Yongqiang Yang^1,2, Zhongmin Wang^3,*

Sound & Vibration, Vol.53, No.3, pp. 51-64, 2019, DOI:10.32604/sv.2019.04004

Abstract Transverse vibration and stability analysis of circular plate subjected to follower force and thermal load are analyzed . B ased on the thin plate theory in involving the variable temperature, the differential equation of transverse vibration for the axisymmetric circular plate subjected to follower force and thermal load is established. Then, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the generalized eigenvalue under three different boundary conditions are calculated. In this case, the change curve of the first order dimensionless complex frequency of the circular plate subjected to the follower force… More >

Dong Zhengzhu, Peng Weihong, Li Shuncai¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.17, No.2, pp. 67-68, 2011, DOI:10.3970/icces.2011.017.067

Abstract Due to the complexity of thermal elastic problems, analytic solutions have been obtained only for some axisymmetrical problems and simply problems. Yu De-hao discussed bending problems of plates with the natural boundary element method. Using the above method, Li Shun-cai discussed the bending problems of solid circular plates] and bending deflections for annular infinite plates under the boundary loads.

On the basis of the same method, expanding the boundary slope into Fourier series, and using several convolution formulae, the boundary integral formula and natural boundary integral equation for the boundary value problems of thermal bending of Circular Plates are… More >

Wei-Ming Lee¹, Jeng-Tzong Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 141-160, 2009, DOI:10.3970/cmes.2009.050.141

Abstract This paper presents the multipole Trefftz method to derive an analytical model describing the free vibration of a circular plate with multiple circular holes. Based on the addition theorem, the solution of multipoles centered at each circle can be expressed in terms of multipoles centered at one circle, where boundary conditions are specified. In this way, a coupled infinite system of simultaneous linear algebraic equations is derived for the circular plate with multiple holes. The direct searching approach is employed in the truncated finite system to determine the natural frequencies by using the singular value decomposition (SVD). After determining the… More >

Cha’o-Kuang Chen^1,2, Hsin-Yi Lai¹, Chin-Chia Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.2, pp. 155-174, 2009, DOI:10.3970/cmes.2009.040.155

Abstract Electrostatically-actuated micro circular plates are used in many micro-electro-mechanical systems (MEMS) devices nowadays such as micro pumps and optical switches. However, the dynamic behavior of these circular plates is not easily analyzed using traditional analytic methods due to the complexity of the interactions between the electrostatic coupling effects. Accordingly, this study develops an efficient computational scheme in which the nonlinear governing equation of the coupled electrostatic force acting on the micro circular plate is solved using a hybrid differential transformation / finite difference approximation method. In deriving the dynamic equation of motion of the micro plate, explicit account is taken… More >

Nikhilkumar D. Abhangi¹, G. M. Deheri¹

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.3, pp. 245-260, 2009, DOI:10.3970/fdmp.2009.005.245

Abstract Efforts have been directed to study and analyze the behavior of a magnetic-fluid-based squeeze film between curved rough circular plates when the curved upper plate (with surface determined by an exponential expression) approaches the stationary curved lower plate (with surface governed by a secant function). A magnetic fluid is used as the lubricant in the presence of an external magnetic field oblique to the radial axis. The bearing surfaces are assumed to be transversely rough and the related roughness is characterized via a stochastic random variable with non-zero mean variance and skewness. The associated Reynolds equation is averaged with respect… More >

D.L. Young^1,2, C.C. Tsai³, Y.C. Lin¹, C.S. Chen⁴

CMC-Computers, Materials & Continua, Vol.4, No.1, pp. 1-10, 2006, DOI:10.3970/cmc.2006.004.001

Abstract This paper describes the method of fundamental solutions (MFS) to solve eigenfrequencies of plate vibrations by utilizing the direct determinant search method. The complex-valued kernels are used in the MFS in order to avoid the spurious eigenvalues. The benchmark problems of a circular plate with clamped, simply supported and free boundary conditions are studied analytically as well as numerically using the discrete and continuous versions of the MFS schemes to demonstrate the major results of the present paper. Namely only true eigenvalues are contained and no spurious eigenvalues are included in the range of direct determinant search method. Consequently analytical… More >