Winkler地基上有限长梁联合共振分析

为进一步完善弹性地基上梁的非线性振动理论以及满足实际工程的需要,本文对三种联合共振情况进行了研究。文中基于已建立的Winkler地基上有限长梁的非线性振动方程,运用Galerkin离散法以及多尺度法推导其稳态运动方程组,分析了主/次联合共振时,结构参数及初始条件对系统幅频响应曲线、调谐-相位曲线的影响,初步探讨了主/超联合共振、次/超联合共振的基本性质。研究结果表明:当且仅当两个激励频率是可公度关系时,联合共振才存在稳态响应;对于一个给定的调谐参数,系统最多存在七个解,而解的最终形式是由初始条件决定;系统参数及初始条件的微小变动,可能会激烈地改变系统的响应;工程中为了较好地抑制结构的振动,必须选择合适的方法提高系统的刚度。     

简谐横荷载作用下Winkler地基上有限长梁1/3次亚谐共振分析

基于Winkler地基模型及Euler - Bernoulli梁理论,建立了Winkler地基上有限长梁的非线性运动方程.运用Galerkin方法对运动方程进行一阶模态截断,得到离散的非线性振动方程,利用多尺度法求得该系统1/3次亚谐共振的一阶近似解.分析了长细比、弹性模量、地基刚度、阻尼、密度等参数对其亚谐共振幅频响...     

Winkler地基梁在温度场中受简谐激励的1/3次亚谐共振分析

研究W inkler地基梁在温度场中受简谐激励作用的1/3次亚谐共振问题。应用弹性理论和Galerk in方法建立W inkler地基梁在温度场中受简谐激励作用的非线性动力方程,根据非线性振动的多尺度法求得系统满足1/3次亚谐共振情况的一次近似解,并对其进行数值计算,分析了温度、调谐值、激励、阻尼、地基刚度等参数对系统的影响。     

Winkler地基梁在温度场中受简谐激励3次超谐共振分析

本文研究W inkler地基梁在温度场中受简谐激励作用的3次超谐共振问题,应用弹性理论和Galerk in方法建立W inkler地基梁在温度场中受简谐激励作用的非线性动力方程,根据非线性振动的多尺度法求得系统满足3次超谐共振情况的一次近似解,分析了温度、阻尼、激励幅值、地基刚度等参数对系统的影响。     

Winkler地基梁在温度场中受简谐激励的主共振分析

研究W inkler地基梁在温度场中受简谐激励作用的主共振问题。应用弹性理论和Galerk in方法建立W inkler地基梁在温度场中受简谐激励作用的非线性动力方程。应用非线性振动的多尺度法,求得系统主共振的近似解。分析不同参数对主共振响应曲线的影响。     

非线性弹性地基上圆形薄板三次超谐共振

本文研究非线性地基上圆形薄板受简谐激励的次谐波共振问题。按照弹性力学理论建立非线性地基上圆形薄板受简谐激励的动力学方程。利用Galerk in方法将其转化为非线性振动方程。应用非线性振动的多尺度法求得系统满足3次超谐共振条件的一次近似解,并进行数值计算。分析阻尼、地基系数、调谐值、激励等参数对共振响应曲线的影响。     

级配砂石地基条件下核安全级廊道结构地震响应分析

级配砂石处理核安全级廊道结构的软弱地基有良好的发展前景,发展级配砂石地基条件下的廊道地震响应分析模型是评价其抗震安全性的关键问题。以某核电厂废液输送机排放廊道为研究对象,通过引入等价线性法描述近场级配砂石地基的非线性特征,在分析模型底部施加黏性边界模拟半无限空间,在截断边界的两侧施加黏性边界考虑波动的逸散效果,通过无厚度Goodman单元模拟廊道结构与周围地基的摩擦效应,并利用基于有限元法的自由场响应分析实现地震动输入,从而建立了级配砂石地基条件核安全级廊道结构地震响应分析计算模型。最后,通过开展级配砂石与回填素混凝土两种地基处理条件的廊道地震响应对比分析,该模型表现出良好的规律性及工程应用效果。研究成果可为在建项目、后续核电项目此类问题的地基处理提供借鉴与参考。     

移动荷载作用下双层Euler梁模型土动力响应分析

本文以弹性波动理论为基础,利用分层法计算了双层连续支撑Euler梁下地基土的位移,同时考虑了不同的车辆荷载模型,并将计算的结果和单层Euler梁下地基土的位移进行了比较,比较表明：轨道结构本身和车辆悬挂体系具有一定的减振功能。因此,该研究对由交通荷载引起的环境振动分析和评价具有一定的应用价值。     

