Hamilton's Principle Research Articles

Dynamic behaviors of general composite beams using mixed finite elements

A novel mixed finite element method is developed and implemented for analyzing the vibration and buckling behavior of general composite beams which consists both transversely layered and axially jointed materials. The governing state-space equations are derived using the Hamilton's principle, where both displacements and stresses are treated as fundamental variables. This semi-analytical method uses transfer relations in the transverse direction and finite element meshing in the longitudinal direction, overcoming the difficulties for general composite beams analysis and providing computational efficiency and analyzing flexibilities. The developed mixed finite element model ensures continuity of both displacements and stresses across the material interface, thereby resolving interfacial stress singularity issues and offering more reliable simulations of boundary conditions at both ends. The proposed method is formulated and validated for the free vibration and buckling analysis of general composite beams. Additionally, it is observed that material properties such as Young's modulus and density, as well as the stiffness of the interface connecting layers, have significant effects on the free vibration and buckling responses of the composite beams. Analysis of periodically distributed and bi-directional composite beams demonstrates the versatility of this method in handling two types of combination forms. The proposed method serves as a valuable reference for obtaining accurate vibration and buckling results while ensuring stress-compatibility for composite beams in practical applications.

Free Vibration of the Magneto-Electro-Elastic Plates Resting on Elastic Foundation Using the Refined Plate Theory with Two Variables

The objective of this article is to investigate the free vibration analyses of the functionally graded magneto-electro-elastic (FG MEE) plates supported by an elastic foundation using the refined plate theory (RPT) with two variables. The elastic foundation is modeled utilizing the Winkler-Pasternak theory. The power-law model is employed to characterize the graded material properties of the FG MEE plates. According to the RPT and Hamilton's principle, the governing equations of the FG MEE plate are derived. The displacement fields and electric and magnetic potentials are approximated using the Non-Uniform Rational B-Splines (NURBS) basic functions of the isogeometric approach (IGA). The proposed model’s advantages and accuracy are demonstrated by comparing the obtained results with those reported in the existing literature. The study comprehensively examines and discusses the impact of several parameters, including the power index, initial external magnetic potential and electric voltage, and the geometry, on the vibration frequency of the FG MEE plates. The numerical findings indicate that an increase in the power index leads to a decrease in the frequency of the FG MEE plates. Besides, the stiffness of FG MEE plates decreases with an increase in the initial external electric voltage, whereas it increases with an increase in the initial external magnetic potential. This article presents valuable perspectives on examining vibration analysis of the FG MEE plates, which can inform the design of innovative materials and structures with customized properties.

Nonlinear Vibrations of the Piezoelectric-Laminated Composite Cantilever Rectangular Plate Subjected to the Transverse and Parametric Excitation

The intelligent structure will be the key to the industrial manufacturing field in the future, piezoelectric materials are the most commonly used active materials in many mechatronic and vibration control systems. In this paper, we illustrated the nonlinear vibration behaviors of the piezoelectric-laminated composite cantilever rectangular plate subjected to transverse and parametric excitation. Two piezoelectric layers are attached to the upper and lower surfaces of graphite/epoxy composite laminated plate. The nonlinear dynamic equations are derived via the classical laminated plate theory, von Karman large deformation theory, the constitutive equation of the piezoelectric materials, and the Hamilton principle. Considering the Galerkin method, the nonlinear ordinary differential equations for the two-order vibration mode of the piezoelectric laminated composite cantilever rectangular plate are achieved. The multiple scale method is applied to obtain the average equations to study the nonlinear vibration characteristic of the stable motion. The primary resonance and the 1:1 internal resonance of the piezoelectric laminated composite cantilever rectangular plate are investigated. The amplitude-frequency response curves, force-amplitude response curves, time histories, phase curves, and bifurcation diagrams are given to investigate the nonlinear dynamic characteristic of the piezoelectric laminated composite cantilever rectangular plate. The detailed parametric analyses show that bubble response curves are separated from the amplitude-frequency response curves with the continuous increase of the external excitation due to the internal resonance. In addition, the results reveal the energy transform between the various order vibration modes of the system. This work is expected to provide theoretical guidance for the nonlinear vibration of the smart piezoelectric laminated composite structure.

