This paper aims to present a modified continuum mathematical model capable on investigation of dynamic behavior and response of perforated microbeam under the effect of moving mass/load for the first time. A size-dependent finite element model with non-classical shape function is exploited to solve the mathematical model and obtain the dynamic response of perforated Timoshenko microbeams under moving loads. To that end, first, equivalent material and geometrical parameters for perforated beam are developed, based on the regular squared perforation configuration. Second, both the stiffness and mass property matrices including the microstructure effect based on modified couple stress theory and Timoshenko first-order shear beam theory are derived for two-node finite element using new shape function. After that, the interaction between the load and beam is modeed and unified with the equation of motion of the beam incorporating mass inertia effects of moving load. The developed procedure is validated and compared. Effects of perforation parameters, moving load velocities, inertia of mass, and the microstructure size parameter on the dynamic response of perforated microbeam structures have been investigated in a wide context. The achieved results are helpful for the design and production of MEMS structures such as frequency filters, resonators, relay switches, accelerometers and mass flow sensors, with perforation.

中文翻译：

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移动载荷作用下timoshenko穿孔微梁的动力学分析

本文旨在首次提出一种改进的连续数学模型，该模型能够研究多孔微梁在移动质量/载荷作用下的动态行为和响应。利用具有非经典形函数的尺寸相关有限元模型求解数学模型，得到带孔铁木辛柯微梁在移动荷载作用下的动力响应。为此，首先，基于规则的方形穿孔配置，开发了穿孔梁的等效材料和几何参数。其次，基于修正偶应力理论和Timoshenko一阶剪切梁理论，利用新的形状函数推导出了包括微观结构效应在内的刚度和质量属性矩阵，用于双节点有限元。之后，载荷和梁之间的相互作用通过结合移动载荷的质量惯性效应的梁的运动方程进行建模和统一。开发的程序经过验证和比较。穿孔参数、移动载荷速度、质量惯性和微观结构尺寸参数对穿孔微梁结构动态响应的影响已经在广泛的背景下进行了研究。所取得的成果有助于设计和生产带有穿孔的频率滤波器、谐振器、继电器开关、加速度计和质量流量传感器等 MEMS 结构。并且已经在广泛的背景下研究了微结构尺寸参数对穿孔微梁结构的动态响应。所取得的成果有助于设计和生产带有穿孔的频率滤波器、谐振器、继电器开关、加速度计和质量流量传感器等 MEMS 结构。并且已经在广泛的背景下研究了微结构尺寸参数对穿孔微梁结构的动态响应。所取得的成果有助于设计和生产带有穿孔的频率滤波器、谐振器、继电器开关、加速度计和质量流量传感器等 MEMS 结构。