共查询到20条相似文献,搜索用时 0 毫秒
1.
The effect of thermal gradient on the free vibration of clamped visco-elastic rectangular plate with linearly thickness variations
in both the directions has been studied here. The governing differential equation has been solved using Rayleigh-Ritz technique.
The frequency equation is derived for the clamped boundary condition on all the four edges. The effect of linear temperature
variation has been considered. Deflection and time period corresponding to the first two modes of vibrations of a clamped
plate have been computed for various values of aspect ratio, thermal constants, and taper constants. 相似文献
2.
XIAO Yong-gang 《应用数学和力学(英文版)》2005,26(8):963-972
IntroductionThe moderate thickness plates on elastic foundation are a kind of important structure instructural engineering. The mechanic characters of the plates on elastic foundation withdifferent boundary conditions have been received considerable atten… 相似文献
3.
选取带有补充项的双重正弦傅里叶级数作为振型函数通解,来解析研究带裂纹矩形板的自由振动特性。先将带裂纹矩形板分割成若干小矩形板,利用各小矩形板的边界条件,并结合振型函数中待定常数的物理意义,简化得到各小矩形板的振型函数,再结合各板的控制方程、未使用的边界条件、公共边协调条件及本文提出公共自由角点的协调条件,建立求解频率的代数方程组,然后将其转化为广义特征值问题来求解带裂纹矩形板的无量纲频率;最后选取具体参数进行计算并与文献结果对比,吻合良好,证明了本文采用的研究方法以及所提出公共角点协调条件的正确性和合理性。由于该振型函数能满足矩形板的任意边界约束,且其中的待定常数具有明确的物理意义,所以可使矩形板问题的求解统一化、简单化和规律化。 相似文献
4.
5.
Analytical solutions of steady vibration of free rectangular plate on semi-infinite elastic foundation 总被引:1,自引:0,他引:1
The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load.And an integral representations for the displacements of the semi-infinite elastic foundation was presented.The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semi- infinite elastic foundation.Some computational results and the analysis on the influence of parameters were presented. 相似文献
6.
A free rectangular plate on elastic foundation 总被引:1,自引:0,他引:1
成祥生 《应用数学和力学(英文版)》1992,13(10):977-982
This article will discuss the bending problems of the rectangular plates with free boundaries on elastic foundations. We talk over the two cases, that is, the plate acted on its center by a concentrated force and the plate subjected to by a concentrated force equally at four corner points respectively. We select a fiexural function which satisfies not only all the geometric boundary conditions on free edges wholly but also the boundary conditions of the total internal forces. We apply the variational method meanwhile and then obtain better approximate solutions. 相似文献
7.
8.
The active vibration control of a rectangular plate either partially or fully submerged in a fluid was investigated. Piezoelectric sensors and actuators were bonded to the plate, and the assumed mode method was used to derive a dynamic model for the submerged plate. The properties of the piezoelectric actuators and sensors, as well as their coupling to the structure, were used to derive the corresponding equations of their behaviour. The fluid effect was modelled according to the added virtual mass obtained by solving the Laplace equation. The natural vibration characteristics of the plate both in air and in water were obtained theoretically and were found to be consistent with the experimental results, and the changes in the natural frequencies resulting from submersion in fluid can be accurately predicted. A multi-input, multi-output positive position feedback controller was designed by taking the natural vibration characteristics into account and was then implemented by using a digital controller. The experimental results show that piezoelectric sensors and actuators along with the control algorithm can effectively suppress the vibration of a rectangular plate both in air and submerged in a fluid. 相似文献
9.
An analysis and numerical results are presented for free transverse vibrations of non-homogeneous visco-elastic elliptic plate
whose temperature and thickness spatial variations both are parabolic along a line through plate centre. The variation in
density is assumed as parabolic along a line through plate centre, which raise non-homogeneity of the plate materials and
make problem interesting as introducing variation in non-homogeneity of the material mass density reduce the problem practical
importance in comparison to homogenous plate. For visco-elastic, the basic elastic and viscous elements are combined. We have
taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the
elastic element means the spring and the viscous element means the dashpot. The governing differential equation of motion
has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement corresponding to the first two
modes of vibrations of a clamped non-homogeneous visco-elastic elliptic plate for various values of taper constant, thermal
constants, non-homogeneity constant and aspect ratio are obtained and shown graphically. 相似文献
10.
