International Journal of Structural Stability and Dynamics

In this study, nonlinear vibrations and stability of multilayer functionally graded (FG) pipes conveying fluid laying on nonlinear elastic foundation and reinforced by graphene nanoplatelets (GPLs) are investigated with an emphasis on optimized analytical method. Various types of GPL distribution patterns are considered and to estimate the mechanical characteristics of the reinforced pipe the Halpin–Tsai micromechanics theory is applied. The nonlinear differential equation of motion is obtained by using Von–Kármán strain relations in conjunction with the Euler–Bernoulli beam theory and applying Hamilton’s principle. The Galerkin technique has been used for discretizing the partial differential equation. The optimized homotopy analysis method (HAM), as a strong analytical method, is utilized to solve the nonlinear differential equation by considering different initial excitations. The convergence-control parameter is taken into account to guarantee the convergence of the analytical solution. In this study, an exact solution based on HAM for the critical flow velocity and $n$th nonlinear frequency is presented. Additionally, series solutions for the nonlinear time responses of the transverse and longitudinal vibrations of fluid-conveying pipe based on optimized HAM are obtained for the first time. In the numerical results, the effects of arbitrary initial conditions and different physical characteristics on the nonlinear frequencies and time responses are extensively examined. It is shown that the nonlinear frequencies and critical flow velocity of the pipe depend not only on the initial excitation amplitude, but also on the entire initial excitation function applied on the pipe.

This paper presents a novel approach to the analysis of large deflection and post-buckling behavior of cantilever nanorods under different load conditions. The proposed approach utilizes a variational method, incorporating the Gurtin–Murdoch surface elasticity theory and the consistent couple stress theory to account for size-dependency effects. By accounting for the strain energy contributions of the bulk material, surface layer, and load conditions, this approach expresses the behavior of the nanorods in terms of their intrinsic coordinates. A finite element method was used to solve this numerical problem, generating a system of non-linear equations that were iteratively solved using the Newton–Raphson method. The results obtained from the finite element method were confirmed by those from the shooting method. Also, it highlights the effectiveness of the variational model in predicting the large deflection and post-buckling behavior of cantilever nanorods while considering both surface stress and couple stress effects. Furthermore, the study investigated the influence of surface stress and couple stress on the response of the nanorods to point and uniform loads. The results showed that incorporating both effects enhanced the stiffness of the nanorods compared to scenarios in which these effects were neglected. In addition, the couple stress effect was found to have a greater influence on the stiffening of nanorods for the same value of unitless parameters compared to surface stress effects. These findings offer valuable insights into the large deflection and post-buckling behavior of cantilever nanorods and highlight the importance of surface stress and couple stress effects. The model proposed in this study has potential applications in advanced technological device designs by providing a comprehensive understanding of the mechanical response of nanorods, allowing for more accurate predictions and enhanced device performance.

This study investigates free vibration analysis of a microplate featuring a honeycomb (HC) core and incorporates two nanocomposite piezoelectric (NP) layers. Carbon nanotubes (CNTs) are hired to enhance the electro-mechanical performance of the piezoelectric patches, which are subjected to an externally applied electric voltage. All layers are tightly bonded together and are supported by an elastic substrate according to the Pasternak model, capable of withstanding both normal and shear loads. To establish the kinematic relations, a trigonometric plate theory is employed. The governing equations of motion are deduced through the application of Hamilton’s principle and variational technique. The modified strain gradient theory, which includes three material length-scale parameters (MLSPs), is used to account for the scale effect. An analytical approach based on Fourier series functions is employed to solve the differential equations of motion. Subsequently, the impact of various factors, such as the geometrical characteristics of the HC core, distribution patterns of CNTs, and other significant parameters, on the normalized frequencies of the model is assessed after validating the accuracy of the results. The outcomes of this research have the potential to facilitate the advancement and production of lightweight and intelligent structures and devices, ultimately enhancing their efficiency.

This paper investigates the inherent nonlinear damping characteristics of a rotary eddy-current damper (RECD) and evaluates its vibration control performance on a single-degree-of-freedom (SDOF) system subjected to harmonic and seismic excitations. First, a RECD prototype was manufactured to experimentally identify its intrinsic nonlinear eddy-current damping characteristics. A magic formula model is then proposed to characterize the relationship between the eddy-current damping force and the velocity of the RECD, and its applicability in depicting the nonlinear damping characteristics of the RECD is evaluated by comparing with the electromagnetic finite-element (FE) model and the commonly used Wouterse’s model. Moreover, by comparing the experimental and analytical frequency–domain responses of an SDOF structure equipped with a RECD, the applicability of the magic formula model in evaluating the structural vibration control performance of the RECD is further verified. Finally, the control performance of the RECD for an SDOF structure subjected to earthquake ground motions is numerically evaluated and compared. Results show that the eddy-current damping force of the RECD presents obvious nonlinear characteristics with increasing velocity, and the proposed magic formula model can adequately depict the nonlinear eddy-current damping characteristics of the RECD. Moreover, the RECD exhibits superior structural control performance under harmonic and seismic excitations.