Nonlinear thermo-electro-mechanical responses and active control of functionally graded piezoelectric plates subjected to strong electric fields

Functionally graded piezoelectric plates (FGPPs) are often exposed to extreme thermal environments and subjected to large amplitude excitation and strong electric fields. Accurately predicting the nonlinear behaviors of FGPPs under large thermo-electro-mechanical loads remains a considerable challenge. This paper proposes a comprehensive nonlinear coupled analysis model that considers geometric nonlinearity, piezoelectric nonlinearity, and the temperature dependence of piezoelectric parameters. The total Lagrangian incremental finite element equations for FGPPs under thermo-electro-mechanical loads are derived using Hamilton's principle, by employing the first-order shear deformation theory and the von Kármán nonlinear strain-displacement relationship. The accuracy of the model is validated through comparative studies. Based on this multi-nonlinear model, we further investigate the effects of geometric nonlinearity, piezoelectric nonlinearity, and temperature dependence on the nonlinear static bending, dynamic responses, and active control of FGPPs. This study demonstrates that considering these factors enables accurate prediction of the static, dynamic, and active control behaviors of FGPPs.

Soundbox-based sound insulation measurement of composite panels with viscoelastic damping

Sound transmission loss (STL), an essential index for assessing the sound insulation performance of composite laminated structures, typically relies on experimental methods to measure. The soundbox method (SBM), a straightforward technique for measuring the STL, is sensitive to microphones’ positions. Within the framework of the Chebyshev-Ritz method, a semi-analytical vibro-acoustic model extended to composite laminated panels with viscoelastic damping (VED) is proposed for the first time. Based on the developed simplified layer-wise theory, the panel is modeled using three layers: the top face layer, the VED layer, and the bottom face layer. A closed cavity is added to the model as the soundbox enclosure used in actual measurements. By employing the Hamilton's principle, the governing equation for the coupling system is derived, and the vibration and internal acoustic responses of the coupling system are calculated. A discretization strategy is introduced to address the frequency-dependent properties of the VED layer, avoiding the need to reconstruct the stiffness matrix at each frequency. To obtain the STL of the panel, sound pressures at external measurement points are calculated based on the Rayleigh integral. The proposed model is validated against numerical results from finite element analyses. The influences of the microphone position inside and outside the cavity on the measured STL are studied. Furthermore, parametric studies over the microphones' positions are performed to enhance the SBM-based evaluation of the composite panel's sound insulation performance. The optimal locations for two internal microphones and one external microphone are recommended. Finally, experimental studies are carried out to guide the implementation of the SBM.

Nonlinear dynamic analysis and vibration reduction of two sandwich beams connected by a joint with clearance

The dynamics and vibration reduction characteristics of the clamped–clamped two sandwich beams jointed with clearance is studied theoretically and experimentally. A transverse and torsional spring system with clearance is used to equivalent the joint model. The homogenization method is used to equivalent the core layer and Rayleigh-Ritz method is utilized to derive the mode function of the interconnected sandwich beam by using a sequence of orthogonal polynomials. The nonlinear motion equation of the two jointed sandwich beam structure with clearance is derived by the application of the Hamilton principle and then solved using an improved Newmark integration approach. In order to validate the accuracy of the natural frequency and vibration mode, the finite element model is established. This paper examines the impact of clearance on the amplitude frequency response and vibration transmission of the two jointed sandwich beam structure, it is found the jointed sandwich beams show obvious nonlinear characteristics and intermittent vibration transmission phenomenon due to the clearance. Moreover, the vibration transmission analysis reveals that the existed clearance demonstrates significant vibration reduction effect, for which an experiment is conducted to validate the results. In general, this work proposes a novel approach for modeling sandwich structures with clearance with improved vibration reduction performance.

A Magneto-Electric Device for Fluid Pipelines with Vibration Damping and Vibration Energy Harvesting.

This study introduces an innovative energy harvesting system designed for industrial applications such as fluid pipelines, air conditioning ducts, sewer systems, and subsea oil pipelines. The system integrates magneto-electric flow coupling and utilizes a dynamic vibration absorber (DVA) to mitigate the vibrations induced by fluid flow while simultaneously harvesting energy through magnetic dipole-dipole interactions in a vibration energy harvester (VEH). The theoretical models, based on Hamilton's Principle and the Biot-Savart Law, were validated through comprehensive experiments. The results indicate the superior performance of the small-magnet system over the large-magnet system in both damping and power generation. The study analyzed the frequency response and energy conversion efficiency across different parameters, including the DVA mass, spring constant, and placement location. The experimental findings demonstrated significant vibration reduction and increased voltage output, validating the theoretical model. This research offers new avenues for energy harvesting systems in pipeline infrastructures, potentially enhancing energy efficiency and structural integrity.