Thermal vibration and apparent thermal contraction of single-walled carbon nanotubes 总被引:2,自引:0,他引:2
It is of fundamental value to understand the thermo-mechanical properties of carbon nanotubes. In this paper, by using molecular dynamics simulation, a systematic numerical investigation is carried out to explore the natural thermal vibration behaviors of single-walled carbon nanotubes and their quantitative contributions to the apparent thermal contraction behaviors. It is found that the thermo-mechanical behavior of single-walled carbon nanotubes is exhibited through the competition between quasi-static thermal expansion and dynamic thermal vibration, while the vibration effect is more prominent and induces apparent contraction in both radial and axial directions. With increasing temperature, the anharmonic interatomic potential helps to increase the bond length, which leads to thermally induced expansion. On the other hand, the higher structural entropy and vibrational entropy of the system cause the carbon nanotube to vibrate, and the apparent length of nanotube decreases due to various vibration modes. Parallel analytical and finite element analyses are used to validate the vibration frequencies and provide helpful insights. The unified multi-scale study has successfully decoupled and systematically analyzed both thermal expansion and contraction behaviors of single-walled carbon nanotube from 100 to 800 K, and obtained detailed information on various vibration modes as well as their quantitative contributions to the coefficient of thermal expansion in axial and radial directions. The results of this paper may provide useful information on the thermo-mechanical integrity of single-walled carbon nanotubes, and become important in practical applications involving finite temperature. 相似文献
11.
应用双重正弦级数展开的方法,推演得到了文克勒地基上计入两块矩形板间接缝传荷效应的级数解。假设接缝传递剪力与板间挠度差成正比、传递弯矩与板间转角差成正比,进而分析了单轮和单轴荷载作用在纵缝边缘中部时,接缝传荷效应对板边最大挠度和最大应力的影响规律;通过引入接缝传荷效应系数和接缝极限传荷的两个挠度比及两个应力比,建立了计入接缝传荷效应的板边最大挠度和最大应力的一般式,总结了不同板尺寸、荷载面积尺寸和类型及板材料泊松比对四个接缝影响系数和四个接缝极限传荷的挠度比及应力比的影响规律。结果表明:不同荷载面积下,受荷板接缝边缘最大挠度、最大应力均随弯矩或剪力传荷刚度系数的增大而减小,且应力的变化幅度相较挠度要小。影响系数fV^w(ξV)、fM^w(ξM)、fM^σ(ξM)与荷载圆相对半径(a/l)、相对板长(L/l)和相对板宽(B/l)无关,且单轮荷载与双轮荷载规律相同;而影响系数fV^σ(ξV)与荷载圆相对半径(a/l)有关,与相对板长(L/l)和相对板宽(B/l)无关;挠度比λV^w与荷载圆相对半径、板尺寸(L/l,B/l)及泊松比v无关,恒等于0.5,而λM^w、λV^σ、λM^σ均与荷载相对半径(a/l)、板尺寸(L/l,B/l)及泊松比v有关,且影响因素中荷载面积尺寸的影响最为显著。 相似文献
12.
The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form, and Poisson’s ratio is constant. A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation, and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads. The validity of the present solution is shown by comparing the present results with those of the classical solution. The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples. The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness. 相似文献
13.
