Conformal analysis of fundamental frequency of vibration of simple-supported elastic ellipse-plates with concentrated substance

Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elasticplates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipseplates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant inplane stress, as well as the concentrated substance mass and positions are analyzed respectively.     

Mapping analysis of vibrating fundamental frequency for simple-supported elastic rectangle-plates with concentrated mass

By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of fundamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.     

Mapping analysis of vibrating fundamenta frequency for simple-supported elastic rectangle-plates with coneentrated mass

By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of ftmdamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.     

损伤简支梁模态频率变化规律有限元分析

为掌握损伤简支梁的频率变化规律,对不同损伤位置及不同损伤程度的简支梁的模态频率进行了有限分析,在分析中以梁截面的刚度折减替代损伤,将有限元分析结果与文献中的RC简支梁的试验结果进行了对比.     

二阶效应的压弯构件振动分析

采用结构振动理论和二阶理论对压弯构件的振动进行了分析,求解构件的二阶自振频率和主振型,并对均匀简谐荷载作用下压弯构件的强迫振动进行了讨论。结果表明,二阶效应将对构件的位移和内力产生极为不利的影响。     

考虑横向剪切变形厚板弯曲的位移型方程及简支矩形板的一般解

基于考虑横向剪切变形厚板的几何方程、本构关系及平衡方程,建立关于一个中面位移和两个中面转角为独立变量的厚板振动的位移型基本方程.该方程退化为薄板振动的位移性方程的正确性说明推导过程的正确性及一般性.文中将双重三角级数作为广义坐标,应用MATLAB工具对简支矩形板的双重三角级数进行求解,求解过程简便,且挠度的收敛性较快.     

多孔有限弹性平面问题的研究

应用弹性力学的复变函数理论,采用多保角变换的方法,推出了含有任意多孔有限大平板的多复变量应力函数的表达式.在内边界上进行复Fourier级数展开,在外边界上采用配点法确定应力函数的未知系数,从而计算有限大弹性板的应力场.以外边界为矩形,内边界为任意多椭圆孔的有限板为例,编制了相应的计算程序,进行了算例分析,给出了内外边界对孔边周向正应力影响的分布图.结果表明,本方法对处理多孔有限大弹性平面问题简单且行之有效.     

机械弹性车轮随机振动理论与数值分析

针对现有轮胎模型不再适用于机械弹性车轮的振动分析的问题,依据其结构特点和铰链组单向传力特性,提出弹性绳索简化模型,推导弹性绳索刚度表达式、总等效刚度表达式以及系统频响函数,建立完整的振动分析数学模型.基于弹性绳索数学模型,进行C级随机不平路面输入激励下的随机振动分析,得到轮毂中心时域位移响应和频域功率谱密度响应.有限元仿真试验结果表明:机械弹性车轮共振频率为19~21 Hz,验证了弹性绳索模型的正确性.     

考虑高阶振型影响的简化PUSHOVER分析方法

为在高层建筑静力弹塑性分析中考虑高阶振型的影响,在模态Pushover分析方法基础上,通过振型叠加构造弹性等效振型.应用弹性等效振型将多自由度体系转化为等效单自由度体系,加载模式采用SRSS组合的层间剪力,应用延性需求谱以及反SRSS分配和SRSS组合,提出了简化的Pushover分析方法.通过实例计算表明,文中方法和模态叠加Pushover法得到的结构弹塑性位移基本一致.对于体型比较规则的高层建筑,应用弹性等效振型可以快速计算结构在罕遇地震下考虑高阶振型影响的弹塑性位移反应.     

高温下含裂纹铝合金梁自由振动频率分析

针对高温下含裂纹梁损伤振动的研究中不考虑温度对材料性能的影响等不足,分析了含裂纹简支梁的振动频率随温度的变化趋势,建立了高温下含裂纹简支梁的振动频率方程,并对高温下含裂纹简支铝合金梁进行了数值模拟运算,分析了其振动频率随温度的变化情况,给出了高温下含裂纹铝合金简支梁的振动频率与弹性模量的关系式.分析结果表明:温度的升高导致了材料弹性模量的下降,而弹性模量的下降又导致了梁自振频率的降低,随着温度的升高,裂纹的相对深度越大,梁自振频率下降幅度越大;裂纹位置离支座越近,对梁自振频率的变化影响越小.