This study focuses on the thermal post-buckling behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) quadrilateral plates, with particular emphasis on the thermal stability characteristics of four geometric configurations: rectangular plates (RP), right-angled trapezoidal plates (RTP), isosceles trapezoidal plates (ITP), and arbitrary quadrilateral plates (AQP). Employing micromechanical methods to characterize temperature-dependent nanocomposite properties, the research derives the governing equations based on first-order shear deformation theory and the minimum total potential energy principle. The generalized differential quadrature method (GDQM) is utilized to solve for thermal buckling loads, while Newton-Raphson iterative schemes combined with mapping techniques enable the standardization of irregular computational domains. Through method validation and parametric studies, the systematic influence of model parameters on the thermal buckling characteristics of FG-CNTRC quadrilateral plates is elucidated. The findings indicate that the RP exhibit the best thermal stability, with the highest critical temperature and smallest deflection, while the AQP perform the worst due to their irregular geometry. In addition, it can be observed that when no initial geometric imperfection exists, the relationship between temperature and deflection takes the form of a bifurcation curve, meaning that deflection occurs only when the temperature change reaches a critical value. In contrast, when an initial geometric imperfection is present, deflection appears as soon as a temperature change is applied.

This paper focuses on sandwich panels with stepped functionally graded material (FGM) layers and initial geometric imperfections, exploring their nonlinear transient behavior when placed on viscoelastic bases and subjected to sinusoidal forces. The three-layer composition involves a uniform core, with upper and lower FGM face sheets exhibiting a stepped thickness profile. The face sheets are divided into two segments of distinct thicknesses along both the length and width directions, achieving optimal stiffness enhancement while maintaining a constant total thickness. The FGM face sheets exhibit thickness-dependent material properties following a power-law distribution. Utilizing the third-order shear deformation theory (TSDT) and incorporating initial geometric imperfections along with von Kármán geometric nonlinearity, a theoretical model was developed. The governing equations are solved via the Galerkin and Runge–Kutta methods, with model accuracy validated against existing literature and finite element analysis results. In the numerical analysis, four different geometric configurations of the sandwich plates are selected to examine the influence of key parameters, including initial geometric imperfections, aspect ratio, thickness ratio, damping coefficient, load amplitude, load duration, and power-law index, on the transient response of the sandwich plates. The findings of this study provide a theoretical basis for the dynamic design and optimization of stepped FGM sandwich structures with initial geometric imperfections.

In engineering applications, annular plates with non-uniform thickness profiles are widely used in various scenarios owing to their characteristics of reducing weight, optimizing material distribution, and maintaining sufficient stiffness and strength. However, the mechanical response of such structures is inherently more complex than that of uniformly thick plates due to the variation in geometric shape. Meanwhile, this complexity is further compounded by the unclear mechanisms governing how bidirectional functionally graded materials (2D-FGMs) and local geometric imperfections affect low-velocity impact responses in rotating variable-thickness annular plates. The present study investigates these nonlinear impact characteristics through a novel analytical framework. By synergistically combining the first-order shear deformation theory (FSDT) with the improved nonlinear Hertz contact theory, the nonlinear governing equations of the plate are derived. The degradation model is validated to ensure the correctness of the proposed model. Finally, numerical analysis is conducted using the Runge-Kutta method to investigate the effects of different parameters, such as material gradient index, thickness coefficient, impact location, and local imperfections, on the nonlinear low-velocity impact response characteristics of the annular plates.

