密度梯度柱壳链的弹性波传播特性研究

均匀圆柱壳链可以调控弹性波传播,引入密度梯度有望进一步提高波形调控能力.通过建立密度梯度柱壳链的细观有限元模型和连续介质模型,研究了密度梯度柱壳链的弹性波传播特性.通过将密度梯度柱壳链等效为变密度连续介质弹性杆,建立了其在应力脉冲作用下的控制方程.运用拉普拉斯积分变换方法,考虑杆中密度遵循线性分布,获得了方程的解析解.以三角形应力脉冲作用为例,通过与细观有限元模拟结果比较,发现解析解可以较好地预测梯度柱壳链中载荷的演化趋势.正梯度链中载荷峰值随着波传播逐渐增大,负梯度链中载荷峰值随着波传播逐渐减小.正梯度链支撑端峰值载荷高于均匀链,负梯度链支撑端峰值载荷低于均匀链,这表明相较于均匀柱壳链,密度梯度柱壳链可以在更大范围内对波形进行调控.线性密度梯度参数对梯度柱壳链的波形调控能力影响较大,梯度参数越小,传递到支撑端的峰值载荷越小;相反,梯度参数越大,支撑端的峰值载荷越大.建立的理论模型及其解析解为研究梯度柱壳链中应力波传播规律及揭示载荷调控机理提供了理论基础.

ELASTIC WAVE PROPAGATION CHARACTERISTICS OF DENSITY GRADIENT CYLINDRICAL SHELL CHAINS

Uniform cylindrical shell chains can control elastic wave transmission, and introducing density gradient may further improve the ability of waveform control. The propagation behavior of elastic waves in the density gradient cylindrical shell chains was studied by developing a mesoscale finite element model and a continuum-based model. By equivalent the density gradient cylindrical shell chain to a variable density elastic rod, the governing equation of the density gradient chains under a stress pulse excitation was established. Based on the Laplace integral transformation and considering the linear density distribution in the rod, the analytical solution of the equation was obtained. Compared with the meso-finite element simulation results, it is found that the analytical solution can well predict the force evolution trend of the graded cylindrical shell chain under the excitation of a triangular stress pulse. The results show that the peak force in the positive gradient chain gradually increases with the wave propagation, while that of the negative gradient chain gradually decreases with the wave propagation. The peak force at the support end of the negative gradient chain is smaller than that of the uniform chain, while that of the positive gradient chain is greater than that of the uniform one. So the waveform control ability of the density gradient cylindrical shell chains is better than the uniform chain. The linear density gradient parameter has great influence on the waveform control ability of the density gradient cylindrical shell chains. The peak force transmitted to the support end increases with the increase of the density gradient parameter, and thus the density gradient cylindrical shell chain can control the stress pulse in a wider range. The theoretical model and its analytical solution provide a theoretical basis for studying the stress wave propagation law and revealing the force regulation mechanism of the graded cylindrical shell chains.