In this paper, the effect of dissipative energy arising from bulk-viscosity on the collapse of a self-gravitating viscoelastic medium permeated with a nonuniform magnetic field and rotation is analyzed using the standard Jeans mechanism. A local solution of the system of nondimensional linearized perturbation equations, having variable coefficients, is obtained using the normal modes analysis method. The Jeans instability criteria are derived from the characteristic equation (valid under the kinetic and hydrodynamic limits) for parallel and perpendicular wave propagation, modified due to bulk viscosity and Alfvén wave velocity. From the calculated critical values of Jeans wavenumber, it is found that the bulk-viscosity and magnetic field have stabilizing influence on the onset of gravitational instability for each mode of wave propagation. It is observed that the nonuniform rotation does not affect the instability criterion, however, the rotation strongly suppresses the growth rate of the Jeans instability in both the hydrodynamic and kinetic limits. Also, a comparison of the impact of various rotational and magnetic field orientations on the growth rate in viscoelastic fluid is also presented. From the analysis, it is also observed that the presence of dissipative energy reduces the growth rate, in both modes of wave propagation.

本文利用标准 Jeans 机制分析了体粘性产生的耗散能对充满非均匀磁场和旋转的自重力粘弹性介质塌陷的影响。使用简正模态分析方法获得了具有变系数的无量纲线性化扰动方程组的局部解。Jeans 不稳定性准则源自平行和垂直波传播的特征方程（在动力学和流体动力学限制下有效），并根据体积粘度和阿尔文波速进行了修改。从计算的 Jeans 波数临界值发现，体粘度和磁场对每种波传播模式的引力不稳定的开始都有稳定的影响。据观察，不均匀旋转不会影响不稳定性准则，但是，旋转强烈抑制了流体动力学和动力学极限中 Jeans 不稳定性的增长率。此外，还比较了不同旋转和磁场方向对粘弹性流体中生长速率的影响。从分析中还可以看出，在两种波传播模式中，耗散能的存在都会降低增长率。