Thermal postbuckling and thermally induced postbuckled flutter of tri-directional functionally graded plates in yawed supersonic flow

The current work examines the thermal postbuckling, aero-elastic flutter and thermally induced postbuckled flutter about a static equilibrium state of tri-directional functionally graded (TFGM) rectangular and tapered plates in yawed supersonic flow. Based on the von Kármán nonlinear strains, the general higher-order shear deformation theory (GHSDT) and the first-order piston theory, the governing equations of motion for TFGM plates in yawed supersonic flow are established via the Hamilton's principle. The isogemetric analysis (IGA), the load continue strategy associated with the Newton Raphson iterative technique are exploited synthetically to capture the postbuckling paths, and then the postbuckled flutter behaviors are acquired with the static equilibrium state being obtained. Comparative and convergence studies are provided to improve reliabilities of the present material model, formulae and code implementations. Subsequently, detailed parametric investigations are carried out to evaluate the influences of material volume fractions, boundary conditions and airflow angles on the thermal postbuckling, aero-elastic flutter and postbuckled flutter behaviors of TFGM plates. The results show that it is the in-plane volume fractions, rather than the thickness volume fraction, that exert a greater influence on the thermal postbuckling and flutter behaviors of TFGM plates. Furthermore, TFGM plates exhibit more diverse postbuckling paths and more complex deformations due to the inhomogeneity of the in-plane material properties compared with z-directional FGM plates.

Bending of bidirectional functionally graded nonlocal stress-driven beam

This paper provides a comprehensive analysis, using nonlocal stress-driven integral theory, of the static behavior of a nanoscale beam of bidirectionally graded materials. After a brief explanation of the mathematical formulation of BDFGMs, the work done and strain energy expressions derived from the displacement field are discussed. Variational formulations and Hamilton's principle are used to develop the equilibrium equation. An analytical development of the nonlocal kernel for stress-driven integral theory and formulated governing equation which was nondimensionalized later. Explicit equations for displacement and moment are obtained by solving this equation using the Laplace transformation. Three different boundary conditions are examined, and differences in the maximum displacement with respect to the nonlocal parameter and the two material FGM parameters are displayed both visually and in table form. The results exhibit excellent agreement and provide a standard for further research when they are closely compared to the existing numerical data. This work contributes to the knowledge of BDFGMs under nonlocal effects generated by stress-driven integral theory and offers solutions that have been confirmed for further investigation.

Random thermal-vibration mechanisms of sandwich ventral fin-type plate-shell systems with porous functionally graded core

The stochastic thermal-vibration mechanisms within a sandwich ventral fin-type plate-shell system, featuring a porous functionally graded (FG) core, are exhaustively analyzed under various random loading conditions employing an innovative node-based, meshless computational approach. The studied structure is decoupled into several plates and open cylindrical panel according to the geometric characteristics, and the mechanical relationships at the structural boundaries or connection interfaces are equivalently simulated by using penalty parameters. Following the general Hamilton's principle, the meshless approach combined with the first-order shear deformation theory (FSDT) incorporating thermal effects is employed to derive the vibration equations of the sandwich ventral fin-type plate-shell systems. Also, the pseudo excitation method (PEM) is introduced to calculate stationary and nonstationary random responses. In order to verify the accuracy of the meshless algorithm in this study, the convergence and correctness are studied comprehensively. And then, the effects of some parameters such as temperature variation, porosity parameters, power-law index and random excitations on the thermal vibration characteristics of the sandwich ventral fin-type plate-shell systems with porous FG core are presented. The results show that the power-law index and temperature can increase the frequency parameter of the structure. The smooth power spectral density (PSD) excitation only affects the amplitude of the response curve, and does not affect the frequency corresponding to the peak. In the analysis of non-stationary random vibration, the influence of modulation parameters on response is very significant.

