圆柱结构中的环向SH波及洞体内表面波不存在性讨论

SH waves in cylindrical structures and discussion on the nonexistence of circumferential SH surface wave in cylindrical cavities

目前有关圆柱结构中的环向SH波研究仅限于实心柱体与圆柱壳体结构。由于无法直接获得圆柱洞体中传播的SH表面波的解析解,对比研究了实心柱体和多种不同类型的圆柱壳体中的环向SH波,从波结构、应变能密度幅值分布与壳体厚度的关系讨论洞体内SH表面波的存在性。建立柱坐标系下均匀弹性材料与功能梯度材料环向SH波的波动方程;分别求得方程的贝塞尔函数解和幂级数渐近解;进一步计算得到其频散曲线、波结构与应变能密度幅值。结果表明:幂级数方法可用于计算圆柱型结构中的变系数波动方程,且具有较高的精度;圆柱型结构中环向SH波的能量集中在外表面或次外表面,并随着壳体厚度的增加,能量集中现象更为明显;通过应变能密度幅值分布规律推论出圆柱洞体内表面无法传播环向SH表面波。最后,针对均质结构和梯度结构,采用反证法证明了无法得到满足洞体内SH表面波衰减条件的解析解,从而证明了该推论。

Considering that research of circumferential horizontal shear wave(SH wave)has been published on the solid cylinders and cylindrical shell structures,aiming to discuss the existence of SH surface waves on the cylindrical cavity.Since it is impossible to directly obtain the analytical solution of SH surface wave propagating in cylindrical cavity,we compare the tendency of wave structures,strain energy density varying along thickness of SH waves on the surface of cylinders and various cylindrical shells.The governing equation of SH wave of homogeneous elastic material and functionally graded material in cylindrical coordinate system is established.The Bessel functions solution and the power series asymptotic solution of the governing equations of homogeneous elastic materials and functionally graded materials are obtained,respectively.Furthermore,the dispersion curves,the wave structures and the strain energy density are calculated.The results show that the power series method can be employed for solving wave governing equations with variable coefficients with high accuracy,the energy of circumferential SH waves in cylindrical structures is concentrated on the outer surface or subsurface,and the phenomenon of energy concentration is more obvious along thickness.It can be deduced from the distribution of strain energy density that the circumferential SH surface wave cannot propagate in the cylindrical cavity.Finally,for homogeneous material structure and functionally graded material structure,the inverse method is used to prove that any analytical solution cannot satisfy the attenuation condition of SH surface wave in the cavity.