扭转弹簧约束复合材料层压梁的自由振动

陈庆远,李静,方鹏亚,裴世勋,刘双燕,苏毅

振动与冲击 ›› 2023, Vol. 42 ›› Issue (13) : 170-176.

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (13) : 170-176.
论文

扭转弹簧约束复合材料层压梁的自由振动

  • 陈庆远,李静,方鹏亚,裴世勋,刘双燕,苏毅
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Free transverse vibration of composite laminated beam restrained by torsion springs

  • CHEN Qingyuan, LI Jing, FANG Pengya, PEI Shixun, LIU Shuangyan, SU Yi
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摘要

本文基于伽辽金法推导了扭转弹簧约束复合材料层压梁自由振动的显式解析解。当复合材料层压梁两端的扭转弹簧刚度系数相等时,层压梁的横向挠度函数由两端简支梁的振动特征函数和两端固支梁修正的振动特征函数线性组合而成;当复合材料层压梁两端的扭转弹簧刚度系数不相等时,层压梁的横向挠度函数则由简支—固支梁的振动特征函数,固支—简支梁修正的振动特征函数和两端固支梁修正的振动特征函数线性组合而成。本文给出的横向挠度函数可以避免扭转弹簧约束复合材料层压梁的经典振动特征函数在高阶(≥11)模态时出现的数值不稳定现象。研究表明本文给出的显式解析表达式能够有效地对扭转弹簧约束复合材料层压梁的自由振动进行分析。

Abstract

Based on the Galerkin method, an explicit analytical solution for free vibration of laminated composite beams with the boundary ends elastically-restrained against rotation is presented. In order to avoid the numerical instability of the classical vibration eigenfunction of higher order (≥11) modes, the transverse deflection functions of the rotationally-restrained laminated composite beams are constructed through a unique weighting combination of (modified) vibration eigenfunctions of hinged-hinged, fixed-fixed, hinged-fixed and fixed-hinged beams. The validity study shows that the present explicit analytical solution is effective in performing free vibration analyses of laminated composite beams with ends elastically-restrained against rotation.

关键词

自由振动 / 扭转弹簧约束 / 复合材料层压梁 / 伽辽金法 / 显式解析解

Key words

free vibration / rotationally-restrained / laminated composite beams / Glerkin method / an explicit analytical solution 

引用本文

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陈庆远,李静,方鹏亚,裴世勋,刘双燕,苏毅. 扭转弹簧约束复合材料层压梁的自由振动[J]. 振动与冲击, 2023, 42(13): 170-176
CHEN Qingyuan, LI Jing, FANG Pengya, PEI Shixun, LIU Shuangyan, SU Yi. Free transverse vibration of composite laminated beam restrained by torsion springs[J]. Journal of Vibration and Shock, 2023, 42(13): 170-176

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