Thermomechanical buckling and vibration of composite sandwich doubly curved shells with carbon nanotube‐reinforced face layers

AbstractIn this paper, the thermomechanical buckling and vibration analysis are investigated for carbon nanotube‐reinforced composite sandwich doubly curved shells (CNCSDS) under the action of both thermal loads and in‐plane compressive loads. Based on the von‐Karman non‐linear kinematic relations, First Order Shear Theory, and Hamilton's principle, the vibration and stability equations for CNCSDS under thermomechanical loads are deduced. For obtaining the critical thermomechanical buckling load and vibration frequency, an exact method is adopted. Subsequently, the results are validated by comparing with the finding in published literature and simulation results. At last, the influence of system parameters on critical thermomechanical buckling load and vibration frequency is studied and displayed graphically. Meanwhile, some new results about thermomechanical buckling and vibration analysis of CNCSDS are proposed for the first time.Highlights Thermomechanical buckling and vibration of carbon nanotube‐reinforced composite sandwich doubly curved shells was studied. Vibration and stability equations under thermomechanical loads was deduced. The change rules of thermomechanical buckling load and frequency were obtained.

Symmetric and asymmetric vibration and buckling of a thermal rotating annular-plate with Pasternak foundation

This paper studies the symmetric and asymmetric vibration and buckling modes of a rotating thermal annular plate resting on a Pasternak foundation. With considering the von Kármán geometric nonlinearity and the first-order shear deformation theory, the governing equations of the system are established via Hamilton's principle, and then solved by using the differential quadrature method. With both inner and outer boundaries constrained, the modes of the rotating system vary differently depending on the mode symmetry. The symmetric modes are mainly affected by the generated centrifugal force, while the asymmetric ones are affected by both centrifugal and Coriolis forces. The additional Coriolis, with mainly two directions, strengthens the forward travelling parts of the asymmetric modes, but makes the backward counterparts buckled more easily. Also, the thermal effect, as well as boundary elasticity and foundation coefficients, are also investigated from the viewpoint of mode symmetry. Results show that the temperature rise can shift the fundamental vibration mode from the symmetric one to the asymmetric one and backward travelling waves for rotation, which also adds to the complexity of mode variation with joint parameters. For the joint effect of the temperature rise and rotating, the annular plate tends to buckle more readily while the effects of the two factors are linearly superimposed.

Finite element approach for free vibration and transient response of bi-directional functionally graded sandwich porous skew-plates with variable thickness subjected to blast load

At the first time, the finite element method was used to model and analyze the free vibration and transient response of non-uniform thickness bi-directional functionally graded sandwich porous (BFGSP) skew plates. The whole BFGSP skew-plates is placed on a variable visco-elastic foundation (VEF) in the hygro-thermal environment and subjected to the blast load. The BFGSP skew-plate thickness is permitted to vary non-linearly over both the length and width of the skew-plate, thereby faithfully representing the real behavior of the structure itself. The analysis is based on a four-node planar quadrilateral element with eight degrees of freedom per node, which is approximated using Lagrange Q4 shape function and C1 level non-conforming Hermite shape function based on refined higher-order shear deformation plate theory. The forced vibration parameters of the non-uniform thickness BFGSP skew-plate are fully determined using Hamilton's principle and the Newmark-β direct integration technique. Accuracy of the calculation program is validated by comparing its numerical results with those from reputable sources. Furthermore, a thorough assessment is conducted to determine the impact of various parameters on the free and forced vibration responses of the non-uniform thickness BFGSP skew-plate. The findings of the paper may be used in the development of civil and military structures in situations that are prone to exceptional forces, such as explosions and impacts load.

Chebyshev–Ritz and Navier's methods for hygro‐magneto vibration of Euler–Bernoulli nanobeam resting on Winkler–Pasternak elastic foundation

AbstractThis research employs Chebyshev–Ritz method along with Navier's method to investigate the vibration characteristics of a nanobeam subject to a longitudinal magnetic field and linear hygroscopic environment. The nanobeam is characterized by a Winkler–Pasternak elastic foundation and follows the nonlocal Euler–Bernoulli beam theory. The governing equation of motion is derived using Hamilton's principle, and non‐dimensional frequency parameters are computed for Simply Supported‐Simply Supported (SS), Clamped‐Clamped (CC), and Clamped‐Free (CF) boundary conditions. The motivation behind this study is to provide a comprehensive and efficient analytical framework for understanding the dynamic behavior of nanobeams in complex environments. By investigating the influence of magnetic and hygroscopic factors on the vibration characteristics of nanobeams, this research aims to offer valuable insights for the design and optimization of nanoscale structures. Employing shifted Chebyshev polynomials as shape functions in Chebyshev–Ritz method offers several advantages in the proposed model. Firstly, these polynomials possess orthogonal properties, which can significantly enhance computational efficiency. The orthogonality of shifted Chebyshev polynomials allow for simpler and more streamlined numerical computations compared to non‐orthogonal basis functions. Additionally, the orthogonality ensures that the resulting system of equations is well‐conditioned, even for higher‐order polynomial approximations. A closed‐form solution for SS boundary condition is obtained through Navier's method. Convergence analysis is performed to validate the accuracy and effectiveness of the proposed model against existing models. The non‐dimensional frequency parameters obtained using both Navier's method and Chebyshev–Ritz method demonstrate strong agreement, further validating the proposed nanobeam model. Additionally, a comprehensive parametric study evaluates the impact of various characteristics, including the small‐scale parameter, Winkler modulus, shear modulus, magnetic parameter, and hygroscopic parameter. The findings contribute to a nuanced understanding of nanobeam vibrations under the influence of a magnetic field and hygroscopic environment, providing valuable insights for the design and optimization of nanoscale structures in practical applications.

