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Abstract: An analytical method is derived for determining the vibrations of two plates which are generally supported along the boundary edges, and elastically coupled together at an arbitrary angle. The interactions of all four wave groups (bending waves, out-of-plane shearing waves, in-plane longitudinal waves, and in-plane shearing waves) have been taken into account at the junction via four types of coupling springs of arbitrary stiffnesses. Each of the transverse and in-plane displacement functions is expressed as the superposition of a two-dimensional (2-D) Fourier cosine series and several supplementary functions which are introduced to ensure and improve the convergence of the series representation by removing the discontinuities that the original displacement and its derivatives will potentially exhibit at the edges when they are periodically expanded onto the entire x–y plane as mathematically implied by a 2-D Fourier series. The unknown expansions coefficients are calculated using the Rayleigh–Ritz procedure which is actually equivalent to solving the governing equation and the boundary and coupling conditions directly when the assumed solutions are sufficiently smooth over the solution domains. Numerical examples are presented for several different coupling configurations. A good comparison is observed between the current results and the FEA models. Although this study is specifically focused on the coupling of two plates, the proposed method can be directly extended to structures consisting of any number of plates. [Copyright &y& Elsevier]

Abstract: This paper discusses sound radiation from a baffled rectangular plate with each of its edges arbitrarily supported in the form of elastic restraints. The plate displacement function is universally expressed as a 2-D Fourier cosine series supplemented by several 1-D series. The unknown Fourier expansion coefficients are then determined by using the Rayleigh–Ritz procedure. Once the vibration field is solved, the displacement function is further simplified to a single standard 2-D Fourier cosine series in the subsequent acoustic analysis. Thus, the sound radiation from a rectangular plate can always be obtained from the radiation resistance matrix for an invariant set of cosine functions, regardless of its actual dimensions and boundary conditions. Further, this radiation resistance matrix, unlike the traditional ones for modal functions, only needs to be calculated once for all plates with the same aspect ratio. In order to determine the radiation resistance matrix effectively, an analytical formula is derived in the form of a power series of the non-dimensional acoustic wavenumber; the formula is mathematically valid and accurate for any wavenumber. Several numerical examples are presented to validate the formulations and show the effect of the boundary conditions on the radiation behavior of planar sources. [ABSTRACT FROM AUTHOR]

Abstract: Arbitrary non-uniform elastic edge restraints represent the most general class of boundary conditions for plate problems, and are encountered in many real-world applications. The vibrations of plates with this kind of boundary conditions, however, are rarely studied in the literature perhaps because there is a lack of suitable analytical or numerical techniques. In this investigation, a general analytical method is derived for the vibration analysis of rectangular plates with elastic edge restraints of varying stiffness. Both rotational and translational restraints can be arbitrarily applied to an edge, and their stiffness distributions are generally described in terms of a set of invariants, cosine functions. The displacement solution is sought simply as a linear combination of several one- and two-dimensional Fourier cosine series expansions. All the unknown Fourier coefficients are treated equally as a set of independent generalized coordinates and solved directly from the Rayleigh–Ritz formulation. Unlike the existing techniques, the current method does not require any special procedures or schemes to deal with different boundary conditions. A few “classical” problems involving non-uniform rotational restraints are first solved and used to check the current solution against some of the existing techniques. The modal results are also presented for plates with more complicated boundary conditions in which an edge is no longer completely restrained in the translational direction. The accuracy and reliability of the current method are repeatedly demonstrated through all these examples. [Copyright &y& Elsevier]

Abstract: This study is concerned with the dynamic behavior of generic multi-span bridges under the action of moving loads. In this multi-span bridge model, each span can be independently supported by up to eight elastic springs, thus allowing a more general and realistic representation of many joints and intermediate supports of practical interest. Additionally, since the displacement and its first derivative are no longer required to be continuous at an intermediate support or at the junctions of spans, this model is capable of accounting for the possible steps and skew angles at these locations which are important to studying the vehicle–bridge interactions. Numerical results are presented with a focus on the dynamic impact of the coupling conditions between spans. It has been shown that the deflection on each span strongly depends upon its local coupling conditions, especially near the critical stiffness values. A fairly large variance of response has also been observed on each span in correspondence to a wide range of stiffness values, which implies a good potential for improving bridge performance through modifying joint parameters or coupling configurations. This model can be readily applied to any boundary and coupling conditions with no need of modifying the formulations or solution procedures. [Copyright &y& Elsevier]

Abstract: In this investigation, the in-plane vibration problems are solved for plates with general elastically restrained boundary conditions. Under the current framework, all the classical homogeneous boundary condition for in-plane displacements can be easily simulated by simply setting the stiffnesses of the restraining springs to either infinite or zero. The vibration problems are solved using an improved Fourier series method in which the in-plane displacements are expressed as the superposition of a double Fourier cosine series and four supplementary functions in the form of the product of a polynomial function and a single cosine series expansion. The use of these supplementary functions is to overcome the discontinuity problems which the original displacement functions will potentially encounter along the edges when they are viewed as a periodic function defined over the entire x–y plane. The excellent accuracy and convergence of the current solution are demonstrated through numerical examples. To the best of authors’ knowledge, this work represents the first time that an analytical solution has been obtained for the in-plane vibrations of a rectangular plate with elastically restrained edges. [Copyright &y& Elsevier]

Abstract: The vibration behaviors of a box-type built-up structure and energy transmission through the structure are investigated analytically. The modeling of the structure is developed by employing the improved Fourier series method and treating the structure as four elastically coupled rectangular plates. The general coupling and boundary conditions are accounted for using the artificial spring technique and can easily be obtained by assigning the springs with corresponding values. The exact double Fourier series solutions considering both the flexural and in-plane vibrations are obtained by using the Rayleigh–Ritz approach, which are validated by comparison with the Finite Element Method (FEM) results. Since the modification of any parameter in this analytical model from one case to another is as simple as modifying the material properties, and does not involve any change to the solution procedures, thus this will make a parametric study and further mechanism analysis easier compared to most existing procedures. Subsequently, special attention is focused on the energy transmission and mechanism of the box-type structure by structural intensity analysis. Numerical analyses cover several important parameters including symmetrical and non-symmetrical coupling conditions and the excitations, and three types of models, namely the rigidly, elastically and weakly coupled models are involved. The results of the power flow and structural intensity are presented to obtain a clear physical understanding of the physical mechanisms of energy transmission. It is shown that the energy transmission behaviors can be significantly influenced by the coupling conditions and location of the excitation as well as the excitation frequency. Some unexpected interesting phenomena on the energy transmission were revealed, especially for the non-symmetrical model, and the corresponding mechanisms were interpreted. This study provides new and interesting insights into the vibration behaviors and energy transmission of the class of built-up box-type structure. [Copyright &y& Elsevier]