In the ABL wind tunnel, three inverted umbrella-shaped membrane structure groups were subjected to simultaneous pressure measurement model test. Time series of the fluctuating wind pressure were collected from 24 different wind angles. Upon examining the correlation coefficient of the fluctuating wind pressure between the upper and lower surfaces at the same pressure tap, it was discovered that the fluctuating wind pressure of the upwind roof exhibited asynchronous changes, which is a characteristic of a negative correlation area and has detrimental effects on the structure’s wind resistance. The local areas with non-Gaussian properties were evaluated by analyzing the probability density function of representative pressure taps. The mechanism behind non-Gaussian wind pressure was elucidated through considerations of the central limit theorem and spatial correlation of fluctuating wind pressure. This study introduces a quantitative classification criterion for identifying the non-Gaussian distribution area of fluctuating wind pressure, setting the threshold at an 80% cumulative probability for both skewness and kurtosis. The analysis showed that the steady airflow of the structure corresponds to the Gaussian distribution area, while the non-Gaussian distribution area is primarily concentrated at the front edge of the upwind roof and the rear edge of the downwind roof. To ascertain the peak factor for the non-Gaussian distribution, the improved peak factor method was utilized, providing insights into the range of peak factor in the non-Gaussian distribution area of this particular roof configuration. This information serves as a foundation for the wind resistance design of this structure.

The influence line of bridge can reflect the performance of the bridge under the moving vehicle load. It has a wide range of applications in structural damage detection, performance evaluation, model correction and bridge weigh-in-motion. Fast moving vehicles will cause the dynamic effect of the bridge, resulting in the change of the bridge response curve and the difficulty of identifying the influence line. In this paper, an influence line identification method based on variational mode decomposition (VMD) combined with improved wavelet threshold denoising is proposed. Firstly, the mathematical model of influence line identification is established based on vehicle load matrix and bridge response. Then, VMD combined with improved wavelet threshold denoising method is used to eliminate dynamic fluctuation effect and noise. Finally, the elastic net penalty term is introduced in the influence line identification problem, and the B-spline basis function is used to reconstruct the influence line. In order to verify the effectiveness of the proposed method, a vehicle-bridge coupling model is established for numerical calculation, and the identification of bridge displacement influence lines under different conditions such as vehicle speed, noise level, road roughness and vehicle weight is investigated. The results show that the proposed method can effectively eliminate the dynamic fluctuation components and noise of the bridge response. In the case of good road roughness, the influence line can still be accurately identified when the vehicle speed reaches 15 m/s.

The bistable morphing composite laminated shell presents promising potential for aerospace morphing structures design, as it is capable of shape-changing under small energy inputs and maintaining two stable states without external loading. The bistable nonlinearity is distinct from the typical geometrical nonlinearity, as it arises from thermal residual stresses that cannot be equalized. During the derivation of a three-degree-of-freedom nonlinear dynamic model, Sanders’ nonlinear strain is incorporated into the strain–displacement relationship, while thermal residual stresses are taken into account in the constitutive relationship. The nonlinear dynamic model effectively captures the snap-through phenomena with orthogonal asymmetry in bistable morphing composite laminated shells. In order to reveal the resonance response and chaotic characteristics due to the interaction of vibrations between degrees of freedom, high-dimensional nonlinear dynamical model is derived by multiple scales method based on the 1:1:1 internal resonance relationship. The resonance response curves reflect the parametric influence law of the dynamical system stability. The nonlinear dynamic behaviors are described by the bifurcation diagrams and the maximum Lyapunov exponent. The significant motions under particular excitation conditions are visualized by phase portraits, time histories and Poincaré maps.

