A recursive formulation is proposed for the method of reverberation-ray matrix (MRRM) to exactly analyze the free vibration of a multi-span continuous rectangular Kirchhoff plate, which has two opposite simply-supported edges. In contrast to the traditional MRRM, numerical stability is achieved by using the present new formulation for high-order frequencies or/and for plates with large span-to-width ratios. The heavy computational cost of storage and memory are also cut down. An improved recursive formulation is further proposed by modifying the iterative formula to reduce the matrix inversion operations. Numerical examples are finally given to demonstrate the effectiveness and efficiency of the proposed recursive formulae. method of reverberation-ray matrix, recursive formulation, free vibration, continuous Kirchhoff plate Multi-span plates with orthogonal straight edges are frequently encountered in civil, aircraft/aerospace and marine engineering as basic structures or the key components of structures. For instance, the aeroplane skins, long-span roofs in building construction, steel bridge decks of oversea bridges and glass window panels may all be modeled as plates with multiple spans. As these plate systems are usually used as key bearing carriers in practice, it is essential to understand their dynamic characteristics. A vast number of researches of free vibration of Kirchhoff plates have been conducted by using different methods during the past several decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] . One of the celebrated techniques is the method of transfer matrix (MTM), which was first formulated by Thomson for free vibration of inhomogeneous beams [21] . But this method was soon recognized to suffer from the inherent numerical instability, when the aspect ratio is large and/or the frequency is high. Although several techniques have been proposed to solve this problem [22][23][24] , the application is still limited because they are only valid or applicable for particular cases. Recently, an alternative approach, called the method of reverberation-ray matrix (MRRM), was proposed by Pao et al. [25][26][27][28] to evaluate the transient response of planar trusses and wave propagation in layered media. A key idea in this method is to set up two local coordinate systems (dual coordinate system) for a single member/layer. The equilibrium/compatibility conditions of all joints are considered to formulate a global scattering matrix, while a global phase matrix is obtained from the wave propagation mechanism in all members. The two matrices are combined to give the reverberation-ray matrix, which characterizes the wave motion of the whole structure. As we will show later, the use of dual coordinate system enables us to avoid the numerical instability during computations effectively. However, for complex structures, with the increase of members and joints, the dimension of the reverberation-ray matrix in MRRM becomes larger, and hence, leading to a heavy computational cost of stor...

Theoretical analysis is performed for the sound radiation of a cylindrical power transformer composed of piezoelectric transducers with radial polarization. The transformer is driven in thickness-stretch mode, and an exact solution is obtained for the sound pressure and sound power level in the surrounding fluid. Representative examples are used to illustrate the sound field induced by the operation of the transformer. Numerical results indicate that the electrical impedance and the thickness ratio of actuatorlsensor to metal core have considerable effects on sound radiation of the cylindrical power transformer.

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