平稳/非平稳激励下中厚圆柱壳随机振动响应的基准解

BENCHMARK SOLUTIONS OF RANDOM VIBRATION RESPONSES FOR MODERATELY THICK CYLINDRICAL SHELLS UNDER STATIONARY/NONSTATIONARY EXCITATIONS

圆柱壳结构被广泛应用于航空航天、船舶、汽车工程等领域.由于服役环境复杂,圆柱壳会受到随机激励作用,从而产生随机振动响应.本文针对考虑横向剪切变形和转动惯量的中厚圆柱壳,将虚拟激励法拓展到连续体结构,高效获得了各类随机激励下响应均方根的基准解.首先,开展了简支条件下中厚圆柱壳的自由振动分析,精确求得各阶自振频率和解析振型函数.其次,根据随机激励形式,利用虚拟激励法和振型叠加技术,构造虚拟激励,将解析精确频率和振型函数引入随机振动分析,导出平稳、非平稳激励作用下中厚圆柱壳的随机振动响应功率谱密度函数解析解,并积分得到响应均方根.解析求解涉及空间域、频域和时间域的积分运算,利用解析积分可获得精确封闭解,但其难度和效率随参振频率的增加而显著增加.为充分发挥虚拟激励法在矩阵运算中的显著优势,将空间域积分解析求解,频域和时域数值求解,进而提出了离散解析法高效获得封闭和开口的中厚圆柱壳随机振动响应.该过程保证了空间上的精确性,高效获得壳内随机振动响应的分布,结果可作为基准解验证其他数值方法.通过与ABAQUS软件、蒙特卡洛模拟结果及文献结果比较,展示了离散解析法的高精度和高效性.最后,阐明了圆柱壳厚径比、载荷形式、非平稳性特性等因素对随机振动响应的显著影响.

Cylindrical shell structures are frequently adopted in aerospace,ship,automobile and other engineering fields.Due to the complexity of service environments,cylindrical shells are unavoidably subjected to various random excitations,resulting in stochastic dynamic responses.Considering the moderately thick cylindrical shells with transverse shear deformation and moment of inertia effect,the pseudo excitation method is extended to the continuum structure,and the exact benchmark solutions of root mean squares of responses under various random excitations are efficiently obtained.Firstly,the exactly analytical natural frequencies and modal functions of moderately thick cylindrical shells with shear diaphragm boundary conditions are given.Then,according to the random excitation form,by using pseudo excitation method and mode superposition technique,the analytical and exact frequencies and modal functions and the constructed pseudo excitation are introduced into random vibration analysis.The power spectral density functions of stochastic responses of moderately thick cylindrical shells under stationary and nonstationary excitations are derived analytically,and the corresponding root mean squares are achieved via integration.The integral computation involves integration operations in the spatial,frequency and time domains.Analytical integration can obtain the closed-form exact solutions,while the difficulty and efficiency increase with increasing number of participated modes.To take full advantage of the merit of matrix operation of PEM,the discrete analytical method(DAM),with analytical spatial integral as well as numerical integral in the frequency and time domains,is proposed to obtain the exact stochastic responses of moderately thick cylindrical shells in closed and open forms.This procedure can ensure the accuracy of spatial integral,and efficiently obtain the exact distribution of random response,which provides the benchmark solutions for other numerical methods.Comparing the results with those of ABAQUS software and Monte Carlo simulation with as well as related literature illustrates the high accuracy and efficiency of the proposed DAM.Finally,the significant effects of ratio of thickness to radius,load distribution form,and time-modulated function on stochastic dynamic responses of cylindrical shell are revealed.