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In comparison with the transverse vibrations of rectangular plates, far less attention has been paid to the in-plane vibrations even though they may play an equally important role in affecting the vibrations and power flows in a built-up structure. In this paper, a generalized Fourier method is presented for the in-plane vibration analysis of rectangular plates with any number of elastic point supports along the edges. Displacement constraints or rigid point supports can be considered as the special case when the stiffnesses of the supporting springs tend to infinity. In the current solution, each of the in-plane displacement components is expressed as a 2D Fourier series plus four auxiliary functions in the form of the product of a polynomial times a Fourier cosine series. These auxiliary functions are introduced to ensure and improve the convergence of the Fourier series solution by eliminating all the discontinuities potentially associated with the original displacements and their partial derivatives along the edges when they are periodically extended onto the entire x-y plane as mathematically implied by the Fourier series representation. This analytical solution is exact in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. Numerical examples are given about the in-plane modes of rectangular plates with different edge supports. It appears that these modal data are presented for the first time in literature, and may be used as a benchmark to evaluate other solution methodologies. Some subtleties are discussed about corner support arrangements. [DOI: 10.1115/1.4000777]

Vibrations of and power flow between coupled beams have been the subject of many investigations, and various techniques have been developed over the years. However, most of the existing methods will require a certain level of modifications or adaptations to account for the variations in the coupling and/or boundary, conditions. In this study, a general analytical method is developed for predicting the vibrations of and power flow between two-coupled beams. The coupling between the beams is generically represented by two (translational and rotational) springs of arbitrary stiffnesses. Thus, many rigid and nonrigid connectors of practical interest can be directly taken into account. In addition, because the beams are elastically restrained at each end, the current method can be universally applied to different boundary, conditions by simply varying the stiffnesses of the boundary springs. Numerical results are presented to show the excellent accuracy of the proposed approach. [DOI: 10.1115/1.2775518]

The main emphasis of this paper is placed on the effectiveness of the proposed optimization method in material identification. The primary motivation of integrating GA, ACO and PSO is to minimize each other’s weaknesses and to promote respective strengths. In the proposed algorithm, the effect of random initialization of GA is subdued by passing the products of GA through the ACO and PSO operators to well organize the exploitative and exploratory search coverage. In return, GA improves the convergence rate and alleviates the strong dependency on the pheromone array in ACO as well as resolves the conflict arisen in identifying the trade-off parameter and further refine the exploitative search of PSO with the introduction of two-point standard mutation and one-point refined mutation. The proposed algorithm has been verified and applied in composite material identification with absolute percentage errors between measured and evaluated natural frequencies not more than 2%. [ABSTRACT FROM AUTHOR]