DSC-element method for free vibration analysis of rectangular Mindlin plates

Application of the DSC-Element method to flexural vibration of skew plates with continuous and discontinuous boundaries

“…[23,24], we found that the solutions of exp½ÀðxÀx k Þ 2 =ð2s 2 Þ r 0:002 or exp½ÀðZÀZ k Þ 2 =ð2s 2 Þ r0:002 in Eqs. (19)-(21) must be excluded in order to maintain the numerical stability for the element grid points N Z13.…”

“…In this paper, the parameters are adopted as r ¼1.8 and D¼2/(NÀ1) [23,24]. The grid point coordinates x k and Z k are along the x and Z directions, respectively.…”

“…This paper aims to generalize the DSC-Element method [23,24] for flexural vibration analysis of skew Mindlin plates with classical and mixed supporting edges. This hybrid approach combines the concept of the finite element method and the usage of the discrete singular convolution (DSC) [22,[25][26][27][28][29][30][31][32] delta type wavelet kernel as a trial function.…”

The wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges

“…Many researchers have studied the free vibration for Mindlin plates [8][9][10][11][12][13][14][15][16][17][18][19][20]. Liew et al [9] used the boundary characteristic orthogonal polynomials to approximate the transverse displacement and rotational functions of Mindlin plates.…”

“…Although much attention has been paid to the free vibration [8][9][10][11][12][13][14][15][16][17][18][19][20] and response in time domain [21,22] for Mindlin plates, few researchers have studied the dynamic response in frequency domain for finite Mindlin plates. Previous works on the vibratory power flow in finite Mindlin plates show that the shear and rotary inertia corrections only influence the power flow at high frequencies [30][31][32].…”