Nonlinear vibrations and control of FG-GRC curved plates with a NES inspired by low-altitude aircraft wings

A review of nonlinear dynamics and vibration in lightweight composite structures: Recent advances and challenges

Nonlinear vibration behavior of a hinged-hinged flexible beam with fractional damping and DTD feedback control

Nonlinear active vibration control of variable-thickness smart sandwich panel under impact loads

Attention-based hybrid convolutional-recurrent network for nonlinear thermally-induced vibration responses

Nonlinear vibration of thickness-tapered laminated rectangular plates undergoing moderately large deflections in hygrothermal environment

Dynamic snap-through and nonlinear vibrations of bistable composite laminated shells

Theoretical and experimental research on nonlinear vibrations of different functionally graded twisted bilayer graphene-reinforced aluminum composite double curved shells

Free vibrations of axially moving beam-like nanostructures have been investigated in recent years; however, vibrations of moving nanochassis traveling over a surface with arbitrarily small irregularities have not been displayed yet due to some complexities in modeling. To address this challenge, a nonlinear, nonlocal surface energy-based composite beam-like model is established to fairly accurately capture the nanochassis' vibrations. The nanocar consists of a composite-like nanochassis and the ends' wheels, where the nanochassis is modeled by an appropriate beam model and the wheels are simulated as rigid solid elements that are attached to the beam's ends. Both differential- and integral-based formulations are presented, and their nonlinear stiffness, as well as the procedure for capturing the nonlocal elastic field, is carefully explained using the assumed mode approach. For several particular cases, the predicted results by the suggested models are verified with those of several analytical solutions, and reasonably good agreements are achieved. Beyond the aforementioned comparison studies, the possible instabilities of the nanochassis that travels over a straight route were also identified and explained under a small deformation regime. Through conducting a fairly comprehensive parametric study, the roles of amplitude and frequencies of the harmonic route, axial velocity, length, diameter, nonlocality, surface energy, and geometrical nonlinearity on maximum deformations and internal forces are examined comprehensively. This study could be considered as basic scrutiny for the nonlinear analysis of more complex traveling nanostructures over arbitrarily shaped surfaces.

The present study aims to examine the large-amplitude free vibration of functionally graded material (FGM) sandwich plates including the combined influences of porosity, geometric imperfection, elevated temperature, flexible constraints of edges, and elastic foundations. The properties of constituent materials are temperature-dependent and effective properties of porous FGM are evaluated taking up a modified version of linear rule of mixture. Two sandwich models constructed from FGM and homogeneous layers are considered, and pores are evenly distributed in materials. Motion and compatibility equations in terms of deflection and stress function are derived on the basis of first order shear deformation theory incorporating initial geometric imperfection and von Kármán nonlinearity. The derived equations are solved by using analytical solutions along with Galerkin procedure to obtain a time nonlinear ordinary differential equation. This differential equation is resolved by means of the fourth-order Runge–Kutta numerical integration to seek the frequencies of nonlinear free vibration of sandwich plates. A parametric study is executed to analyze different effects of porosity volume fraction, imperfection, tangential restraints of boundary edges, elastic foundations, and elevated temperature on the natural frequencies and frequency ratio-amplitude response. It is revealed that tangential edge constraints dramatically affect the linear and nonlinear frequencies, especially at high temperatures. Additionally, the support of elastic foundations increases the natural frequencies of the plates, but also weakens the frequency nonlinearity.

This research presents an analytical investigation into the nonlinear vibrational behavior of graphene nanoplatelet-reinforced polymer (GPL-R) plates subjected to external excitation. The novelty of the proposed methodology lies in establishing a direct test-to-dynamics framework in which tensile-test-derived Mooney-Rivlin constants are embedded into the forced nonlinear vibration formulation of GPL-reinforced polymer plates, rather than treating the nanocomposite as an equivalent linear elastic or purely homogenized material. To develop a more realistic constitutive model for the nanocomposite plate, this study integrates experimentally derived hyperelastic parameters of GPL-epoxy nanocomposites into a nonlinear plate vibration model governed by a Mooney-Rivlin strain-energy formulation. Following the derivation of the nonlinear governing equations of motion via Hamilton's principle, Galerkin's method is applied to discretize the system. The effective mechanical properties of the nanocomposite are obtained through experimental tensile testing performed on specimens containing varying concentrations of graphene nanoplatelets. Subsequently, the discretized equations are solved numerically to characterize the nonlinear dynamic behavior of the system. To this end, the influence of key parameters on various nonlinear phenomena is assessed using time-history responses, phase-plane portraits, Poincaré maps, and frequency-response curves. The experimentally calibrated analytical-numerical methodology avoids arbitrary hyperelastic-parameter assumptions and enables direct transfer of the measured GPL-dependent nonlinear material behavior into the vibration model. The results demonstrate that increasing the GPL content up to 1.0 wt% increases the resonant frequency by 57.9% and reduces the maximum vibration amplitude by 50% compared with pure epoxy. Furthermore, the formulation captures a softening-to-hardening transition governed by the competition between Mooney-Rivlin material nonlinearity and von Kármán membrane stretching. Accounting for hyperelastic material behavior is shown to be crucial for accurately predicting the dynamic response, particularly at larger amplitudes, where linear elastic models overestimate deflections.

