## 1 Introduction  
Laminated cylindrical shell structures find extensive applications in the aviation, aerospace, maritime, and nuclear industries, and beyond, owing to their lightweight, simple structure, and remarkable mechanical properties. However, the operational life of equipment has suffered significantly due to the amplified effects of internal vibrations and various types of noise on system reliability, stability, and concealment [1]. Therefore, in recent years, research into the acoustic and vibration performance of laminated cylindrical shells and vibration reduction and noise mitigation techniques has become increasingly prominent. Micro-perforated structures have become extensively used in many noise reduction fields owing to their numerous advantages, such as being lightweight, easy to construct, environmentally friendly, cost-effective, and corrosion-resistant. These applications include indoor sound field adjustment [2; 3], muffler design [4; 5], sound barriers [6; 7], acoustic windows [8], and more. [PERSON] et al. [9; 10] suggest that when subjected to external plane waves or external turbulent boundary layer pressure excitation, the micro-perforation theory of the inner shell can theoretically enhance the mid-frequency sound insulation performance of double-walled cylindrical shells. However, in both of these cases, addinga lining in the annular space of the double-walled cylindrical shell does not improve the structural sound insulation performance. Subsequently, [PERSON] [11] integrated the Biot theory [12] and an earlier proposed model to create a novel theoretical model for investigating sound propagation in micro-perforated double-walled cylindrical shells under the stimulation of incident plane waves. [PERSON] suggested that the utilization of lining porous material to perforate the inner shell of a sandwich structure could improve sound transmission loss below the ring frequency. Improving the low-frequency sound insulation performance of this structure could be attained by increasing the imaginary part of the impedance constant, pore size, or perforation ratio. Nevertheless, the research had a somewhat restricted range of choices regarding porous materials. In practical engineering design, sound-absorbing or sound insulation materials are often utilized to reduce or isolate noise transmission through a structure [13]. A significant amount of related research has been conducted by scholars both domestically and internationally. [PERSON] et al. [14] investigated the acoustic transmission performance of double-layer cylindrical shells with interior porous elastic materials based on the Biot model. The research indicated that high-flow-resistance, low-density foam exhibits superior sound insulation properties. However, it is important to note that the study only took into account excitation from external turbulent boundary layers and not other possible sources of excitation. [PERSON] et al. [15], based on statistical energy analysis theory, conducted a study on the propagation patterns of sound in thin-walled cylindrical shells from both theoretical and experimental perspectives. The results showed that the use of sound-absorbing materials effectively reduced noise levels inside the cylinder but was less effective at lower frequencies. [PERSON] et al. [16], based on the first-order shear deformation theory, combined circumferential and axial modal analyses to explore the vibroacoustic performance of finite-length cylindrical shells containing porous materials. The outcomes demonstrated that a longer porous elastic shell efficiently decreases sound transmission within the high-frequency range. Meanwhile, low-frequency sound insulation improves as the radius of the shell decreases. However, this study yielded less favorable results at low frequencies. [PERSON] et al. [17] used the extended boundary element method to establish an analytical model for analyzing the vibroacoustic performance of corrugated-core sandwich cylindrical shells filled with porous materials.