End jitter suppression using FONFTSMC for rigid-flexible coupling systems of PMSpM based on NDO

A permanent magnet spherical motor (PMSpM) with three degrees of freedom rotation characteristics in the rigid rotor has broad application prospects. But the adding flexible material will inevitably produce end jitter issue in the process of the rigid-flexible coupling system (RFCs) movement. To solve the above problem, a fractional order non-singular fast terminal sliding mode control method with a disturbance observer was proposed for the rigid-flexible coupling system of a permanent magnet spherical motor (RFCs-PMSpM). Firstly, a dynamic model of RFCs-PMSpM was established by using the Hamilton principle and Euler–Bernoulli beam theory. Secondly, the influences on the end jitter were discussed from the perspectives of load mass, material parameters, and driving torque of the flexible shaft. The sensitivity analysis is carried out, and the key factors affecting the jitter are obtained. Then, a fractional order non-singular fast terminal sliding mode controller based on a nonlinear disturbance observer (NDO-FONFTSMC) is proposed. The stability of the closed-loop control system was proved by the Lyapunov method. Finally, the effectiveness of the proposed jitter suppression strategy was validated and compared with existing approaches, which also provides an important reference for the future application of RFCs-PMSpM in high-precision industry.

Flutter in functionally graded conical shell under follower force

Truncated conical shells are essential components of rocket booster nozzles and thrust vector control (TVC) systems for the propulsion of multi-stage launch vehicles. The TVCs assist the ascent of launch vehicles by directing the resultant thrust from the boosters, acting as a follower force that might trigger instability. Previous studies on the instability of aerospace structures have mostly focused on beams, plates, and cylindrical shells. This study analyses a truncated conical shell under a follower force of constant magnitude, considering thickness-wise gradation of material properties employed for thermal management. The governing equations are derived following Hamilton's principle, considering first-order shear deformation theory, and solved using the finite element method. Clamped and free boundaries are assumed at the small and large ends. The influence of mass and stiffness proportional damping is considered. Although strong flutter appears as the dominant instability mode, instances of erratic weak instabilities are also observed for undamped and lightly damped cases. Damping enhances stability, but its effect becomes saturated. The flutter loads are presented for varying non-dimensional parameters, characterizing the shell geometry and material properties.

Numerical fatigue damage analysis and mathematical modeling of articular cartilage under cyclic load via hyperelasticity theory

The paper presents the modeling of damage to articular cartilage under cyclic daily loads using a curved beam model and hyper-elasticity theory. Mainly, articular cartilage (AC) is a kind of very important biological tissue that has the fundamental role of withstanding applied mechanical loads and providing smooth movement of joints. The existence of mechanical loads, however, has a huge influence on the behavior and the entire healthiness of AC. These loads, over time, can cause injury through fatigue-type damage because of frequent stresses. The basic aim of this study is to mainly offer a detailed mathematical model measuring the damage caused in AC under the action of mechanical forces incorporating different variants like age, body mass index, metabolic activity, functionally graded, porosity and prestresses. The structural energies including potential energy according to the neoHookean model as well as kinetic energy and external work are achieved through the use of strain-displacement and stress-strain relations. Then, the nonlinear governing equations of the articular cartilage are derived using Hamilton's principle. Furthermore, the mathematical model has been implemented numerically through the differential quadrature method (DQM). A qualitative correspondence between the numerical predictions and experimental data has led us to conclude that this model has the potential to serve as a valuable tool for physicians and therapists. The results of this research indicate that among the factors affecting the increase of damage in cartilage, the most important factor is the body mass index, followed by a person's age, hormonal conditions, and cartilage thickness with a negative effect. The probability of damage for an athlete is about 33 percent higher than a normal person, and for a weightlifter (heavy sports) it is about 140 percent higher than a normal person.

