CAJ | 학술논문

利用黏弹性材料本构关系的 Laplace 变换与弹性材料的形式相似性，得到了分数阶 Kelvin 黏弹性模型弹性模量和泊松比的 Laplace 变换解。将固体推进剂药柱视为黏弹性介质，并利用分数阶 Kelvin 本构模型来描述其应力‐应变关系。在推进剂药柱应力弹性解的基础上，运用弹性‐黏弹性对应原理得到了分数阶 Kelvin黏弹性模型描述的推进剂药柱在均布内压作用下内力的拉氏解，通过 Laplace 逆变换求得了其时域解。研究结果表明：推进剂药柱径向应力总是压应力，而环向应力总是拉应力，分数阶 Kelvin 黏弹性模型的解可以退化到经典 Kelvin 黏弹性模型的解，分数导数的阶数越大，应力的绝对值越大。
이용점탄성재료본구관계적 Laplace 변환여탄성재료적형식상사성，득도료분수계 Kelvin 점탄성모형탄성모량화박송비적 Laplace 변환해。장고체추진제약주시위점탄성개질，병이용분수계 Kelvin 본구모형래묘술기응력‐응변관계。재추진제약주응력탄성해적기출상，운용탄성‐점탄성대응원리득도료분수계 Kelvin점탄성모형묘술적추진제약주재균포내압작용하내력적랍씨해，통과 Laplace 역변환구득료기시역해。연구결과표명：추진제약주경향응력총시압응력，이배향응력총시랍응력，분수계 Kelvin 점탄성모형적해가이퇴화도경전 Kelvin 점탄성모형적해，분수도수적계수월대，응력적절대치월대。
Using the similarity between the transformation of viscoelastic materials constitutive relation and elastic materials ,the Laplace transform solutions of elastic modulus and Poisson’s ratio of fractional Kelvin vis‐coelastic model were obtained .The solid propellant grain was regarded as viscoelastic medium ,and the stress‐strain relationship of solid propellant grain was described by the fractional derivative Kelvin constitutive model . The Laplace solutions of the stress of solid propellant grain described by fractional derivative viscoelastic model under uniform internal pressure were obtained by using the elastic‐viscoelastic correspondence principle based on the elastic solution of stress ,and the solutions in time domain were also got by the inverse Laplace transform . The results indicated that the radial stress is always compressive stress and the circumferential stress is always pulling stress ,and the solution of fractional derivative Kelvin viscoelastic model can be degenerated to the solu‐tion of classic Kelvin viscoelastic ,and the absolute value of stress will be greater if the order of fractional deriva‐tive is greater .