Natural frequencies of shear deformable porous orthotropic laminated doubly-curved shallow shells with non-uniformly distributed porosity using higher-order shear deformation theory

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Thin-Walled Structures Pub Date : 2025-01-27 DOI:10.1016/j.tws.2025.112951

Ferruh Turan , Ertugrul Zeren , Muhammed Karadeniz , Vu Ngoc Viet Hoang

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Abstract

Porous materials, characterized by a network of voids, offer unique functional properties such as reduced density, high stiffness-to-weight and strength-to-weight ratios, and resistance to mechanical and thermal shocks. Despite their advantages, there is a lack of study on the free vibration behavior of porous laminated doubly-curved shallow shells. This study investigates the natural frequencies of porous orthotropic laminated doubly-curved shallow shells with different porosity distribution patterns. Porosity-dependent material properties are graded in the thickness direction using special cosine and sine functions. The equations of motion are established using Hamilton’s principle based on the higher-order shear deformation theory and solved by Galerkin’s method and an auxiliary function of simply supported boundary conditions to achieve natural frequency formulation. The formulation is confirmed by comparing the results with those in the existing literature, and an excellent agreement is observed. A parametric study is employed to analyze the effect of porosity coefficients, porosity distribution patterns, orthotropy, lamination sequences and orientations, shallow shell types, and geometrical characteristics on the natural frequencies of porous orthotropic laminated doubly-curved shallow shells. The results reveal that porosity distribution significantly influences dynamic behavior. Uniform porosity distribution (UDP) exhibits consistent effects across parameters, while non-uniform distributions (NUDP1, NUDP2, NUDP3) induce complex, often wavy variation, particularly in hyperbolic paraboloidal shells (HPS). Spherical shells (SS) consistently show higher natural fundamental frequencies (N-FNFs) compared to HPS, with this difference becoming more pronounced with increasing aspect ratios and diminishing orthotropy ratios. Unexpectedly, single-layered configurations in HPS sometimes exhibit higher N-FNFs than multi-layered ones, a contrast to the behavior observed in SS. Orientation angles also play a critical role, with certain ranges leading to wavy variations in N-FNFs, particularly under non-uniform porosity distributions. These findings highlight the intricate interplay between porosity, lamination, geometry, and orthotropy, offering valuable insights for optimizing porous material design in advanced engineering structures.

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利用高阶剪切变形理论研究具有非均匀分布孔隙率的剪切变形多孔正交层叠双曲浅壳的固有频率

多孔材料以空隙网络为特征，具有独特的功能特性，如密度小、刚度-重量比和强度-重量比高、抗机械冲击和热冲击。尽管多孔材料具有这些优点，但目前还缺乏对多孔层叠双曲浅壳自由振动行为的研究。本研究探讨了具有不同孔隙率分布模式的多孔正交层叠双曲浅壳的固有频率。使用特殊余弦函数和正弦函数对厚度方向上与孔隙率相关的材料特性进行分级。在高阶剪切变形理论的基础上，利用汉密尔顿原理建立了运动方程，并通过伽勒金方法和简单支撑边界条件的辅助函数进行求解，从而实现了固有频率公式。通过与现有文献中的结果进行比较，证实了该公式的正确性，并观察到了极佳的一致性。采用参数研究分析了多孔系数、多孔分布模式、正交性、层叠序列和方向、浅壳类型和几何特征对多孔正交层叠双曲浅壳固有频率的影响。结果表明，孔隙率分布对动态行为有显著影响。均匀孔隙率分布（UDP）对各参数的影响是一致的，而非均匀分布（NUDP1、NUDP2、NUDP3）会引起复杂的、通常是波浪形的变化，特别是在双曲抛物面壳（HPS）中。与 HPS 相比，球壳（SS）的固有基频（N-FNFs）一直较高，随着高宽比的增加和正交比的减小，这种差异变得更加明显。出乎意料的是，HPS 中的单层结构有时比多层结构显示出更高的 N-FNF，这与 SS 中观察到的行为形成了鲜明对比。定向角也起着至关重要的作用，某些范围的定向角会导致 N-FNF 呈波浪形变化，特别是在孔隙率分布不均匀的情况下。这些发现凸显了孔隙率、层压、几何形状和各向同性之间错综复杂的相互作用，为优化先进工程结构中的多孔材料设计提供了宝贵的见解。

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来源期刊

Thin-Walled Structures 工程技术-工程：土木

CiteScore

9.60

自引率

20.30%

发文量

801

审稿时长

66 days

期刊介绍： Thin-walled structures comprises an important and growing proportion of engineering construction with areas of application becoming increasingly diverse, ranging from aircraft, bridges, ships and oil rigs to storage vessels, industrial buildings and warehouses. Many factors, including cost and weight economy, new materials and processes and the growth of powerful methods of analysis have contributed to this growth, and led to the need for a journal which concentrates specifically on structures in which problems arise due to the thinness of the walls. This field includes cold– formed sections, plate and shell structures, reinforced plastics structures and aluminium structures, and is of importance in many branches of engineering. The primary criterion for consideration of papers in Thin–Walled Structures is that they must be concerned with thin–walled structures or the basic problems inherent in thin–walled structures. Provided this criterion is satisfied no restriction is placed on the type of construction, material or field of application. Papers on theory, experiment, design, etc., are published and it is expected that many papers will contain aspects of all three.