Nonlinear acoustic propagation plays a crucial role in many practical applications, such as medical therapy and underwater communications. However, the nonlinear propagation behavior of multi-frequency acoustic waves radiated from nonlinear vibrating structures remains insufficiently understood. This study develops a coupled structural-acoustic model to numerically investigate the nonlinear acoustic radiation and propagation from a hyperelastic structure undergoing nonlinear vibration. Both geometric and material nonlinearities are incorporated into the finite element model of the structure, while nonlinear acoustic propagation in the surrounding fluid is solved using a high-order finite-difference time-domain scheme. The fluid-structure coupling is achieved through an improved immersed boundary method, which ensures the implicit satisfaction of compatibility conditions at the interface. Based on this framework, the nonlinear transient acoustic responses of the hyperelastic structure are examined, and the effects of the fluid nonlinearity parameter B/A and excitation amplitude on multi-frequency wave interactions are systematically analyzed. The numerical results demonstrate that the multi-frequency response induced by structural nonlinearity provides the necessary foundation for nonlinear wave-wave interactions, which, in turn, redistribute energy in different frequency components and modify the spatial patterns of high-order acoustic harmonics.

Investigation on nonlinear vibration characteristics of cantilever bistable laminated plates:Theory and experiment

Experimentally validated nonlinear vibration absorber attached to a rotor

This paper proposes a novel rolling bearing fault diagnosis method to address the difficulty of accurate feature extraction from nonlinear and non-stationary vibration signals. First, a Levy–Cauchy Optimized Sparrow Search Algorithm (LOCSSA) is developed to optimize the two core parameters (decomposition level and penalty factor) of Variational Mode Decomposition (VMD), and the optimized VMD is used to decompose raw vibration signals to obtain optimal intrinsic mode functions (IMFs). Second, the extracted IMF features are fed into a convolutional neural network (CNN) for local pattern extraction, followed by a bidirectional long short-term memory (BiLSTM) network to model temporal dependencies, with the final fault classification completed via a fully connected layer. Comparative experiments and ablation studies with five benchmark models are conducted to verify the effectiveness of the proposed framework. The results show that the proposed method achieves 96.33% accuracy, 96.67% recall, and 96.54% F1-score, outperforming all benchmark models. Ablation analysis confirms that both LOCSSA-optimized VMD and BiLSTM contribute significantly to performance improvement (p < 0.05), validating the rationality of the proposed method.

In this study, nonlinear vibrations of a slightly curved Timoshenko beam with nonlinear boundary conditions are investigated. The formulation is developed based on Timoshenko beam theory, incorporating shear deformation and rotary inertia effects. Geometric nonlinearity is introduced through the von Karman strain–displacement relations, and the governing equations of motion are derived using Hamilton’s principle. The resulting partial differential equations are reduced to a set of ordinary differential equations via the Galerkin method, where the mode shapes of a linear straight Timoshenko beam with linear spring boundary conditions are employed as admissible functions. The temporal response of the system is obtained using the method of multiple scales. Validation of the proposed formulation is carried out by examining the limiting case of vanishing curvature and by comparison with the nonlinear response of straight Timoshenko beams and thick shallow arch models. The results reveal that both hardening and softening behaviors may occur due to the presence of second- and third-order nonlinear terms. The proposed semi-analytical framework provides an efficient tool for analyzing nonlinear vibrations of slightly curved Timoshenko beams, capturing the combined effects of geometric nonlinearity, shear deformation, rotary inertia, and boundary flexibility.

Actively and smoothly tunable mechanical metamaterials are in high demand for adaptive, variable-stiffness structures in smart machines. However, existing designs are largely restricted to tunable transverse deformation, reciprocal response, and linear dynamics. Here, we propose a novel gear-based design paradigm-using Taiji planar gears and planetary gear assemblies as building blocks-that overcomes these limitations by enabling simultaneous control of translational and torsional stiffnesses, shear nonreciprocity, and programmable nonlinear dynamics. Our metamaterials achieve in situ, continuous tuning of shear stiffness by 30-100×, break reciprocity under positive versus negative loads, and allow the nonreciprocity ratio to be tuned by over 100×. Meta-resonators constructed from these units showcase an application example exhibit broadly tunable transverse and torsional resonant frequencies. Furthermore, we demonstrate that static nonreciprocity serves as a precise control knob for dynamic nonlinearity-a property traditionally fixed and nearly impossible to tune in conventional materials. Analytical models and analyses elucidate the underlying mechanisms and extendable design freedoms. This work bridges the critical gaps in mechanical metamaterials and dynamics, offering a practical pathway to control both linear and nonlinear structural deformations, elastic waves, and vibrations.

Nonlinear thermal vibration of variable stiffness composite laminated plates

Flow modification and nonlinear vortex-induced vibrations in flat box girders with vertical plate attachments

Nonlinear vibration suppression of a beam subjected to concentrated mass loads with an X-shaped local isolator