共查询到17条相似文献,搜索用时 171 毫秒
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基于振动固支弹性异型板基波频率值的求解问题,采用共形映射理论,为了寻求复杂域与单位圆域的共形映射函数,将复杂边界域插值点序列分为奇偶两序列并相互迭代;提出了三角插值数学方法及其法向收敛方法,求得了共形映射函数的复系数。应用Galerkin的方法,完成复杂振动板域振动微分方程的基波频率解析。以椭圆板域求解为示例,分析了偏心率e和面积对基波频率系数的影响。 相似文献
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本文研究两对边简支,另两对边离散支承矩形的自由振动问题,推导出了用支点反力表示的矩形板自由振动的振型函数,即Green函数,利用支点处的位移相容性,确定支点反力和频率方程,可以求解任意阶的固有频率和振型。 相似文献
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本文研究受任意个同心弹性环支图板的横向自由振动问题,给出了一个新的解析解法。对弹性环支反力表示为作用于圆板上的待定外力,在求得圆板受迫振动的解析式后,由圆板的边界条件决定积分常数,利用环支处板位移与环支反力之间的线性关系得环支反力,并得频率方程。它是一阶数等于环支个数的行列式,可由行列式搜根法数值计算各阶固有频率,而振型函数则用一解析式表示,本文最后给出了一个算例,并与已有结果进行了比较。 相似文献
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应变模态振型决定了结构动应变分布规律。基于梁应变与曲率的正比关系,提出一种直接求解悬臂梁结构曲率模态的积分方法,适用于任意形式的刚度和质量函数。通过与数值和解析解比较模态频率与振型,验证了该方法的准确性。此外,该方法将连续体模态求解问题转化为有限自由度的广义特征值形式,进一步证明可以应用Nelson法求解该形式的特征灵敏度,获得了曲率模态振型对于结构设计参数的灵敏度显式表达。为了更加明显地表现动应变变化,提出了曲率梯度模态的概念,其参数灵敏度可由曲率模态灵敏度获得。算例结果表明,该方法可以有效地优化结构参数、避免动应变集中。该方法同样也适用于固支—固支和固支—简支这两种边界条件。 相似文献
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自振特性在结构的动力分析中具有重要的意义。将回传射线矩阵法(MRRM)推广到地基梁自振特性的研究中,通过节点力平衡和位移协调方程及对偶局部坐标系下单元相位关系,建立两端简支、两端自由、两端固支、简支-自由、简支-固支及固支-自由这六种边界条件下黏弹性Pasternak地基上的Bernoulli-Euler梁的回传射线矩阵,进而得到其频率方程。根据单一局部坐标系下的边界条件,推导出模态函数解析表达式,进一步根据正交归一化条件求解模态函数表达式中的未知参数。通过具体算例验证了回传射线矩阵法求解的正确性,并对不同边界条件下的自振频率、衰减系数及模态函数进行了分析。为黏弹性地基梁的振动特性研究提供理论基础。 相似文献
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弹性地基上矩形贮液结构的液-固耦合振动特性 总被引:1,自引:0,他引:1
针对无旋、无粘和不可压缩的理想液体,根据Winkler弹性地基上矩形贮液结构的液-固耦合振动分析模型,通过引入无量纲参数建立了矩形贮液结构的液-固耦合系统的振动方程。为简化计算,根据梁的振型函数和频率方程,将三维问题转化为一维问题来处理,利用振型函数的正交性求解了Winkler弹性地基上矩形贮液结构的液-固耦合振动频率。最后,为便于工程应用,结合工程实际讨论了无量纲参数对矩形贮液结构液-固耦合振动频率的影响,从而为以后工程结构中矩形贮液结构的设计计算提供了理论依据。 相似文献
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Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory 总被引:1,自引:0,他引:1
This paper deals with elastic buckling analysis of stiffened and un-stiffened corrugated plates via a mesh-free Galerkin method
based on the first-order shear deformation theory (FSDT). The corrugated plates are approximated by orthotropic plates of
uniform thickness that have different elastic properties along the two perpendicular directions of the plates. The key to
the approximation is that the equivalaent elastic properties of the orthotropic plates are derived by applying constant curvature
conditions to the corrugated sheet. The stiffened corrugated plates are analyzed as stiffened orthotropic plates. The stiffeners
are modelled as beams. The stiffness matrix of the stiffened corrugated plate is obtained by superimposing the strain energy
of the equivalent orthotropic plate and the beams after implementing the displacement compatibility conditions between the
plate and the beams. The mesh free characteristic of the proposed method guarantee that the stiffeners can be placed anywhere
on the plate, and that remeshing is avoided when the stiffener positions change. A few selected examples are studied to demonstrate
the accuracy and convergence of the proposed method. The results obtained for these examples, when possible, are compared
with the ANSYS solutions or other available solutions in literature. Good agreement is evident for all cases. Some new results
for both trapezoidally and sinusoidally corrugated plates are then reported. 相似文献
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Yong YK Stewart JT Detaint J Zarka A Capelle B Zheng Y 《IEEE transactions on ultrasonics, ferroelectrics, and frequency control》1992,39(5):609-617
Finite-element solutions for the fundamental thickness shear mode and the second-anharmonic overtone of a circular, 1.87-MHz AT-cut quartz plate with no electrodes are presented and compared with previously obtained results for a rectangular plate of similar properties. The edge flexural mode in circular plates, a vibration mode not seen in the rectangular plate is also presented. A 5-MHz circular and electroded AT-cut quartz plate is studied. A portion of the frequency spectrum is constructed in the neighborhood of the fundamental thickness-shear mode. A convergence study is also presented for the electroded 5-MHz plate. A new two-dimensional (2-D) technique for visualizing the vibration mode solutions is presented. This method departs substantially from the three-dimensional (3-D) ;wire-frame' plots presented in the previous analysis. The 2-D images can be manipulated to produce nodal line diagrams and can be color coded to illustrate mode shapes and energy trapping phenomenon. A contour plot of the mass-frequency influence surface for the plated 5-MHz resonator is presented. The mass-frequency influence surface is defined as a surface giving the frequency change due to a small localized mass applied to the resonator surface. 相似文献
