## 1 Introduction  
In the last few decades, due to their high potential in terms of mechanical and thermal properties such as tensile and yield strength, Carbon Nanotubes (CNTs) have attracted the interest of many scientists and researchers trying to find convenient applications for these types of nanostructure [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. The application of CNTs has mainly been as a reinforcement constituent of composite materials, which are, nowadays, widely used, especially in the aerospace field and in the automotive industry [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. This has led to the birth of a new class of composites called nanocomposites. In spite of the numerous works that have been written on this subject, CNTs still remain an open topic for discussion. The curiosity with regard to the effects of CNT reinforcement on various structures has led to the development of different techniques and approaches for estimating these effects as well as possible, optimized between the goals of simplicity and accuracy [27]. The theory of mixtures, due to its simplicity, is the most common approach used to describe the mechanical properties of these types of nanostructure [30; 31]. Despite its simplicity, this approach neglects several aspects of the micromechanics of CNT particles, which, due to their characteristic shape, tend to agglomerate in different areas of the reinforced polymer composite. A more precise approach has been proposed in the work by [PERSON] et al. [32], presenting a two-parameter theoretical model that closely describes the agglomeration effect of the CNT particles, whereby the homogenization,based on the Eshelby-Mori-Tanaka scheme for granular composite materials [33], and mechanical properties are obtained. This scheme uses the so-called Hill's elastic moduli [34; 35] to describe the constitutive relations of the CNT particles. For the sake of completeness, some examples concerning the agglomeration of CNTs can be found in the papers [36; 37; 38]. The present paper aims to use this approach to study the effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite plates and shells resting on the elastic foundation. Although the high structural performance of plates and shells made from conventional composites has been proved by a number of papers [39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56], by employing CNTs as a reinforcing phase, their performance can be improved even further. A gradual variation of the volume fraction of the CNT particles trough the thickness of the composite has been employed, which is characteristic to functionally graded materials (FCMs). FCMs are a recent class of composite materials designed to deal with problems of stress concentration and mechanical discontinuity [57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83; 84]. Therefore, the term Functionally Graded Carbon Nanotubes (FG-CNTs) was introduced to refer on this type of CNT-reinforced composite. For the sake of completeness, it should be mentioned that several papers concerning structural models suitable for the mechanical analysis of these kinds of structure have been published recently [85; 86; 87; 88; 89; 90; 91; 92; 93]. In particular, the gradient elasticity theory was proposed by [PERSON] et al. [85] to this end. Alternatively, a nonlocal model can be used for this purpose, as proved in the papers by [PERSON] and [PERSON] [86], [PERSON] et al. [87], [PERSON] and [PERSON] [88], and [PERSON] et al. [89]. To capture the proper mechanical behavior of these structures, adequate structural models must be considered. The use of classical shell theories may result in inaccurate results; therefore, the use of Higher-order Shear Deformation Theories (HSDTs) is required. Recent developments in the area of HSDTs are found in the works by [PERSON] [94; 95; 96; 97; 98], introducing the so-called Carrera Unified Formulation (CUF).