تحليل ديناميكي و بررسي پايداري تير انعطافپذير ترك دار متصل به پايه چرخان

Dynamic and Stability Analysis of a Cracked Rotating Flexible إBeam

در اﻳﻦ ﻣﻘﺎﻟﻪ رﻓﺘﺎر ارﺗﻌﺎﺷﺎت آزاد، اﺟﺒﺎري، و ﭘﺎﻳﺪاري ﻳﻚ ﺳﺎزه اﻧﻌﻄﺎفﭘﺬﻳﺮ ﺗﺮكدار ﺑﻠﻨﺪ ﺑﺎ ﭘﺎﻳﻪ ﭼﺮﺧﺎن ﺑﺎ اﺳﺘﻔﺎده از روش ﻫﻮﻣﻮﺗﻮﭘﻲ ﭘﺮﺗﻮرﺑﻴﺸﻦ ﻣﻮرد ﺑﺮرﺳﻲ و ﺗﺤﻠﻴﻞ ﻗﺮار ﮔﺮﻓﺘﻪ اﺳﺖ. ﺗﺮك در ﻣﺴﺌﻠﻪ ﺣﺎﺿﺮ ﺑﺎ ﻓﺮض اﻟﻤﺎن ﻓﻨﺮ ﭘﻴﭽﺸﻲ ﺑﺪون وزن ﺑﺮ روي ﺳﺎزه ﺑﺎ ﭘﺎﻳﻪ ﭼﺮﺧﺎن )ﻛﻪ رﻓﺘﺎر آن از ﺗﺌﻮري اوﻳﻠﺮ ﺑﺮﻧﻮﻟﻲ ﺗﺒﻌﻴﺖ ﻣﻲﻛﻨﺪ( ﻣﺪﻟﺴﺎزي ﺷﺪه اﺳﺖ. ﻣﻌﺎدﻻت ﻏﻴﺮﺧﻄﻲ ﺣﺮﻛﺖ ﺳﻴﺴﺘﻢ ﺑﺎ ﻟﺤﺎظ ﺗﻐﻴﻴﺮﺷﻜﻞﻫﺎي ﺧﺎرج ﺻﻔﺤﻪاي و ﻧﻴﺮوﻫﺎي ﮔﺮﻳﺰ از ﻣﺮﻛﺰ و ﺑﺎ ﺑﻪﻛﺎرﮔﻴﺮي ﺣﺴﺎب ﺗﻐﻴﻴﺮات و روش ﻣﻮدﻫﺎي ﻓﺮﺿﻲ اﺳﺘﺨﺮاج ﺷﺪه اﺳﺖ. ﺑﺎ اﻋﻤﺎل روش ﮔﻠﺮﻛﻴﻦ، ﺑﻌﺪ ﻣﻜﺎﻧﻲ ﻣﺴﺌﻠﻪ اﺳﺘﺨﺮاج و ﺑﻌﺪ زﻣﺎﻧﻲ ﺑﻪ ﻳﻚ ﻣﻌﺎدﻟﻪ دﻳﻔﺮاﻧﺴﻴﻞ ﻣﺮﺗﺒﻪ دوم ﻏﻴﺮﺧﻄﻲ در ﺣﻮزه زﻣﺎن ﺗﺒﺪﻳﻞ ﻣﻲﺷﻮد. ﻧﺘﺎﻳﺞ ﺑﻪ ازاء ﺗﻐﻴﻴﺮ ﭘﺎراﻣﺘﺮﻫﺎي ﻣﻬﻢ ﻣﺴﺎﻟﻪ از ﺟﻤﻠﻪ ﺳﺮﻋﺖ دوران ﭘﺎﻳﻪ، ﻣﻮﻗﻌﻴﺖ و ﺳﻔﺘﻲ ﺗﺮك، ﺷﺮاﻳﻂ اوﻟﻴﻪ و داﻣﻨﻪ ﺗﺤﺮﻳﻚ در ﻗﺎﻟﺐ ﻧﻤﻮدارﻫﺎي ﭘﺎﺳﺦ زﻣﺎﻧﻲ، ﻧﻤﻮدار ﻓﺎزي و دوﺷﺎﺧﮕﻲ ﺑﺮرﺳﻲ و ﺗﺤﻠﻴﻞ ﺷﺪه اﺳﺖ. ﻧﺸﺎن داده ﺷﺪه اﺳﺖ ﻛﻪ ﺑﺎ اﻓﺰاﻳﺶ ﺳﺮﻋﺖ زاوﻳﻪاي، ﻳﻚ ﻧﻴﺮوي ﻛﺸﺸﻲ در اﻣﺘﺪاد ﻣﺤﻮر ﺳﺎزه اﻳﺠﺎد ﺷﺪه ﻛﻪ ﻣﻨﺠﺮ ﺑﻪ اﺳﺘﺤﻜﺎم ﺗﻴﺮ ﺗﺮك ﺧﻮرده، ﺣﺮﻛﺖ ﻧﻤﻮدار دوﺷﺎﺧﮕﻲ ﺑﻪﺳﻤﺖ راﺳﺖ و ﺗﻐﻴﻴﺮ رﻓﺘﺎر ﻏﻴﺮﺧﻄﻲ ﺳﻴﺴﺘﻢ ﻣﻲﺷﻮد.

The free and forced vibration analysis of a rotating large flexible structure with a single crack is investigated using the Homotopy Perturbation Method (HPM). The crack is modeled with a torsional spring element on a structure that follows the Euler-Bernoulli theory. The nonlinear equations of motion of the co-rotational system considering centrifugal forces are derived using the calculus of variation and the Assumed Mode Method (AMM). Applying the Galerkin method, the spatial domain is extracted and the time domain is transformed into a second-order nonlinear differential equation. The results of time response, phase plane, and bifurcation diagrams for different functional parameters variations such as base angular velocity, crack position and stiffness have been analyzed. Moreover, it is shown that as the base angular velocity increases, a tensile force appears along the cracked structure axis, stiff it, and shifts the backbone to the right, this can highly affect the nonlinear features of the system.