This paper takes functionally graded carbon nanotube reinforced composite (FG-CNTRC) sandwich cylindrical-conical coupled shells as research objects, and establishes a dynamic model based on first-order shear deformation theory (FSDT), von Kármán nonlinear strain theory and Isogeometric analysis (IGA). A numerical solution framework combining modal coordinate reduction and explicit time integration is proposed: low-order orthogonal modal bases are extracted to transform high-dimensional nonlinear motion equations into low-dimensional modal space equations, significantly reducing computational complexity. Meanwhile, p-order refinement, h-mesh refinement and k-continuity refinement (p/h/k-refinement), three typical refinement schemes in IGA, are adopted to clarify the convergence conditions for calculating structural vibration characteristics and verify the reliability of the method. The influences of carbon nanotube volume fraction, distribution patterns and structural geometric parameters on vibration response are systematically investigated. This work, for the first time, combines IGA with efficient model order reduction techniques, effectively addressing the high computational cost caused by large matrix bandwidth under the IGA framework in the nonlinear dynamic response analysis of complex FG-CNTRC coupled shells. The proposed approach features superior computational efficiency and accuracy, and reveals the regulation mechanism of key material and geometric parameters on structural dynamic performance. The present study provides an efficient theoretical tool and scientific basis for the vibration-resistant optimization design of FG-CNTRC cylindrical-conical coupled shell structures.

This research analyzes nonlinear dynamics in straight-edged quadrilateral graphene platelet-reinforced metal foam (GPLRMF) plates of arbitrary shape, focusing on the unique case of 1:3 internal resonance. The equivalent mechanical properties of GPLRMF composite materials were evaluated using the mixture rule and Halpin-Tsai model. Based on the first-order shear deformation theory (FSDT) and von Karman geometric nonlinearity assumption, the lateral vibration control equation for quadrilateral plates was derived through Hamilton's principle, accounting for in-plane displacement, rotational inertia, and shear deformation effects. The generalized differential quadrature method (GDQM) was used to discretize the control equations and boundary conditions in space, followed by the numerical Galerkin method to transform them into Duffing-type nonlinear equations. Subsequently, the modulation equations for 1:3 internal resonance in polar and Cartesian coordinate systems were established using the multiscale method. By employing the Runge-Kutta algorithm and nonlinear equation solver, the study traced the nonlinear dynamic solutions and steady-state equilibrium solutions, and constructed the bifurcation characteristic diagram accordingly. Finally, the influence mechanisms of the damping coefficient, external excitation amplitude, detuning parameters, and material parameters on the 1:3 internal resonance nonlinear dynamic behavior were analyzed. The results demonstrate that systematically varying the vertex angles (beta L, beta R) of a quadrilateral plate adjusts structural asymmetry and stiffness, thereby shifting resonance peaks and expanding the multi-valued solution region. Furthermore, an optimal frequency detuning parameter enhances inter-modal energy transfer efficiency.

Under the trend of high-speed lightweight design for aero-engines, turbine fan blades face dynamic instability risks in complex aerothermal-rotational coupled environments. While annular sector plates optimize aerodynamic adaptability and centrifugal stress distribution via curvature effects, traditional homogeneous and composite materials struggle to meet the demands of matching the 3D stress field. Furthermore, existing research often neglects the coupling effects between variable thickness and multidimensional functionally graded materials (MDFGM), and lacks systematic analysis of blade dynamic responses under transonic flow fields. ‌This paper establishes a coupled aero-thermal-elastic model for annular sector plates with variable thickness made of MDFGM. Based on the First-order Shear Deformation Theory (FSDT), the rotational-thermal field coupled governing equations are derived by combining artificial spring boundary conditions with Hamilton’s principle. The Generalized Differential Quadrature Method (GDQM) is employed to efficiently discretize the spatially varying gradient coefficients, coupled with the Runge–Kutta method to solve ‌forced vibration amplitude-frequency response under subsonic unsteady aerodynamics and transient flutter limit cycle oscillation (LCO) and chaotic evolution in supersonic flow fields. ‌The study reveals the synergistic control mechanisms of gradient parameters and elucidates the influence laws of variable thickness, material gradation, and multi-physics coupling on structural stability. It fills the research gap concerning the dynamic characteristics analysis of MDFGM blades under complex operating conditions, providing theoretical foundations for the design of high-reliability engine blades.

