Author
X. Liu
Bio: X. Liu is an academic researcher from University of Kentucky. The author has contributed to research in topics: Vibration of plates & Deflection (engineering). The author has an hindex of 2, co-authored 2 publications receiving 31 citations.
Papers
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TL;DR: In this article, the Analytical Strip Method (ASM) is presented for the free flexural vibration problem of rectangular plates with intermediate flexible supports and different edge conditions, where the plate is divided into strips, the number of which depends on the geometric discontinuities.
27 citations
6 citations
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TL;DR: In this paper, closed-form solutions for free vibration analysis of orthotropic plates are obtained based on two variable refined plate theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors.
83 citations
TL;DR: In this article, the first known exact solutions for buckling and vibration of stepped rectangular Mindlin plates with two opposite edges simply supported and the remaining two edges being either free, simply supported or clamped are presented.
68 citations
TL;DR: In this article, the vibrational properties of a simple finite-element model of a piano soundboard are considered and the main focus is on the behavior of the mechanical impedance in the musically important frequency range ∼50-104 Hz.
Abstract: The vibrational properties of a simple finite-element model of a piano soundboard are considered. The main focus is on the behavior of the mechanical impedance in the musically important frequency range ∼50–104 Hz. The model includes the effects of elastic anisotropy and the ribs. It is argued that the ribs are an essential ingredient for producing the behavior of the impedance which is observed experimentally.
43 citations
TL;DR: In this paper, the free transverse vibrations of a system of two simply supported thin plates connected by a homogeneous Winkler elastic layer are investigated analytically, and the small vibrations of the system are described by a set of two partial differential equations, based on the Kirchhoff-love plate theory.
38 citations
TL;DR: In this paper, the free vibration problem of a stepped plate supported on nonhomogeneous Winkler elastic foundation with elastically mounted masses is formulated based on Hamilton's principle, and a set of C 1 continuous functions are chosen as the longitudinal interpolation functions in the finite strip analysis.
Abstract: The free vibration problem of a stepped plate supported on non-homogeneous Winkler elastic foundation with elastically mounted masses is formulated based on Hamilton's principle. The stepped plate is modelled by finite strip method. To overcome the problem of excessive continuity of common beam vibration functions at the location of abrupt change of plate thickness, a set of C 1 continuous functions have been chosen as the longitudinal interpolation functions in the finite strip analysis. The C 1 continuous functions are obtained by augmenting the relevant beam vibration modes with piecewise cubic polynomials. As these displacement functions are built up from beam vibration modes with appropriate corrections, they possess both the advantages of fast convergence of harmonic functions as well as the appropriate order of continuity. The method is further extended to the buckling analysis of rectangular stepped plates. Numerical results also show that the method is versatile, efficient and accurate.
35 citations