TY - JOUR
T1 - Transverse vibration of trapezoidal plates of variable thickness. Symmetric trapezoids
AU - Liew, K. M.
AU - Lim, M. K.
PY - 1993/1/1
Y1 - 1993/1/1
N2 - A set of simple two-dimensional polynomial functions is employed as the admissible displacement function in the Rayleigh-Ritz energy approach for the free transverse vibration analysis of symmetric trapezoidal plates with linearly varying thickness. The admissible function consists the product of (i) a two-dimensional polynomial function and (ii) a basic function. The basic function is defined by the product of the equations of the prescribed continuous piecewise boundary shape each raised to the power of 0, 1 or 2, corresponding to a free, simply supported, or clamped edge, respectively. The set of functions generated ensures the satisfaction of all the kinematic boundary conditions at the outset. The proposed method is applied to solve several symmetric trapezoidal plates with different combinations of boundary conditions and variable thickness. The results, for some cases, are compared with the available published values from the open literature. These new results may serve as benchmark data for the development of other numerical methods.
AB - A set of simple two-dimensional polynomial functions is employed as the admissible displacement function in the Rayleigh-Ritz energy approach for the free transverse vibration analysis of symmetric trapezoidal plates with linearly varying thickness. The admissible function consists the product of (i) a two-dimensional polynomial function and (ii) a basic function. The basic function is defined by the product of the equations of the prescribed continuous piecewise boundary shape each raised to the power of 0, 1 or 2, corresponding to a free, simply supported, or clamped edge, respectively. The set of functions generated ensures the satisfaction of all the kinematic boundary conditions at the outset. The proposed method is applied to solve several symmetric trapezoidal plates with different combinations of boundary conditions and variable thickness. The results, for some cases, are compared with the available published values from the open literature. These new results may serve as benchmark data for the development of other numerical methods.
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U2 - 10.1006/jsvi.1993.1242
DO - 10.1006/jsvi.1993.1242
M3 - RGC 21 - Publication in refereed journal
VL - 165
SP - 45
EP - 67
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
SN - 0022-460X
IS - 1
ER -