This paper introduces a novel analytical model to investigate the nonlinear supersonic flutter characteristics of auxetic metamaterial plates exhibiting a negative Poisson's ratio (NPR). The plate consists of multiple layers through its thickness, each made from a copper (Cu) matrix reinforced with a specific weight fraction of Graphene Origami Auxetic metamaterial (GOAM). Three patterns of graphene origami (GO) distribution are considered. Utilizing classical plate theory with von-K & aacute;rm & aacute;n nonlinear strains and linear supersonic piston theory, the nonlinear governing equations of motion are presented. Bernstein polynomials are employed to formulate mode shapes that satisfy the boundary conditions within the spatial domain. Then, Galerkin approximation is used to transform the nonlinear partial differential equations of motion to nonlinear time-dependent ordinary differential equations. The Runge-Kutta method is employed to attain the nonlinear dynamic post-flutter behaviors of GOAM plate. Furthermore, linear flutter characteristics are obtained through eigenvalue analysis. To validate the accuracy of the proposed approach, comparisons are conducted with results available in published literature, demonstrating excellent agreement. The impacts of material parameters, GO distribution patterns, and boundary conditions on flutter behaviors of plate are examined. This model offers applicability in analyzing solid-fluid interaction studies relevant to aerospace, ocean engineering, and mechanical systems.

This study investigates the nonlinear dynamic response of rotating cylindrical shells made of axially-functionally-graded graphene-platelet reinforced metal-foam (AFG-GPLRMF) under low-velocity impact in thermal conditions. Three distinct distribution patterns of graphene platelets (GPLs) are examined, including both uniform and functionally graded distributions through the shell's thickness. Material properties of the GPL-reinforced composites are determined using a temperature-sensitive micromechanical model. The governing equations are formulated based on nonlinear Donnell's shell theory, incorporating von K & aacute;rm & aacute;n geometric nonlinearity. Through numerical simulations employing the Runge-Kutta method, parametric studies are conducted to evaluate the effects of various factors including: initial geometric defects, rotational speed, boundary constraints, GPL dispersion patterns, foam distribution characteristics, porosity parameter, GPL concentration, thermal variation, impactor dimensions and velocity, applied axial loads, and damping properties on the impact response characteristics.

This paper investigates the nonlinear low-velocity impact response of an axially moving functionally graded (FG) conical shell. The nonlinear equations of motion are derived based on Reddy's shell theory and von K & aacute;rm & aacute;n geometric nonlinearity. With simply supported boundary conditions, the time histories of deformation and contact force are solved numerically by combining the fourth-order Runge-Kutta method with the Galerkin technique, and the impact force is determined using the modified Hertzian contact model and Newton's second law. A key finding regarding the optimal volume fraction is that an intermediate ceramic content minimizes the central deflection under low-velocity impact, indicating a trade-off between stiffness and energy absorption. Additional numerical results reveal several key findings: (1) Increasing the prestress reduces the maximum central deflection while having negligible effect on the peak contact force, indicating an enhanced energy dissipation capability. (2) A larger damping coefficient accelerates the return to equilibrium after impact but only slightly decreases the maximum deflection. (3) Raising either the impactor radius or its initial velocity increases the peak deflection and contact force; however, a larger radius prolongs the contact time, whereas a higher initial velocity shortens it. (4) The axial motion speed of the conical shell affects the deflection more significantly than the contact force, suggesting that contact stiffness remains nearly unchanged. (5) The semi-vertex angle of the conical shell has a weak influence on the impact response. (6) Increasing porosity or the functionally graded index (i.e., reducing ceramic content) reduces structural to contact

