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Purpose <p>Current investigation deals with the large amplitude vibrations in an annular plate which is subjected to rapid surface heating. Plate is attached to a Pasternak-type elastic foundation which acts in tension as well as in compression. It is assumed that plate is made from through-the-thickness functionally graded materials. Each of the thermomechanical properties of the constituents is assumed to be temperature dependent. It is considered that ceramic-rich surface of the plate is subjected to sudden temperature elevation or heat flux.</p> Methods <p>The one-dimensional heat conduction equation for the plate is established and solved using the well-known generalized differential quadrature method. This equation is nonlinear since the material properties are assumed tobe temperature dependent. After evaluation of temperature profile, thermally induced force and moment are obtained and inserted into the equations of motion of the plate. The equations of motion are established by means of the first order shear deformation theory of plates and von Kármán type of kinematics. The complete set of governing equations of boundary conditions are extracted via the Hamilton principle. These equations and boundary conditions are discreted using the generalized differential quadrature method. Also, temporal evolution of quantities are estimated via the Newmark time marching scheme. It should be noted that Picard algorithm is implemented to deal with the nonlinear nature of the equations of motion.</p> Results <p>Results of this study are compared with the available data in the open literature and after that novel results from the current investigation are provided in graphical presentation.</p> Conclusions <p>It is shown that power law index, boundary conditions, temperature dependence, boundary conditions, foundation factors and plate geometry are all important factors on the dynamics of annular plate subjected to thermally induced vibrations. Also as shown thermally induced vibrations indeed exists especially when plates are thin. Furthermore,unlike simply supported plates, clamped plates may exhibit the dynamic bifurcation type of instability.</p>

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Large Amplitude Oscillations in Suddenly Heated Heterogeneous Annular Plates Resting on an Elastic Medium

  • 期刊论文

  • 发表日期：

    2025年1月4日

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  • Mostafa Mirzaei,
  • Somayeh Ebadi

摘要

Purpose

Current investigation deals with the large amplitude vibrations in an annular plate which is subjected to rapid surface heating. Plate is attached to a Pasternak-type elastic foundation which acts in tension as well as in compression. It is assumed that plate is made from through-the-thickness functionally graded materials. Each of the thermomechanical properties of the constituents is assumed to be temperature dependent. It is considered that ceramic-rich surface of the plate is subjected to sudden temperature elevation or heat flux.

Methods

The one-dimensional heat conduction equation for the plate is established and solved using the well-known generalized differential quadrature method. This equation is nonlinear since the material properties are assumed tobe temperature dependent. After evaluation of temperature profile, thermally induced force and moment are obtained and inserted into the equations of motion of the plate. The equations of motion are established by means of the first order shear deformation theory of plates and von Kármán type of kinematics. The complete set of governing equations of boundary conditions are extracted via the Hamilton principle. These equations and boundary conditions are discreted using the generalized differential quadrature method. Also, temporal evolution of quantities are estimated via the Newmark time marching scheme. It should be noted that Picard algorithm is implemented to deal with the nonlinear nature of the equations of motion.

Results

Results of this study are compared with the available data in the open literature and after that novel results from the current investigation are provided in graphical presentation.

Conclusions

It is shown that power law index, boundary conditions, temperature dependence, boundary conditions, foundation factors and plate geometry are all important factors on the dynamics of annular plate subjected to thermally induced vibrations. Also as shown thermally induced vibrations indeed exists especially when plates are thin. Furthermore,unlike simply supported plates, clamped plates may exhibit the dynamic bifurcation type of instability.