of k b e¼mke where the radiation is dominated by the fundamental drum mode.…”

Low-Frequency Vibration and Radiation Performance of a Locally Resonant Plate Attached with Periodic Multiple Resonators

“…As illustrated in Section 2.1, the four boundaries of the plate are supported by a linear spring with stiffness k and a torsional spring with stiffness K. The free, simply supported, and clamped boundary conditions can be simulated by using specific stiffness values of k and K: the free boundary condition can be expressed when k = 0 and K = 0; the simply supported boundary condition can be expressed when k tends to infinity and K = 0; and the clamped boundary condition can be expressed when both k and K tend to infinity. The variation of the boundary conditions can result in the difference in the vibration response and acoustic performance [29,30]. In this paper, three kinds of different boundary conditions are applied to the plate, including fully free boundary conditions ('FFFF'), fully simply supported boundary conditions ('SSSS'), and fully clamped boundary conditions ('CCCC').…”

“…Figure 12c) that the acoustic behavior behaves quite different when no constraints are applied to the plate. It has been explained in reference [29] that the acoustic power in the low-frequency range radiated from the FFFF bare plate is mainly dominated by three rigid body modes. The rigid body motion and rotation of the FFFF plate make the first few flexural modes inefficiently radiating ones, and then the acoustic power at these modal frequencies is not highlighted, unlike the results of the finite plates with higher constraints.…”

Comparison for the Effect of Different Attachment of Point Masses on Vibroacoustic Behavior of Parabolic Tapered Annular Circular Plate

“…Lee and Singh [26] used a simplified disk brake rotor to investigate the acoustic radiation through a semi-analytical method. Thompson et al [27,28] analyzed the modal approach for different boundary conditions to calculate the average radiation efficiency of a rectangular plate. Rayleigh [29] determined the sound radiation from flat finite structures.…”