周界固定带裂纹薄圆板的振动基频

在将裂纹板挠度表示为正交多项式的基础上，用分区技术的瑞利一里兹方法求解了含不同长度径向裂纹和弧向裂纹的周界固定圆板的振动基频。实验上用小球撞击法测定了裂纹圆板的辐射声场频谱，并得出了谱的基频。此外用有限元法对裂纹板作了理论计算。三项结果基本符合。探究了裂纹长度对圆板基频的影响规律。     

A boundary perturbation method for circularly periodic plates with a core

Fundamental frequencies of vibrating circularly periodic plates with a circular core have been determined analytically. A boundary perturbation method is developed to extract the fundamental eigenvalue of the governing biharmonic boundary value problem. The method is then applied to wavy and polygonal plates with clamped and simply supported outer boundary conditions. Clamped, simply supported, and free circular cores are considered. Approximate analytical formulations of the fundamental frequency for such plates with core are obtained.     

A simple frequency formula for clamped rectangular plates

A simple formula is proposed to predict the vibration frequencies of completely clamped rectangular plates, of arbitrary aspect ratio, vibrating in any mode. The development is based on experimental evidence obtained using the technique of holographic interferometry. Comparisons are made with both published results from the literature and experimental values obtained by the authors, and show excellent agreement in all cases.     

Fundamental frequency of vibration of clamped plates of arbitrary shape subjected to a hydrostatic state of in-plane stress

The present paper makes use of conformal mapping and Galerkin's method to determine the fundamental frequency of vibration of clamped plates of arbitrary shape subjected to uniform in-plane stress. Numerical results are presented for several plates of regular polygonal shape. Frequency curves obtained by means of Lurie's expression are also given for simply supported plates.     

Fundamental frequency of vibrating rectangular,non-homogeneous plates

An approximate solution is obtained in the present paper using the classical Ritz method. The use of polynomial coordinate functions allows for the treatment of edges elastically restrained against rotation.     

Vibration of plates with straight-line,clamped and free edges

This paper deals with vibration problems of thin plates having straight-line, mutually perpendicular, clamped and free edges and subjected to a load consisting of a set of transverse, arbitrarily located random forces. It is assumed that the number of edges of a plate forming recurring figures is optional but each of these edges is either clamped or free along its entire length. The procedure for solving the boundary problem based upon the R-functions method and for estimation of transverse displacements based upon the correlation analysis is presented. Numerical calculations are carried out for two example plates.     

Vibrational frequencies of clamped plates of variable thickness

A method is presented for computing lower and upper bounds for vibrational frequencies of clamped plates with general thickness variations. The method is illustrated for plates with linear tapers.     

Fundamental frequency of vibration of thin elastic plates elastically supported along internal segments

The title problem is approximately solved in a unified manner in the case of rectangular and circular plates elastically restrained against rotation along the boundary.Polynomial coordinate functions and a variational approach are used in order to obtain an approximate frequency equation. Judging from the excellent accuracy attained using the present methodology in the case where no internal supports are present, it is reasonable to expect that the results presented in this study will be sufficiently accurate for engineering purposes in the situations considered.     

具有固支边的强厚度层合板的一种新解法

在文[1~3]的基础上,通过引入边界位移函数,对具有固支边的强厚度层合板建立了在任意荷载作用下的状态方程,给出静力问题的解析解。算例表明,该法具有收敛快,边界应力连续等特点。     

Experimental investigation of free vibrations of clamped sector plates

The real time technique of time-averaged holographic interferometry has been applied to determine the natural frequencies and the corresponding mode shapes for the transverse vibrations of clamped wedge-shaped and ring-shaped sector plates. Over 200 resonant modes have been obtained for wedge-shaped sector plates and over 170 for ring-shaped sector plates. The natural frequencies obtained have been expressed in terms of a dimensionless frequency parameter, and the results are shown graphically as a function of the sector angle for the wedge-shaped plates and of the radii ratio for the ring-shaped sector plates, respectively. Some of the present results for wedge-shaped plates are compared with the analytical values obtained by other authors.     

Transverse vibration of clamped trapezoidal plates having rectangular orthotropy

This paper deals with the free transverse vibration of orthotropic trapezoidal plates clamped at the edges. A series-type method is applied for obtaining an analytical solution of the problem, and the resulting frequency equation is presented for symmetric trapezoids. In the numerical study, accurate frequency parameters and mode shapes of the plates are calculated for the first several modes, and the effects of the orthotropy are discussed.     

Casimir forces between plates with periodic longitudinal inhomogeneity

A method is proposed for computing the Casimir forces between plates with longitudinal inhomogeneities based on utilization of the modified impedance boundary condition. Corrections are found to the Casimir forces between flat plates in first and second order perturbation theory with respect to the relative degree of the inhomogeneity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 43–46, December, 1988.     

Free vibration of rectangular plates of arbitrary thickness with one or more edges clamped

Frequencies of free vibration of rectangular plates of arbitrary thickness, with different support conditions, are calculated by using the Method of Initial Functions (MIF), proposed by Vlasov. Sixth and fourth order MIF theories are used for the solution. Numerical results are presented for three square plates for three thickness ratios. The support conditions considered are (i) three sides simply supported and one side clamped, (ii) two opposite sides simply supported and the other two sides clamped and (iii) all sides clamped. It is found that the results produced by the MIF method are in fair agreement with those obtained by using other methods. The classical theory gives overestimates of the frequencies and the departures from the MIF results increase for higher modes and larger thickness ratios.     

Large amplitude vibrations of clamped circular plates of linearly varying thickness

The large amplitude vibrations of clamped circular plates of linearly varying thickness are investigated, by applying the procedure proposed by Banerjee and Datta [1].