借助瑞利商函数的直接极小化计算结构的临界压力和固有频率

根据能量原理,结构由稳定平衡转向不稳定平稳的临界压力值,由下述方程确定:V-U=0(1)式中,V 为结构的挠曲变形能,U 为外压力所作的功.对于工程中感兴趣的很多情形,外压力只依赖于一个参数,因此可得:U=p(?) (2)F=V/(?) (3)于是,临界压力p_(cr)可由下式算出:p_(cr)=minF(4)结构振动时的固有频率,同样可出与(1)式相类似的下列方程确定:V_(max)-U_(max)=0 (5)此时,V_(max)为结构在极端位置时的应变能,即应变能的幅值;U_(max)为结构在零位置时     

求解梁变形的一种新方法——固定端法

自由端挠度和转角通用公式 设梁上分别作用载荷 M,P,q_0 x~n/a~n(n=0,1,2,…)如图1(a)、(b)、(c)所示.由莫尔积分知其自由端变形为: ...     

判别保守系统平衡稳定性的一种方法

<正> 1.理论推导研究具有 n 个自由度的完整、定常约束的保守力学系统,选取 n 个广义坐标 q_1,q_2,…,q_n,系统的势能可表示为 V(q_1,q_2,…,q_n),势能的增量     

对于WKB近似解的一个简单物理解释

<正> Liouville 和 Green 在1837年同时考虑了如下的二阶线性常微分方程d~2y/dx~2+[λ~2q_1(x)+q_2(x)]y=0 (1)其中 q_1(x)在区间[a,b]中有二阶连续导数,且q_1(x)>0 (当 x∈[a,b]) (2)q_2(x)在[a,b]中连续,且     

分析力学教材中的一个问题

周衍柏编“理论力学教程”1986年第二版中增加了一个内容,讲用广义坐标及拉格朗日乘子来求约束反力(见该书p.279—280),笔者认为是错误的.为讨论方便起见,先将该段内容摘引如下,其中重点号为笔者所加.“首先,应当利用(5.1.8)式把(5.2.12)式中3n个x、y、z 改用S 个广义坐际q_(?)(α=1,2,…s)表出,则约束方程将变为(?)(q_1,q_2,…q_(?))=0(β=1,2,…k)(5.2.22)k 为体系所受到完整约束的数目,而虚位移δq。则应     

分析力学教材中的一个问题

周衍柏编"理论力学教程"1986年第二版中增加了一个内容,讲用广义坐标及拉格朗日乘子来求约束反力(见该书p.279-280),笔者认为是错误的.为讨论方便起见,先将该段内容摘引如下,其中重点号为笔者所加."首先,应当利用(5.1.8)式把(5.2.12)式中3n个x、y、z 改用S 个广义坐际q_(?)(α=1,2,…s)表出,则约束方程将变为(?)(q_1,q_2,…q_(?))=0(β=1,2,…k)(5.2.22)k 为体系所受到完整约束的数目,而虚位移δq。则应 ...     

完整系统具有非定常约束时的平稳运动的条件

对具有非定常约束的完整系统,其相对平衡问题,应满足等效势能V_c取极值的条件其中V_c=V+(-T_0) (2)V为势能,(-T_0)为离心势能,q_1,…,q_n为系统的广义坐标。对于具有定常约束、存在循环坐标的完整 ...     

结构动力学直接积分的一个数值方法

1 基本算式 结构动力学归结为求解如下的振动方程 M+C+Kδ=P(t) (1)M,C,K是离散化系统的质量矩阵、阻尼矩阵、刚度矩阵,δ是位移矢量,其上一点表示对时间t的导数,P(t)是载荷矢量。把方程(1)在t_n-1至t_n时段对t积分一次,二次,设时段长度为τ,则得     

Extended airy function and differential equations with n-turning points

This paper studies a second order linear ordinary differential equation with n-turningpoints(d~2y)/(dx~2) [λ~2q_1(x) q_2(x)]y=0Where q_1(x)=(x-μ_1)(x-μ_2)...(x-μ_n)f(x),f(x)≠0 ,and λis a largeparameter.The formal uniformly valid asymptotic solution of the equation is obtained based onthe analysis of the three points by means of the matched method.By the work a method isdeveloped and the applicability of this method to the n-turning points is demonstrated.     

The boundedness and asymptotic behavior of solutions of differential system of second-order with variable coefficients

In this paper, the differential system of second-order withvariable coefficients is studied. and some criteria of theboundedness and asymptotic behavior for solutions are given.Consider a system of differential equationsdx_1/dt=p_(11)(t)x_1 p_(12)(t)x_2dx_2/dt=p_(21)(t)x_1 p_(22)(t)x_2Now we studg the boundedness and asymptotic behavior of its so-lutions. In the case of Pij(t)being periodic functions. it wasinvestigated by Burdina; in the case of Pij(t) being arbitraryfunctions. it has not been investigated yet. Besides. the me-thod used by Burdina is only oppropriate for the former but notfor the latter case. In this paper we shall give a method whichis appropriate for both cases.     

ACOUSTICAL TRANSMISSION LINE MODEL FOR ULTRASONIC TRANSDUCERS FOR WIDE-BANDWIDTH APPLICATION

An improved model for ultrasonic transducers is proposed.By considering only the first symmetric mode,each layer is represented as an acoustical transmission line in modeling of bulk wave transducers.In imaging applications,wide bandwidth and short time duration are required.The approach we have used consists of impedance matching the front face of the piezoelectric transducer to the propagating medium with a quarter wavelength impedance matching layer and inserting an unmatching quarter wavelength acoustical layer between the rear face and backing material.A heavy backing would degrade the wide-band phenomena,but show a time duration shorter than 0.5 μs for imaging applications.PSPICE code of the controlled source model is implemented to precisely predict the performance of the matched transducers such as impedance,insertion loss,bandwidth and duration of the impulse response.Good agreement between the simulation and experimental results has been achieved.     

INFORMATION FOR CONTRIBUTORS

Contributions： The Journal, Acta Mechanica Solida Sinica, is pleased to receive papers from engineers and scientists working in various aspects of solid mechanics. All contributions are subject to critical review prior to acceptance and publication.     

各向异性弹性力学一般边值问题的广义Stroh公式

当边值问题是简单的,即是应力边值问题时,Stroh公式是很有效的。对于混合边值问题,倒如滑动边界条件,Stroh公式中的简洁的矩阵表达式就失效了。我们提出了一个广义的Stroh公式,它可应用于一大类一般的边界条件。简单的边界条件和滑动边界条件是这一类一般边界条件的特殊情形。值得指出的是,这个关于Stroh公式所作的修正并不大。广义的公式和最后的解答看起来很类似于未修正的原公式和原来的解。然而这个修正却可应用于相当广的边界条件。