In this work,we are concerned with the Timoshenko-Fourier system in both equal and non-equal wave speeds,which admits a non-symmetric dissipation.Furthermore,the dissipative mechanism of regularity-loss type will occu...In this work,we are concerned with the Timoshenko-Fourier system in both equal and non-equal wave speeds,which admits a non-symmetric dissipation.Furthermore,the dissipative mechanism of regularity-loss type will occur in the case of non-equal wave speeds.We establish the global-in-time existence of solutions to the Timoshenko-Fourier system in critical Besov spaces with the regularity s=3/2.展开更多
根据傅里叶变换推导具有两个广义位移的铁木辛柯梁固有振动的基本解.利用加权残量方法,从控制微分方程出发建立边界积分方程,进而根据边界条件得到频率方程,采用代数特征值方法和影响系数方法求解频率,并分析了两种方法的特点.以杆为例...根据傅里叶变换推导具有两个广义位移的铁木辛柯梁固有振动的基本解.利用加权残量方法,从控制微分方程出发建立边界积分方程,进而根据边界条件得到频率方程,采用代数特征值方法和影响系数方法求解频率,并分析了两种方法的特点.以杆为例证明了对于一维均匀结构,对不同的边界条件利用边界元方法 (BEM,Boundary Element Meth-od)都可以得到精确频率.将铁木辛柯梁的BEM结果与有限元结果和精确解进行了比较.展开更多
Based on the Timoshenko beam theory and Bernoulli-Fourier method, a single-elastic beam model is developed for transverse vibrations of single-walled carbon nanotubes under additional axial load, which includes the ef...Based on the Timoshenko beam theory and Bernoulli-Fourier method, a single-elastic beam model is developed for transverse vibrations of single-walled carbon nanotubes under additional axial load, which includes the effects of the elastic medium around them. Explicit expressions are derived for the natural frequencies and transversal responses of simply supported single-walled carbon nanotubes. The influence of addition axial load and the properties of elastic medium on the vibrations are discussed. The results showed that the effects of addition axial load on the lower natural frequencies of single-walled carbon nanotubes are sensitive to the lower vibration modes and the stiff elastic medium. The lower natural frequencies depend on the axial load;they become smaller with increasing axial load and vary with the vibration modes. In addition, except for the first mode, the effects of the axial load on the stiff elastic medium are considerably greater than those on the flexible one. However, the constants of the elastic medium have little effect on the first mode. The critical axial buckling stress and strain for simply-supported single-walled carbon nanotubes are also obtained.展开更多
基金supported by the National Natural Science Foundation of China(No.12001269)the Fundamental Research Funds for the Central Universities of China.
文摘In this work,we are concerned with the Timoshenko-Fourier system in both equal and non-equal wave speeds,which admits a non-symmetric dissipation.Furthermore,the dissipative mechanism of regularity-loss type will occur in the case of non-equal wave speeds.We establish the global-in-time existence of solutions to the Timoshenko-Fourier system in critical Besov spaces with the regularity s=3/2.
文摘根据傅里叶变换推导具有两个广义位移的铁木辛柯梁固有振动的基本解.利用加权残量方法,从控制微分方程出发建立边界积分方程,进而根据边界条件得到频率方程,采用代数特征值方法和影响系数方法求解频率,并分析了两种方法的特点.以杆为例证明了对于一维均匀结构,对不同的边界条件利用边界元方法 (BEM,Boundary Element Meth-od)都可以得到精确频率.将铁木辛柯梁的BEM结果与有限元结果和精确解进行了比较.
文摘Based on the Timoshenko beam theory and Bernoulli-Fourier method, a single-elastic beam model is developed for transverse vibrations of single-walled carbon nanotubes under additional axial load, which includes the effects of the elastic medium around them. Explicit expressions are derived for the natural frequencies and transversal responses of simply supported single-walled carbon nanotubes. The influence of addition axial load and the properties of elastic medium on the vibrations are discussed. The results showed that the effects of addition axial load on the lower natural frequencies of single-walled carbon nanotubes are sensitive to the lower vibration modes and the stiff elastic medium. The lower natural frequencies depend on the axial load;they become smaller with increasing axial load and vary with the vibration modes. In addition, except for the first mode, the effects of the axial load on the stiff elastic medium are considerably greater than those on the flexible one. However, the constants of the elastic medium have little effect on the first mode. The critical axial buckling stress and strain for simply-supported single-walled carbon nanotubes are also obtained.
