326 / 2021-06-21 21:54:26

A highly accurate and efficient analytical spectral dynamic stiffness method for acoustic and vibration problems within the whole frequency range

Vibration; Acoustic; SDS method; Wittrick-Williams algorithm; Modal analysis; Response analysis

Vibro-acoustic systems have gained immense attention which are widely used as the fundamental components in aerospace, automobiles, biomechanics and many other technological applications. The analyses of acoustic and vibration problems are the crucial step to design the vibro-acoustic systems. For such problems, however, traditional methods such as FEM whose shape functions are approximate is generally applicable to the low-frequency range, whereas energy based methods such as SEA are limited to high-frequency ranges. In this paper, an efficient analytical spectral dynamic stiffness (SDS) method is presented for acoustic and vibration problems within the whole frequency range. The method combines the advantages of the classical dynamic stiffness method (DSM) with those of the spectral method. First, the general solutions satisfying exactly the governing differential equations are first derived by applying the proposed modified Fourier series (MFS). Any arbitrary boundary conditions are also represented accurately in the form of the MFS. Then the SDS matrix for an element is formulated symbolically using the general solutions and boundary conditions. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Both modal and dynamic response analyses are then carried out by applying the Wittrick-Williams algorithm with enhancements and other solution techniques. The formulation is widely applied to acoustic/membrane, plate elements and their assemblies as well as plate structures stiffened by beams and plane elastodynamic problems. The proposed SDSM gives exact results with excellent computational efficiency, which exhibits a predominant advantage over the FEM and other methods. This new method offers an ideal tool for efficient and reliable analytical modelling as well as parametric and optimization studies of structures, especially in the vibro-acoustic analysis within mid- to high-frequency ranges.