基于广义变分原理得到的磁力计算公式,采用塑性增量理论,Mises屈服准则和有效的增量有限元计算方法,研究了线性强化材料铁磁矩形板的磁弹塑性弯曲行为。在文中定量模拟了铁磁简支矩形板在外加磁场作用下的挠度特征曲线,铁磁板发生塑性变形时的构型图和不同外加磁场下的中截面构型,以及铁磁板在卸载后的残余挠度特征曲线等力学特征,分析了塑性区域随磁场增加而扩展的情况。数值结果表明:当铁磁矩形板上的部分区域发生塑性屈服后,其变形明显大于相同磁场条件下铁磁板发生的弹性变形值;且随着外加磁场倾角的增大(0°<α≤45°),铁磁板进入塑性屈服状态的临界屈服磁场值减小;铁磁板的中截面构形为双半波型,其塑性区域由铁磁板两侧挠度最大的区域向板的中心区域扩展,板的中心最后进入塑性区域等。 相似文献
14.
This paper analyzes the stability of the elastic rectangular thin plates with sinusoidal changes in the plate thickness. The buckling load is defined in a weighted residual approach for different boundary conditions. The influence of the plate thickness variation and the edge ratio on the critical loads is investigated. The results are compared to the case of uniform thickness. 相似文献
15.
一边固定一角点或二角点支承的矩形板弯曲统一求解方法 总被引:4,自引:0,他引:4
本文的统一法可以解决悬壁板或带有角点支承时在任意荷载作用下的弯曲。这种方法求解思路清晰、收敛速度快,计算精度高。 相似文献
16.
BENDING SOLUTION OF A RECTANGULAR PLATE WITH ONE EDGE BUILT-IN AND ONE CORNER POINT SUPPORTED SUBJECTED TO UNIFORM LOAD 总被引:3,自引:0,他引:3
BENDING SOLUTION OF A RECTANGULAR PLATE WITH ONE EDGE BUILT-IN AND ONE CORNER POINT SUPPORTED SUBJECTED TO UNIFORM LOADXuQilo... 相似文献
17.
Basic equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness 总被引:1,自引:0,他引:1
黄家寅 《应用数学和力学(英文版)》2004,25(7):812-816
Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction ( z-direction ), the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given; then introducing the dimensionless variables and three small parameters, the dimensionaless governing equations of the deflection function and stress function are given. 相似文献
18.
Here, thermal gradient effect on vibration of non-homogeneous orthotropic rectangular plate having bi-direction linearly thickness
variations is studied. The non-homogeneity is assumed to arise due to the variation in the density of the plate material.
Rayleigh Ritz method is used to evaluate the fundamental frequencies and deflection function. The two-dimensional thickness
variation is taken as the Cartesian product of linear variations along the two concurrent edges of the plate. Yet the method
used for the solution of present problem provides an approximate solution but it is quite convenient and authentic one. A two-term
deflection function is used. Frequency corresponding to first mode of vibration is calculated for clamped plate for different
values of temperature gradient, taper constants and non-homogeneity constant. In special cases, comparisons have been made
with results that are available in the literature. 相似文献
19.
Two-dimensional boundary characteristic orthonormal polynomials are used in the Rayleigh–Ritz method to study the free vibration
of rectangular orthotropic elliptic plates resting on a Winkler elastic foundation. Two types of varying thickness are considered:
(1) linearly varying with respect to the concentric ellipses, (2) linearly varying along both the principal axes simultaneously.
Numerical results for frequencies are presented in tables. Nodal lines are shown in figures. Effects of stiffness of elastic
foundation, aspect ratios of plates, degree of orthotropy, and types of thickness variation on vibration frequencies of elliptical
plates are also discussed. 相似文献
20.
构造了带有补充项的双重正弦傅里叶级数通解来求解各种边界条件的多层正交各向异性矩形薄板的弯曲、振动和稳定问题.将坐标轴取在中性面上,求出用挠度表示的应力表达式,然后由横截面上每单位宽度的应力合成板的内力;再将层合板的内力代入板的平衡方程中得到板的控制方程,将多层板的物理参数折算为等价的单层板物理参数;最后联立控制方程与边界条件,求得未知量的系数并代入本文的通解中.本文的通解不需要叠加即可求解各种边界条件的板的弯曲、振动和稳定问题;现有的对于单层板的研究都可以用本文的方法拓展到多层板领域;对于复杂边界条件的板,也可以使用该通解分析. 相似文献