端部任意弹性约束变截面地基梁的自由振动特性分析

研究端部弹性约束地基梁的自由振动特性。将梁的弯曲位移用传统傅里叶级数与辅助函数表示,即应用改进傅里叶级数形式,以突破传统傅里叶级数不能满足端部弹性约束条件的局限;基于地基梁的拉格朗日函数,由瑞利-里兹方法把振动问题转化为矩阵特征值问题,得到地基梁的固有频率;研究经典边界地基梁的多个算例,通过调整边界处约束弹簧的刚度值,获得端部弹性约束地基梁的各阶固有频率。所得固有频率值与已有文献结果一致,验证了本文方法的快速收敛性和正确性。本文方法具有一定的通用性和实际工程应用价值,为扩展至其他工程梁、板等结构的动态特性分析提供了良好的借鉴。     

薄膜横向振动的有限元分析

构造了一种3节点三角形膜单元,以适用于平面薄膜横向振动的有限元分析.在给出单元形函数的基础上,根据最小势能原理建立了薄膜自由振动方程,并推导了单元刚度矩阵和单元质量矩阵.研究结果表明,单元刚度矩阵和单元质量矩阵形式简单,且自由度少;通过两个典型算例,证明3节点三角形膜单元的计算结果非常接近理论解,同时可以达到很高的精度...     

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

Free vibration of statically thermal postbuckled functionally graded material （FGM） beams with surface-bonded piezoelectric layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric layers subject to thermo-electro- mechanical loadings are formulated. It is assumed that the material properties of the middle FGM layer vary continuously as a power law function of the thickness coordinate, and the piezoelectric layers are isotropic and homogenous. By assuming that the amplitude of the beam vibration is small and its response is harmonic, the above mentioned non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations. One is for the postbuckling, and the other is for the linear vibration of the beam superimposed upon the postbuckled configuration. Using a shooting method to solve the two sets of ordinary differential equations with fixed-fixed boundary conditions numerically, the response of postbuckling and free vibration in the vicinity of the postbuckled configuration of the beam with fixed-fixed ends and subject to transversely nonuniform heating and uniform electric field is obtained. Thermo-electric postbuckling equilibrium paths and characteristic curves of the first three natural frequencies versus the temperature, the electricity, and the material gradient parameters are plotted. It is found that the three lowest frequencies of the prebuckled beam decrease with the increase of the temperature, but those of a buckled beam increase monotonically with the temperature rise. The results also show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and the natural frequency.     

Three-to-one internal resonance in multiple stepped beam systems

In this study, the vibrations of multiple stepped beams with cubic nonlinearities are considered. A three-to-one internal resonance case is investigated for the system. A general approximate solution to the problem is found using the method of multiple scales （a perturbation technique）. The modulation equations of the amplitudes and the phases are derived for two modes. These equations are utilized to determine steady state solutions and their stabilities. It is assumed that the external forcing frequency is close to the lower frequency. For the numeric part of the study, the three-to-one ratio in natural frequencies is investigated. These values are observed to be between the first and second natural frequencies in the cases of the clamped-clamped and clamped-pinned supports, and between the second and third natural frequencies in the case of the pinned-pinned support. Finally, a numeric algorithm is used to solve the three-to-one internal resonance. The first mode is externally excited for the clamped-clamped and clamped-pinned supports, and the second mode is externally excited for the pinned-pinned support. Then, the amplitudes of the first and second modes are investigated when the first mode is externally excited. The amplitudes of the second and third modes are investigated when the second mode is externally excited. The force-response, damping-response, and .frequency- response curves are plotted for the internal resonance modes of vibrations. The stability analysis is carried out for these plots.     

固有频率法评估损伤的阈值研究

通过分析损伤可测性的影响因素,对固有频率法判断损伤阈值的估算方法进行了研究,并以悬臂梁模型为例,应用该方法研究了悬臂梁的损伤阈值. 数值及理论计算的结果表明：在已知频率测量精度及方法偏差时,该方法可以判别固有频率法损伤识别的阈值,在早期损伤阶段,该方法判别的阈值与数值模拟结果吻合良好.     

基于小波分析的建(构)筑物爆破振动安全评估

基于现场实测爆破振动数据,采用小波分析技术对爆破振动信号的能量特征进行分析,得到了信号不同频带上的能量分布,根据受控结构体对爆破振动动态响应特征,探索建立了能考虑爆破振动的强度、频率和持续时间以及受控建(构)筑物本身的动态响应特性(固有频率和阻尼比)等因素的综合安全判据响应能量判据,并用工程实例验证了该判据的可行性和可靠性。响应能量判据能准确地描述爆破振动对受控建(构)筑物的影响程度,较现行的速度-频率安全判据,更能全面地反映爆破振动对建(构)筑物危害的本质。     

变截面梁横向振动固有频率数值计算

根据边界条件对变截面梁横向振动四阶变系数微分方程降阶, 形成关于挠度和弯矩的二 阶非显式递推变系数微分方程组; 利用有限差分法, 研究了变截面简支梁横向振动固有频率 的数值计算方法及其精度. 理论分析和正交计算的算例表明: 数值计算算法简单, 计算精度 取决于计算步长的数目和梁横截面竖向渐变率, 与梁宽和梁长无关; 对于给定的计算步长或 数目, 可以估算数值计算的精度; 对于给定的精度要求, 可以确定合理的计算步长或数目.     

超临界轴向运动梁横向非线性振动频域分析

数值方法研究超临界速度下轴向运动梁横向非线性振动前两阶固有频率.通过对非平凡平衡位形做坐标变换,建立超临界轴向运动梁的标准控制方程,一个积分-偏微分非线性方程.利用有限差分法数值离散梁两端简支边界下控制方程,计算轴向运动梁中点的横向振动位移,并将计算结果作为时间序列,运用离散傅立叶变换得到超临界轴向运动梁横向振动的频率.通过数值算例,讨论了系统参数对前两阶固有频率在超临界范围随轴向速度变化的影响.     

四边简支正交各向异性蜂窝型夹层板固有频率计算

该文以四边简支的方形蜂窝矩形夹层板为例,在经典夹层板理论的基础上,运用离散结构形式的运动控制方程和线性微分算子的可交换性,给出了一种把具有蜂窝型夹心的夹层板的包含三个广义位移的控制方程组化为,仅包含一个广义位移函数的单一方程的简单方法,并给出了四边简支蜂窝型夹层板的固有频率的精确解。研究结果对蜂窝夹层板的结构设计和工程应用具有指导意义。