Aero-thermo-elastic stability is essential for composite thin-walled structures in high-temperature service environments. Nevertheless, the nonlinear aero-thermo-elastic coupling mechanism of perforated arbitrary triangular plates remains insufficiently clarified, especially regarding how the inner hole size modulates the dynamic stability. In this work, taking the graphene platelet reinforced composite (GPLRC) as an example, and based on Isogeometric analysis (IGA) combined with the von Kármán large deflection nonlinear theory, an efficient numerical framework is established. The modal reduction method improves calculation efficiency, and numerical verification validates the accuracy and reliability of the proposed IGA model. The effects of vertex angle, perforation size and ambient temperature are systematically investigated. A key finding is that increasing the perforation size delays the onset of flutter instability and improves the critical flutter pressure, despite the reduction in initial structural stiffness, namely a result of the altered modal coupling due to local flexibility near the hole. The thermal post-buckling deflection and limit cycle oscillation (LCO) are further analyzed. Results demonstrate that perforation size shows a counterintuitive stabilizing effect: larger holes lead to higher flutter margins. Reasonable geometric designs further improve aeroelastic stability, while high temperature causes elastic modulus degradation and induces thermal buckling. As aerodynamic pressure rises, the structure undergoes three typical evolution stages: thermal post-buckling stabilization, aerodynamic suppression of thermal deformation, and LCO. This study clarifies the parametric influence laws of GPLRC arbitrarily perforated triangular plates under aero-thermo-elastic coupling, providing a theoretical reference for the dynamic design of high-temperature aerospace composite structures, with particular emphasis on the beneficial role of perforations in flutter suppression.

Suppressing panel flutter has emerged as a significant challenge in the field of supersonic aircraft development. With the continuous increase in aircraft speed requirements and the extensive application of composite materials, the flutter phenomenon has become increasingly complex, sometimes even leading to catastrophic consequences. In light of this, the present work innovatively proposes the utilization of nonlinear energy sinks with nonlinear damping (ND-NES) to suppress the nonlinear aeroelastic responses of graphene platelets reinforced (GPLRC) foams plate. Compared to traditional NES, the damping introduced in this study exhibits geometric nonlinearity characteristic, significantly broadening the effective working frequency band of NES. Based on the principle of energy, a nonlinear aero-thermo-elastic model for the ND-NES and plate is constructed. Subsequently, the reduced-order model obtained through the Rayleigh-Ritz method is solved using the Runge-Kutta method. Comparing the bifurcation diagrams of plate responses, it is demonstrated that the ND-NES exhibits excellent flutter suppression performance, with a maximum amplitude reduction rate of 99.05%. The targeted energy transfer (TET) mechanism between the ND-NES and plate is analyzed from the perspectives of frequency-domain and energy. The results indicate that nonlinear damping effectively improves flutter suppression performance by enhancing the nonlinear coupling between ND-NES and plate and reducing their triggering energy threshold. Furthermore, this study delves into the influence of ND-NES parameters, temperature fluctuations, and material properties of plate on the efficacy of flutter suppression.

Currently, there exists a lack of dynamical studies on magneto-electro-elastic (MEE) cylindrical shells under moving load. Given this context, this article delves into such a problem. First, utilizing the classical theory and Maxwell's equation, the nonlinear motion equations are formulated. Subsequently, the Runge-Kutta technique is adopted to determine the dynamic deflection. Finally, the influences of various factors on nonlinear dynamic response of MEE cylindrical shells subjected to moving load are discussed. It can be found that decreasing the BaTiO3 content can enhance the structural stability. Contrary to the electric potential, increasing the magnetic potential will effectively reduce the dynamic deflection.

