Reply to the comments of M.E. Golmakani and J. Rezatalab,Comment on “Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates” (by R. Aghababaei and J.N. Reddy,Journal of Sound and Vibration 326 (2009) 277–289), Journal of Sound Vibration, 333 (2014) 3831–3835

Golmakani and Rezatalab [1] suggested in their paper that the deflection of a simply supported nonlocal elastic plate under uniform load is not affected by the small length scale terms. They based their proof on the use of Navier?s method using a sinusoidal-based deflection solution. This insensitivity of the deflection solution of a simply supported nonlocal elastic plate with respect to the small length terms of Eringen?s model is not correct, as already detailed in the literature (for example, see [2] for beam problems). In fact, the deflection of the nonlocal plate (in the Eringen sense) is larger than the one of the local case, as shown in many papers available in the literature. We prove in this reply to the authors that the Navier?s method has to be correctly applied for highlighting the specific sensitivity phenomenon of the deflection solution, as compared to exact analytical solution.     

瑞士恩斯特教授(R.R.Ernst)荣获1991年诺贝尔化学奖

Richard R.Ernst 教授 1933年生于瑞士Winterhur。他在苏黎世瑞士联邦高等工学院(ETH)化学系毕业后,于1958—1962年在母校物理化学教研室师从Hans Primas教授,攻读博士学位。从1963年到1968年,他在美国加州Varian Asc.公司工作,其间他开发了付氏变换核磁共振(NMR)方法。1968年起,他一直领导ETH—研究组,从事NMR和顺磁共振(ESR)的方法研究,他担任过讲师、助教授、副教授。1976年任教授至今。他曾获1969年Ruzicka奖、1983年国际医学磁共振学会金奖、1985年瑞士洛     

Comment on “Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates (by R. Aghababaei and J.N. Reddy,Journal of Sound and Vibration 326 (2009) 277–289)”

This paper aims to prove the inaccuracy of the Navier solution presented by Aghababaei and Reddy [1] for the bending analysis of nanoplates based on the nonlocal theory of Eringen. According to the derived relations for bending of the nonlocal plate model, the main cause of this inaccuracy is attributed to an incorrect approximation of the Navier solution for a uniform transverse load. Of course, this problem does not inherently occur for the Navier solution in cases such as free vibration or the buckling of a nonlocal plate model in which the amount of transverse load is zero. In order to obtain further verification the results reported based on the Navier solution by Aghababaei and Reddy (2009, [1]) for the bending analysis of a nanoplate are compared with those computed by the differential quadrature (DQ) and finite difference (FD) methods. As shown, the results obtained by both the FD and DQ methods are consistently alike and unlike the solutions reported by Aghababaei and Reddy (2009, [1]) they are independent from small scale effect.