On the electromechanical bandgap of microscale vibration isolation metamaterial beams with flexoelectric effect

In this paper, a type of metamaterial isolation beam consisting a cantilever beam with flexoelectric film attached is provided. Electrodes interconnect on the surface to create parallel resonant shunt circuits, enabling band-stop filtering. The electromechanical control equations are derived using the Hamiltonian principle. A closed-form analytical expression for the bandgap range is obtained via the root locus method. Theoretical results are validated through finite element methods. Findings reveal that the operational bandgap of millimeter-scale flexoelectric metamaterial isolation beams is 5.2 times greater than that of conventional piezoelectric metamaterial beams. Furthermore, the vibration excitation amplitude is reduced by 99.9%. These results highlight the significant advantages of flexoelectric materials for microscale high-frequency passive isolation, providing superior stability in complex vibration environments. The research investigates the effects of end mass, electrode plate count, and external resistance on the vibration isolation performance of flexoelectric metamaterial beams. The study also examines the variations in relative bandgap width between flexoelectric and piezoelectric metamaterial beams concerning material, size, and structural parameters, identifying optimal values. Notable differences in bandgap characteristics are observed between flexoelectric and piezoelectric beams; for instance, while piezoelectric beams have an optimal substrate elastic modulus, flexoelectric beams do not, and the optimal film thickness for flexoelectric beams is 2.2 times that for piezoelectric beams.

Non-linear dynamics and bandgap control in magneto-rheological elastomers metamaterials with inertial amplification

Sandwich plate structures are extensively utilized in engineering due to their favorable stiffness-to-weight ratio. Nonetheless, these lightweight thin-walled structures frequently encounter challenges related to inadequate low-frequency vibration performance, which significantly restricts their applications, particularly in the realm of precision instruments which is sensitive to vibration. This study introduces an innovative design of an active nonlinear metamaterial, to achieve tunable broadband low-frequency bandgaps for sandwich plates. The nonlinear oscillator incorporates an inertia amplification mechanism (IAM), Euler-buckled beams, mass elements, and magneto-rheological elastomers (MREs), which are modulated via external magnetic fields to adjust the material's stiffness dynamically. Employing Hamilton's principles and the plate wave expansion method (PWE), the dispersion relations for the metamaterial plate are derived, elucidating the dispersion surfaces and the band structures within its sandwich-like plates.The dynamical equations of the metamaterial plate are formulated and validated through numerical simulations using the Galerkin method, confirming the theoretical predictions. The results demonstrate effective control over low-frequency and broadband bandgaps under low mass ratio conditions through strategic manipulation of the inertia amplification factor and magnetic flux. The study extensively explores the nonlinear dynamic responses of the metamaterial, highlighting the significant impact of excitation amplitudes on the amplitude-dependent bandgaps.

Frequency analysis of open/closed polygonal channel aerostructures made of hybrid nanocomposite materials and supported by piecewise elastic foundation using GDQE technique

This research delves into the theoretical exploration of the generalized differential quadrature element (GDQE) method for analyzing the dynamic response and natural frequency of aerospace structures, specifically polygonal channels found in aircraft, satellites, and space vehicle components. These structures are critical in aerospace engineering, serving in various capacities such as airframe components and fluid conveyance systems. Emphasizing the practical significance of these structures, the study incorporates the influence of ground or support conditions, employing a two-parameter piecewise elastic foundation model. The investigated open or closed channels are characterized as laminated functionally graded hybrid nanocomposites, specifically denoted as FG-HNC, reinforced with Carbon nanotubes (CNTs) and Clay nanoparticles (CNP). Each composite layer is reinforced with randomly oriented and uniformly distributed tubes and particles. The homogenization of the hybrid composite domain is performed using the hierarchy Halpin-Tsai micromechanical rule. Utilizing the GDQE technique, the channels are discretized into plate elements, and motion equations for each plate element are calculated based on first-order shear deformation theory and Hamilton's principle. The resulting equations are then solved using the standard GDQ method, with subsequent application of appropriate continuity conditions at shared element boundaries. In this comprehensive study, the research scrutinizes the effects of structure dimensions, channel sides crank angles, composite characteristics, and boundary conditions on the free vibration behavior of the polygonal channels. By offering detailed insights into the vibrational characteristics of FG-HNC structures, this study contributes to the advancement of aerospace engineering design and analysis.