In this study, the 1:1 nonlinear internal resonance of graphene reinforced metal foam (GPLRMF) plate with initial geometric imperfection under non-uniform temperature field was investigated for the first time. A dynamic model of GPLRMF plate was constructed based on the first-order shear deformation theory and Galerkin principle considering geometric nonlinearity and thermal effects. The modulation equations for the first two modes of coupled vibration were obtained using a multiscale method, and the equations were solved using the RungeKutta method and a nonlinear solver. The amplitude-frequency response curve, amplitude-force response curve, limit cycle evolution diagram, bifurcation diagram, time history diagram, and phase diagram of the system were analyzed. The study examined the effects of temperature gradients, initial geometric imperfections, and external excitations on the nonlinear dynamic characteristics of GPLRMF plate under 1:1 internal resonance. The results indicate that thermal effects induced by specific temperatures can induce 1:1 internal resonance in GPLRMF plate, and temperature and geometric imperfection have significant effects on the spring characteristics of the system. Within a certain range, smaller detuning parameters can facilitate better energy transfer between the first two modes.

The nonlinear transient response of rotating beams with crack damage is a critical research topic in aerospace engineering. Since existing studies on rotating beams neglect crack effects, this study aims to fill this gap. By accounting for crack-rotation coupling, a rotational spring model is employed to simulate crack damage in rotating beams. The dynamic model of the cracked rotating beam is developed using first-order shear deformation theory and geometric nonlinearity, with governing equations derived via Hamilton's principle. Using the assumed mode method, a novel modal function is proposed to obtain approximate analytical solutions for the nonlinear equations under diverse boundary conditions. Numerical results are generated via the fourth-order Runge-Kutta method. The effects of crack parameters, rotational speed, boundary conditions, impulse load characteristics, damping/elastic coefficients, graphene sheet distribution (including mass fraction), and porosity parameters on the transient response are systematically analyzed. Results indicate that crack damage, rotational motion, and their coupling effects significantly suppress the nonlinear transient response of beams under blast loads.

A systematic analysis of nonlinear behavior in subaqueous graphene platelets-reinforced metal foams (GPLRMF) blades is presented, targeting 1:2 internal resonance phenomena. A dynamic model is established by integrating higher-order shear deformation theory (HSDT) with potential flow theory. The governing equations, derived via Hamilton's principle and the Galerkin method, are reduced to a set of modulation equations using the method of multiple scales. The system's response is then analyzed via frequency and force response curves, bifurcation diagrams, and stability maps. The results reveal that rotational speed is a critical parameter for activating the 1:2 internal resonance. The blade's underwater position governs system stability by controlling hydrodynamic damping. Furthermore, stability analysis based on the Routh-Hurwitz criterion indicates that the interaction of detuning parameters can induce the appearance of coexisting attractors.

This article aims to investigate the thermal and post-buckling issues of magneto electro thermal elastic plates with initial geometric defects. Firstly, the nonlinear vibration equation is derived applying first-order shear deformation plate theory and energy method, which the influence of geometrical nonlinearity and geometric defects of the structure are considered. Then, during the solution process, we take into account three different boundary conditions and employ the Galerkin method to obtain the thermal buckling loads and thermal post-buckling path. The solution results of this article are well consistent with existing literatures, thus ensuring the reliability of the research. Finally, we are focused on the effects of material properties, electric potential, magnetic potential, geometric defects, and boundary conditions on the thermal and post-buckling responses of MEE plates. The results indicate that when there is initial geometric imperfection (W1 not equal 0) in the MEE plates, as long as the temperature changes, the MEE plates will undergo bending deformation. As the voltage ascends or the magnetic potential descends, the thermal buckling loading and the thermal post-buckling strength will decline accordingly.

Recent years have witnessed the boosting of the aerospace, automotive, and new energy industry, which leads to a growing demand of various professional equipment, especially rotating machinery. Annular plate with variable thickness (APVT), due to its lightweight and high-strength characteristics, can significantly reduce equipment weight while ensuring structural strength. Therefore, the rotating machinery manufacturing industry has also generated a huge demand for high-performance APVT. However, research on the nonlinear dynamic analysis of APVT with spinning motion is extremely limited. This article studies the nonlinear dynamic characteristics of APVT with initial geometric imperfection for the first time, in which the physical model of the plate using twodirectional functionally graded material (2D-FGM) whose material properties follow a power-law distribution along the axial and radial axes is constructed. To ensure the rationality and accuracy of the current results, the degradation model is verified. In the end, the numerical analysis is performed to explore the effects of different parameters such as thickness coefficient, gradient index, spinning speed, and imperfection on the nonlinear dynamic characteristics of the plate.