考虑水平力作用的弹性地基梁位移及内力解析解

考虑水平力作用下弹性地基梁受力特点,针对Winkler地基模型不能考虑梁底面间与地基切向相互作用的不足,在地基与梁体接触面上引入一系列各自独立的水平弹簧。假定弹簧反力与梁底和地基间的切向相对位移成正比,根据弹性力学基本原理,结合小变形条件下梁体几何方程和线弹性本构关系,建立力学分析模型,导出基本微分方程组并利用微分算子级数法进行求解,获得了考虑水平力作用时地基梁位移及内力解析解。最后通过实例分析,验证了该解析解的正确性和合理性,并对切向地基反力系数等影响因素进行了探讨。其结果可为工程设计提供借鉴参考。     

多尺度阵列嵌套组合反演宾川气枪源区横波速度结构

本文基于多尺度阵列嵌套组合的方式,利用频率-贝塞尔变换法（Frequency-Bessel,F-J方法）提取背景噪声面波频散信息,通过多个阵列融合的频散曲线反演得到宾川气枪发射台周边不同深度的横波速度结构.结果显示：浅层一阶面波频散信息的加入,使得基阶反演结果更加收敛,反演深度加深到8 km;深度在8 km以下的结构的研究利用多尺度阵列（密集台阵-宾川气枪台网-云南区域地震台网）嵌套组合的方式,面波基阶低频信息从0.55 Hz拓宽到0.008 Hz,使横波速度结构的反演深度显著增加,同时对反演过程提供约束,使得70 km深度以上的横波速度更收敛.由此本文所得的横波速度结构为该区地下结构的探测提供基础,多尺度阵列嵌套组合频散谱的研究方式也为以后区域结构的研究提供一种新的方法和思路.

     

Investigation of the dynamic response of rigid footings on tensionless Winkler foundation

The dynamic response of a rigid footing resting on an elastic tensionless Winkler foundation is examined. A parametric investigation, concerning the effect of the main parameters on the response, is performed for harmonic excitation. The parameters examined include the stiffness and the damping of the foundation, the excitation frequency and the superstructure characteristics and loads. The maximum rocking response, the minimum length of contact after uplift, the maximum stress developed at the soil and the factor of safety with respect to the bearing capacity of the soil are used to measure the effect of each dimensionless parameter. An example for earthquake excitation is also given for a plane frame. The results are compared to the ones of a simplified static approach based on the maximum values of the applied loads, similarly to the procedure that is usually applied in practice. The results show that the static approach can predict the response satisfactorily if resonance does not happen, if the stiffness of the foundation is not large compared to the stiffness of the superstructure and if the dynamic part of the axial force of the column is not large; in these cases, it may underestimate or overestimate the response significantly, depending on the sign of the dynamic axial force that is considered.     

Analysis of wave propagation in a plate resting on a Winkler foundation with a sample application to vibration control

A variational statement in the field of complex numbers and its semi-analytical solution are presented to study the wave propagation in plates resting on a Winkler foundation. The method and its computer program are verified by comparison with the available results for a freely supported plate and performing a time domain analysis for a plate-Winkler foundation system. A variety of wave propagation phenomena is observed, and useful information can be extracted from the results. The foundation is found to act as a low frequency band-stop filter for flexural modes, and a stiffer foundation leads to wider widths of these stop bands. As a sample application, a barrier design for controlling flexural motions in the system is proposed. The effectiveness of the design is also demonstrated.     

A model of creep deformation in the lithosphere as a non-isothermal linear viscous circular plate on a Winkler foundation

The lithosphere is known to deform under geologic loads such as those due to surface volcanoes and submerged magma chambers. The lithosphere is modelled here as a linear viscous circular plate supported on the underlying asthenosphere, which in turn is modelled as a Winkler foundation. A two-dimensional steady creep relation is used to derive the governing partial differential equations for deflection, stress and bending moment. The temperature variation through the thickness of the lithosphere is of major importance and is included in the analysis. Solutions to the governing equations are obtained both in general and for an illustrative set of geometric, loading, material and thermal parameters.     

Exact dynamic member stiffnesses for a beam on an elastic foundation

This paper gives exact Bernoulli–Euler dynamic flexural member equations for a uniform beam on an elastic foundation. These enable exact results to be obtained when the beam is included in free or sinusoidally forced vibration calculations for a plane or space frame, at any frequency. In addition, information is presented to ensure that no natural frequencies are missed in a free vibration analysis.     

基础梁与上部结构的相互作用计算

考虑了基础与上部结构的相互作用，根据两部分接触面上位移协调和力的平衡条件，求出了基础梁的内力，据此内力即可进行基础设计。