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D. Wang J. S. Jiang W. H. Zhang 《International journal for numerical methods in engineering》2004,61(10):1584-1602
In this paper, the position optimization of simple supports is implemented to maximize the fundamental frequency of a beam or plate structure. Both elastic and rigid supports are taken into account. First, the frequency sensitivity with respect to the movement of a simple support is derived using the discrete method. By means of the shape functions of the finite element method, closed‐form sensitivity formulations are developed straightforwardly. Then, a heuristic approach, called evolutionary shift method, is presented for optimizing support positions with a fixed grid mesh scheme. Based on the design sensitivity analysis, the support with the highest efficiency is shifted in priority along the elementary edges with the interval (step) of the elementary size. To facilitate the convergence of the process, the interpolation technique is employed to evaluate the solution more accurately. Finally, three numerical examples are presented to demonstrate the validity of the sensitivity analysis and the effectiveness of the optimization method. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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考虑圆形水池池壁剪切变形的影响、底板对池壁的径向约束作用和转动约束作用,将圆形水池底板与池壁的相互作用简化成端部受切向弹性约束和转动弹性约束下的弹性地基Timoshenko梁,基于Timoshenko梁振动的修正理论,导出了底部环向简支、顶部分别为自由、铰支和固支三种边界条件下的振动频率超越方程;根据池壁和弹性地基梁微分方程的类比性,阐述了利用ANSYS建立圆形水池振动模态分析的有限元方法。利用二分法对底板环形简支的圆形水池的振动频率进行了计算,分析了顶部不同边界条件、池高、池的半径和底板对池壁弯曲约束刚度对池壁振动频率的影响。得到了圆形水池轴对称振动可采用弹簧-质量模型进行基频估算、该文所建立的分析方法只能分析圆形水池的轴对称振动模态、圆形水池底板与池壁相互作用对基频影响不明显、壁厚的剪切变形和转动惯量对高阶振动影响大等结论。 相似文献
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Nosek J. Pustka M. 《IEEE transactions on ultrasonics, ferroelectrics, and frequency control》2006,53(1):10-14
The quartz homeotype gallium orthophosphate (GaPO/sub 4/) is a representative of piezoelectric single crystals of large electromechanical coupling factor. It is known that its coupling factor k/sub 26/ associated with the resonators vibrating in the thickness-shear mode is approximately two times greater than that of quartz. This property increases the spacing between the series and parallel resonance frequencies of resonators, as well as the difference between the resonance frequency temperature dependencies of the fundamental and harmonic resonance frequencies of resonators vibrating in the thickness-shear mode. In this paper, the methods for determination of the coupling factor k/sub 26/ are presented, and the computed values are compared with the measured ones. The influence of the coupling factor to the resonance-frequency temperature dependencies of the fundamental and third harmonics of selected rotated Y-cut GaPO/sub 4/ resonators vibrating in the thickness-shear mode is presented. The purely elastic case for a laterally unbounded plate, which corresponds closely to the limiting case of high harmonic resonance frequency-temperature behavior was assumed for the calculations. The computed temperature coefficients for the Y-cut orientation and calculated turnover point temperatures T/sub TP/ for different (YX1) orientations are presented. 相似文献
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Jaroslav Nosek Martin Pustka 《IEEE transactions on ultrasonics, ferroelectrics, and frequency control》2006,53(1):10-14
The quartz homeotype gallium orthophosphate (GaPO4) is a representative of piezoelectric single crystals of large electromechanical coupling factor. It is known that its coupling factor kappa26 associated with the resonators vibrating in the thickness-shear mode is approximately two times greater than that of quartz. This property increases the spacing between the series and parallel resonance frequencies of resonators, as well as the difference between the resonance frequency temperature dependencies of the fundamental and harmonic resonance frequencies of resonators vibrating in the thickness-shear mode. In this paper, the methods for determination of the coupling factor kappa26 are presented, and the computed values are compared with the measured ones. The influence of the coupling factor to the resonance-frequency temperature dependencies of the fundamental and third harmonics of selected rotated Y-cut GaPO4 resonators vibrating in the thickness-shear mode is presented. The purely elastic case for a laterally unbounded plate, which corresponds closely to the limiting case of high harmonic resonance frequency-temperature behavior was assumed for the calculations. The computed temperature coefficients for the Y-cut orientation and calculated turnover point temperatures TTP for different (YX1) orientations are presented. 相似文献