弹性地基上受压矩形纳米板的自由振动与屈曲特性

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Abstract Based on the Eringen’s nonlocal elasticity theory and the classical thin plate theory, the governing differential equation for free vibration of in-plane compressed orthotropic nanoplate resting on Winkler-Pasternak elastic foundation was derived by using the Hamilton’s principle.Then the dimensionless form of the governing differential equation was also obtained.The dimensionless governing differential equation and boundary conditions were transformed to the equivalent algebraic equations by using a semi-analytic method called differential transformation method (DTM), which can derive characteristic equations of dimensionless natural frequencies and buckling loads.The influence of dimensionless foundation stiffness coefficients, pressure intensity, load parameter, aspect ratio and nano-scale factor on the dimensionless natural frequency of orthotropic rectangular nanoplate under different boundary conditions was numerically presented and the critical buckling load values of different dimensionless foundation stiffness coefficients, load parameter and nano-scale factor were given.The results show that the dimensionless natural frequency of orthotropic rectangular nanoplate increases with dimensionless foundation stiffness coefficients, load parameter and aspect ratio; decreases with nano-scale factor.The critical buckling load increases with dimensionless foundation stiffness coefficient, decreases with nano-scale factor.

Key words： Eringen’s nonlocal elasticity theory Winkler-Pasternak elastic foundation non-dimensional natural frequency;bucklingcritical load Differential Transform Method (DTM)

Received: 01 February 2018 Published: 15 August 2019

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	TENG Zhaochun1
	LIU Lu1
	HENG Yazhou2

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TENG Zhaochun1,LIU Lu1,HENG Yazhou2. Free vibration and buckling characteristics of compressed rectangular nanoplates resting on elastic foundation[J]. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(16): 208-216.

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http://jvs.sjtu.edu.cn/EN/ OR http://jvs.sjtu.edu.cn/EN/Y2019/V38/I16/208

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