Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.

Investigation of the Free Vibrations of Radial Functionally Graded Circular Cylindrical Beams Based on Differential Quadrature Method

In the current research,an effective differential quadrature method(DQM)has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient.Based on the high-order theory of transverse vibration of circular cross-section beams,lateral displacement equation was reconstructed neglecting circumferential shear stress.Two equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as eigenvalue.Then,differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation into a set of algebraic equation eigenvalue problems.Natural frequencies of the free vibrations of cylindrical beams with circular cross-sections were calculated at one time,and corresponding modal functions were solved together.The obtained numerical results indicated that the natural frequencies of functionally graded(FG)circular cylindrical beams obtained using differential quadrature method agreed with the results reported in related literatures.In addition,influences of varying gradient parameters on the modal shapes of circular cylindrical beams were found to be strongly consistent with previous studies.Numerical results further validated the feasibility and accuracy of the developed differential quadrature method in solving the transverse vibration of FG circular cross-section beams.

自然冷却和遇水冷却后高温花岗岩力-声特性试验研究

以松辽盆地露天花岗岩为研究对象,对自然冷却和遇水冷却后高温花岗岩进行单轴压、拉和声波测定试验.研究不同方式冷却后花岗岩温度(100℃、200℃、300℃、400℃、500℃、600℃、700℃、800℃,以下简称100℃-800℃)与表观形态、纵、横波波速、弹性模量、泊松比、抗压强度、抗拉强度间关系,并将纵、横波波速与抗压强度、弹性模量建立联系.同时考虑遇水冷却后静置过程对花岗岩力-声性质影响.研究表明:(1)静置0 h-2 h是质量损失、纵波波速下降主要时段,静置6 h后变化率可以忽略;自由水损失量与力-声特性损失量存在一定线性关系;(2)温度升高,自然冷却后花岗岩纵、横波波速、弹性模量、抗压强度、抗拉强度呈线型下降,遇水冷却后呈凹线型下降;高于300℃,自然冷却后花岗岩力-声参数均大于遇水冷却,泊松比变化率与其相反,600℃时冷却方式不同对花岗岩纵、横波波速、弹性模量、抗压强度影响达到最大,遇水冷却比自然冷却分别低33.33%、31.88%、53.33%、31.74%,700℃-800℃时冷却方式对花岗岩力声特性影响减小;(3)温度变化,花岗岩纵、横波波速与抗压强度、弹性模量呈良好相关性.所得结论可以提高花岗岩力-声特性测量准确性,为力学特性预测提供一个可行方法,并为岩体工程安全稳定性评估提供依据.