تحليل ارتعاشات غيرخطي متقارن‌محوري واداشته از حرارت در پوسته‌ي كروي ساخته‌شده از مواد هدفمند

Nonlinear Axisymmetric, Thermally Induced Vibrations of a Functionally Graded Spherical Cap

خواص پوسته از رابطۀ كسر حجمي به‌ دست‌ آمده، وابستگي حرارتي از رابطه تولوكيان لحاظ شده است. بارگذاري متقارن محوري مي باشد. سطح سراميكي در دماي ثابت و سطح ديگر در دماي پايينتر (يا عايق) است. توزيع دما از معادله گذراي غيرخطي غيركوپل انتقال حرارت محاسبه مي شود. از تئوري مرتبه اول پوسته و روابط كرنش-تغييرمكان فون-كارمن براي استخراج معادلات استفاده گرديده، معادلات ديناميكي از اصل هميلتون و روش ريتز بدست آمده و بوسيله روش هاي نيومارك و نيوتن-رافسون حل شده است. معادله انتقال حرارت با روش تفاضل محدود و كرنك-نيكلسون حل شده است. اثر توزيع خواص، نوع بار حرارتي و هندسه در پاسخ بررسي شده است.

In this study, thermally induced vibrations of a Functionally Graded Material (FGM) Spherical Cap discussed. Distribution of shell properties in the direction of thickness is calculated from volume fraction relationship. Dependency to temperature is expressed based on the Touloukian formula. Thermal loading on the shell is axisymmetric and the response of the shell have been considered axially symmetric. Ceramic rich surface of the shell is subjected to temperature rise, whereas the metal rich surface of the shell is kept at reference temperature or thermally insulated. Temporal evolution of temperature profile across the shell thickness is obtained through solution of one-dimensional heat conduction equation. This equation is originally nonlinear since temperature dependency of thermal conductivity is taken into account. The first-order shear theory and Von-Karman compatibility relations has been used for deriving the equation. Dynamics equations are derived using Hamilton's principle with the application of Ritz method has become a set of nonlinear time-dependent algebraic equations. Solving this set of equations is done with Newmark integral method help with numerical method Newton-Raphson. Solution of the transient one dimensional heat conduction equation with the arbitrary type of time-dependent boundary conditions is carried out employing the central finite difference method combined with the Crank–Nicolson time marching scheme. After validating the developed computer code, some parametric studies are accomplished to show the influences of various involved parameters. It is shown that temperature dependency, geometrical non-linearity, shell thickness, power law index, and the type of thermal loading, all affect the temporal evolution of plate characteristics.