Theoretical analysis of sound radiation of an elastically supported circular plate

Active control of structures and sound radiation modes and its application in vehicles

“…Yamaguchi et al 6 used force radiation modes to reduce the sound radiation of structures and systematically studied the position and amplitude of forces. Rdzanek et al 7 theoretically studied the sound radiation problems of the plate with flexibly supported, simply supported and free boundary conditions, and verified the studied result through the numerical simulation. Lee and Singh 8 applied two methods to compute sound radiation problems of the circular plate from structural modes of radial vibrations.…”

Vibroacoustic Response of an Annular Sandwich Electrorheological Disc

“…Moreover, the variation of the total work done by the external force q(r, ϕ, t) is written as (9) Next, direct substitution of the strain-displacement relations (2) and (3) in (6) yields where the moment resultants in the above equation are defined as [34] (11) Now, employing (9), (10), and (12) into Hamilton's principle (Eq. 5), and making use of the so-called gradient theorem (see Appendix A), while taking advantage of the fundamental lemma of calculus of variation [32], results into the general form of equations of motion for forced vibrations of the ERF-based sandwich annular plate: (13) where i = 1, 3; δ 1 = 1 and δ 3 = −1, are given in Eqs. (7b), and the relevant shear resultants in the top and bottom skin layers are defined as [34]: (14) where i = 1, 3.…”

“…The authors used the Rayleigh integral formula to examine the effect of rotary inertia and shear deformations on the acoustic sound radiation. In a series of papers, Rdzanek and coworkers used integral formulation techniques and the method of stationary phase to analyze time-harmonic sound radiation from thin circular/annular plates with various edge conditions [11][12][13][14][15]. Rdzanek and Zawieska [16] investigated far-field sound radiation control from a vibrating clamped-guided annular plate under an external pressure, by direct application of a shaker clamped into the internal edge of the plate.…”

Study of the sound radiation of a rectangular plate resting on a winkler elastic foundation

“…Some previous works by Ascione and Grimaldi [2], Salari et al [3], Zheng and Zhou [4], Leissa [5], Ghosh [6], Wang [7], and Bhaskara and Kameswara [8] have analyzed the vibration characteristics of plates resting on elastic foundations. Other studies presented by Arenas and Crocker [9], Rdzanek et al [10][11], Arenas [12][13] and Arenas et al [14] have reported methods for estimating the sound power radiated from vibrating plates. However, there is a relative scarcity of information in the literature for the relationship between the sound power radiated from a vibrating plate resting on an elastic foundation and the stiffness of the elastic foundation.…”