In the degradation evaluation process of the crane girder structure under moving loads, the complex vibration response and low accuracy of health index standards are the main factors limiting the performance of the evaluation method. A method for identifying and evaluating damage to crane girder structures under moving loads has been proposed. In this method, optimized empirical wavelet transform (EWT) is used for decomposing the vibration signal of the crane girder structure to obtain sensitive components. A health indicator based on power spectrum maximum sequence is constructed by combining structural vibration simulation and response characteristics analysis under moving loads. A degradation index acquisition scheme based on an optimized sparse autoencoder is proposed, which utilizes a simulated annealing algorithm to optimize the model parameters of the sparse autoencoder. The effectiveness of the proposed method is verified through girder structure crack tests under moving loads.

Because of the introduction of modal coupling, discontinuous boundaries have a significant impact on the vibration characteristics of annular plates. Based on the spectral element method (SEM) and parametric equivalent method (PEM), the vibration calculation and analysis of internally perforated annular plate with discontinuous boundary are explained. Firstly, a uniform annular plate is regarded as a spectral element, and the vibration response of an annular plate with general elastic boundaries is obtained based on the motion equation of the annular plate and the virtual spring method (VSM). The displacement solution is described by the Bessel function, and a fitting method of discontinuous spring stiffness coefficient based on the weighted least square norm least square method is proposed. Based on the force equilibrium condition, the vibration response of an annular plate with a discontinuous boundary is derived, and the reasons for the change of vibration characteristics with a discontinuous boundary are explained from modal superposition. The dynamic stiffness matrix method is used to establish the vibration equation of an annular plate with a discontinuous boundary, and the influence of internal openings on the vibration characteristics of an annular plate is effectively calculated by the parametric equivalent method. Finally, a finite element simulation model is established to test the accuracy and stability of the proposed method. The influence of general discontinuous boundary conditions on structural dynamic behavior is analyzed by numerical examples, which provides useful guidance for structural vibration analysis with discontinuous boundary conditions.

The flexural vibrations of a thin rectangular plate with multiple rigid-point supports were examined theoretically, numerically, and experimentally. The analytical resonant frequencies and mode shapes obtained via the superposition method were compared with the finite element method (FEM) solutions. Experimental measurements were obtained using an amplitude-fluctuation electronic speckle pattern interferometer (AF-ESPI). The investigations considered two boundary conditions: (1) a completely free rectangular plate with one bolt and stand-off support at the center and (2) a rectangular plate with five bolts and stand-off supports along the short edge. In both cases, the plate was actuated using four macro-fiber composites (MFCs). The vibration characteristics of the plate varied significantly with the number and position of the rigid-point supports and the configuration of the MFC driving voltage. An analytical solution is proposed for frequency selection and mode control through the strategic placement of the rigid-point supports. The proposed solution provides a simple and efficient approach for controlling the vibration mode of the plate in various applications, such as vibration suppression, energy harvesting, and structural health monitoring.

This paper presents a new semi-analytical approach for the nonlinear vibration and dynamic responses of functionally graded graphene platelet-reinforced composite (FG-GPLRC) panels with complex curvature reinforced by orthogonal and/or inclined stiffeners in the thermal environment resting on the nonlinear viscoelastic foundation with the nonlinearities of von Kármán in the framework of the higher-order shear deformation theory (HSDT). The three curvature types of complexly curved panels are considered to be cylindrical, sinusoid, and parabola panels. Orthogonal and/or inclined stiffeners are modeled utilizing an improved smeared stiffener technique. The stress function form is estimated by applying the like-Galerkin method for complexly curved panels. By applying the Lagrange function and Euler–Lagrange equation, the nonlinear equations of motion of the panels are obtained. The viscous damping effects of the viscoelastic foundation are considered by utilizing the Rayleigh dissipation function. Numerical results are examined utilizing the Runge–Kutta method to acquire the time-deflection curves, and by utilizing the Budiansky–Roth criterion, the critical dynamic buckling loads are determined. From the investigated results, it is possible to evaluate the nonlinear vibration and buckling dynamic responses of three forms of panels with stiffeners.

The internal damping has a significant influence on the dynamic performance of carbon fiber-reinforced plastic (CFRP) drive shaft. In this paper, the traditional damping strain energy model of composite structures was modified using the reverse off-axis transformation. The damping ratio of CFRP hollow tube pieces is then tested using the vibration method, and the accuracy and efficiency of the modified damping numerical model are verified. Meanwhile, the modified model was proposed to study the damping characteristics and contribution rate of the CFRP hollow tube. The results show the influence law of the laminate parameters on the bending and torsion damping of the CFRP hollow tube. How the strain energy dissipation affects the damping of the CFRP hollow tube is discussed, and the mechanism relationship between the laminate parameters and damping is explored. This study provides theoretical guidance for the design of the bending and torsion damping of CFRP hollow tube.