Resonance-induced failures pose critical challenges to engineering structures. However, existing literature lacks research on the resonance characteristics of graphene platelet-reinforced metal foam (GPLRMF) coupled plates. To address this gap, this paper investigates the resonance characteristics of GPLRMF coupled plates under arbitrary boundary and coupling configurations. Based on the simplified first-order shear deformation theory (S-FSDT), the governing equations of the GPLRMF coupled plate are derived through Hamilton’s principle. To simulate diverse boundary and coupling conditions, a virtual spring technique is introduced for modeling flexibility. Subsequently, the natural frequencies of the coupled plate and its transverse displacement under external excitation are determined using the method of reverberation-ray matrix (MRRM), which efficiently handles wave propagation in complex structures. Numerical calculations are performed for four distinct plates through systematic variations of material parameters, boundary conditions, and coupling configurations. The results reveal that alterations in the material properties, boundary constraints, and coupling configurations exert significant and nonlinear influences on the vibration response of the coupled plates.

At present, the dynamics research of beams is mostly limited to free vibration and forced vibration, and the research on nonlinear transient response is little, and no one has studied the nonlinear transient response of beams with initial geometric imperfection under pulse loads. Based on this fact, the transient response characteristics of graphene platelet reinforced metal foams (GPLRMF) beams with initial geometric defects are discussed for the first time in this paper. Firstly, three kinds of graphene platelet (GPL) distribution patterns and foam metal porosity distribution patterns were considered, and the material properties were calculated by means of micromechanical models and mixture diffusion rules, and then, considering initial geometric defects, a dynamic model was established based on Euler-Bernoulli beam theory and von-K & aacute;rm & aacute;n nonlinear theory. Then, based on the Hamilton principle, the motion equation of the GPLRMF beam is derived. Finally, the corresponding transient response curve is obtained using the fourth-order Runge-Kutta method. In the study, the convergence of the model is verified to ensure the rationality and accuracy of the analysis results. In addition, a detailed study is conducted, including the distribution patterns and coefficients of porosity, the dispersion and weight fraction of GPLs, pulse load parameters, initial geometric imperfections and damping coefficient.

Shallow arches lose stability under transverse loading if the load surpasses a critical threshold, leading to a sudden and significant deformation as they transition to a new stable configuration. This snap-through buckling behavior can be beneficial in certain applications, such as toggle switches or detrimental in others. Consequently, understanding the factors that influence snap-through behavior is essential for designing structures that perform reliably under such conditions. Therefore, this study aims to investigate the large amplitude response and post-buckling stability of shallow thick arches whose material properties can vary along thickness and length according to three different patterns. Further, the material can be porous through the arch thickness according to three different porosity distribution types. Based on the Reddy's higher-order shear deformation theory and the von K & aacute;rm & aacute;n type of geometric nonlinearity, the porous BFGM shallow arch resting on nonlinear Pasternak foundation is modeled as a set of nonlinear governing partial differential equations. By using the numerical differential quadrature method (DQM) and Newton's method, the governing equations are solved. An incremental approach is proposed to obtain the load-deflection curves. Several comparison and parametric studies are presented to validate the model and solution methodology and to demonstrate the potential of porous BFGM shallow arches in optimizing structural behavior. Results show that several factors influence and control the snap-through characteristics of porous BFGM arches including arch geometry, material composition, porosity, and elastic foundations. The initial shape and curvature of the arch play a crucial role. Arches with a higher rise-to-span ratio and thin arches are more susceptible to snap-through. This model may introduce new opportunities for managing this instability, enabling the development of structures with customized instability characteristics.