ارتعاشات آزاد ميكروتيرهاي چرخان ساخته شده از مواد هدفمند

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در اين مقاله به بررسي ويژگي‌هاي ارتعاشي ميكروتيرهاي چرخان اويلر-برنولي ساخته شده از مواد هدفمند در محيط گرمايي بر اساس تئوري تنش كوپل اصلاح شده پرداخته مي‌شود. جهت در نظر گرفتن اثرات نيروي گريز از مركز براي ميكروتيرهاي چرخان هدفمند از انرژي جنبشي ميكروتير چرخان استفاده شده كه قادر به اصلاح اشتباه رايج در ميكروتيرهاي چرخان هدفمند بوده كه اثر نيروي گريز از مركز تنها به‌صورت يك نيروي محوري در نظر گرفته مي‌شود. تأثير پارامتر اندازه، تغيير دما، ضريب قانون تواني ماده هدفمند و نسبت لاغري بر فركانس طبيعي اول و شكل مودهاي اول و دوم بررسي مي‌گردد.

The free vibration features of rotating functionally graded microbeams in thermal environment are presented in this paper. The governing equations are extracted on the basis of the Euler- Bernoulli beam assumptions beside the modified couple stress theory. The finite element method is applied on the weak form of the strain and the kinetic energies to extract the natural frequencies and the associated modeshapes. The nonlinear static equations of motion due to the rotation and the thermal environment are treated employing the Newton-Raphson technique. Moreover, the natural frequencies are estimated from the linearized equations of motion about the static configuration. After the validation of the present results, the rotation speed, the material length scale parameter, the temperature change, the power law exponent and the slenderness ratio impacts on the fundamental natural frequency and the first and the second modeshapes are examined. The outcomes indicate the increment of the natural frequency after a threshold value of the power law exponent depends on a given rotation speed for the rotating microbeams in comparison with the stationary microbeams. Furthermore, the modeshapes of rotating functionally graded microbeams vary by the power law exponent while for stationary functionally graded microbeams the modeshapes are invariant with respect to the power law exponent even in the presence of the thermal environment.