International Journal of Structural Stability and Dynamics

In this research, the natural frequency behavior of functionally graded (FG) porous joined hemispherical–cylindrical–hemispherical shell vessels reinforced by graphene platelet (GPLs) has been studied for the first time. Three various types of porosity distribution are assumed through the thickness direction of shell vessel. In the two types of porosity patterns, a pattern of porosities in metal matrix is symmetric and the other one is uniform. Besides, five GPL patterns are assumed for dispersing of GPLs in metal matrix. Extended role of mixture and Tsai-Halpin is used to determine the mass density and Young’s modulus of elasticity of the structure, respectively. By employing 3D elasticity theory, Hamilton’s Principal and FEM in conjunction with Rayleigh–Ritz method, the governing equations of motion of the joined shell vessel are obtained and natural frequencies are extracted. The impact of various factors such as coefficient of porosity, several porosity patterns along with different GPLs distributions and weight fraction of graphene nanofillers on natural frequency behavior of FG porous joined hemispherical–cylindrical–hemispherical shell vessels reinforced by GPLs nanofillers has been reported for the first time.

In this paper, thermoelastic dissipation or thermoelastic damping (TED) in micro/nanorings with rectangular cross-section is examined by accounting for small-scale effect on both structural and thermal areas. The modified couple stress theory (MCST) and nonlocal dual-phase-lag (NDPL) heat conduction model are exploited for incorporating size effect within constitutive relations and heat conduction equation. By employing simple harmonic form for asymmetric vibrations of the miniaturized ring and solving the heat conduction equation, for one-dimensional (1D) and two-dimensional (2D) cases of heat transfer, the solution of temperature distribution in the ring is extracted in the form of infinite series. By employing the definition of TED on the basis of entropy generation approach, an analytical relation in the series form containing structural and thermal scale parameters is established to estimate TED value. To appraise the precision and validity of the developed solution, a comparison study is performed by utilizing the outcomes of researches published in the literature. An exhaustive parametric study is then conducted to ascertain the role of structural and thermal scale parameters in the magnitude of TED. The influence of some key parameters such as vibration mode, geometrical properties, directions of heat conduction (1D and 2D model) and material on TED is also addressed.

The assembled tube-gusset K-joint by bolts is a commonly used connection form in steel tubular transmission towers. At present, main existing research or design codes for steel tubular transmission towers regard this K-joint as either rigid or pinned connections, which do not consider the semi-rigid behavior of K-joint. In this paper, the semi-rigid behavior of K-joint in steel tubular transmission towers is investigated and a direct prediction (DP) method is proposed to evaluate the semi-rigid behavior of K-joints based on the support vector regression (SVR) model, especially to predict the moment–rotation curve of semi-rigid K-joints. First, the establishment and validation of the finite element (FE) model of semi-rigid K-joints are conducted. Second, a dataset of 144 samples generated by the FE model is used to train and test the SVR model. Finally, the accuracy assessment of the proposed DP method and comparison with other existing methods, including the Kishi–Chen model, EC3 model and ANN-based two-step prediction method, are presented. The accuracy assessment shows that predicted values of the proposed DP method based on the SVR model exhibit good agreement with the numerical analysis values, which indicates the quite high accuracy of this method. Additionally, the comparison reveals that the proposed DP method based on the SVR model for predicting moment–rotation curves is rather more accurate than other aforementioned methods. Therefore, the proposed DP method based on the SVR model is of high reliability in predicting the semi-rigid behavior of K-joints in steel tubular transmission towers, which affords an alternative way for further engineering analysis and initial design purposes.

For some transmission shafting, nonlinear supports are connected to beam structures through the pattern of the contact surface. Nonlinear foundations are typically installed to the beam structure for a limited range. The unsuitable installation mode of nonlinear foundations will make the parameters of nonlinear foundations no longer uniform. Most existing studies ignore the boundary rotational restraints of beam structures and concentrated mass introduced by the nonlinear supports or foundations. To improve the engineering acceptance of beam structures with nonlinearity, it is of great significance to study the dynamic behavior of the generally restrained pre-pressure beam structure with a partial non-uniform foundation of nonlinear stiffness. This study establishes the nonlinear vibration model of the beam structure with a local non-uniform nonlinear stiffness distribution. Nonlinear dynamic responses of the beam structure are predicted by the Galerkin truncation method (GTM). Mode functions of the generally restrained pre-pressure beam structure are set as the trail and weight function. The correctness of the GTM for dynamic prediction of the beam structure with a partial non-uniform nonlinear foundation is verified by using the harmonic balance method (HBM). The influence of sweeping ways of excitations and parameters of the partial non-uniform nonlinear foundation on nonlinear dynamic responses of the beam structure are investigated. Dynamic responses of the beam structure with a partial non-uniform nonlinear foundation are sensitive to their initial values. Vibration states of the beam structure are transformed effectively by changing parameters of the partial non-uniform nonlinear foundation. The vibration at both ends of the beam structure can be suppressed by applying suitable parameters of the partial non-uniform nonlinear foundation.

This paper proposes a modified segmented rod method (MSRM) in order to facilitate the introduction of boundary conditions in the analysis of free vibrations and buckling of Euler–Bernoulli beams. First, the basic idea of proposed modifications is presented in the case of elementary length beam, and then the idea is generalized to the full-length beam. In addition to facilitating the introduction of boundary conditions, by comparing the results of MSRM with segmented rod method (SRM) and Hencky bar-chain method (HBM), a faster convergence of MSRM results to the exact ones was observed. Although the case of uniform beam is considered in this paper, proposed MSRM may contribute to greater use of segmented beam approach in solving of various static, free vibration or buckling problems of non-uniform beams. Also, it was shown that MSRM can be easily adapted for the analysis of beams that resting on partial elastic foundation.

In this paper, the dynamic buckling of functionally graded (FG) porous shallow arches under hygro-thermal loading is studied through a numerical approach. Even and uneven porosity imperfections, hygroscopic stresses generated due to the nonlinear rise in moisture concentration, and the temperature dependence of material properties are all taken into account. The transient heat conduction equation is solved to derive the temperature profile. Hygro-thermo-mechanical properties of the arch are obtained applying the modified Voigt’s rule of mixture. The first-order shear deformation theory, the von-Kármán geometrical nonlinearity assumption, and the hygro-thermal strains are considered concomitantly to derive the equations of motions based on Hamilton’s principle. The generalized differential quadrature method (GDQM) and Newmark-beta integration schemes are also employed in conjunction with an iterative approach to solve the set of nonlinear governing differential equations of motion. The Budiansky–Hutchinson stability criterion is utilized to capture the dynamic buckling temperature of the structure. A parametric study is conducted in order to investigate the effects of porosity distribution, FG index, geometrical parameters, hygroscopic loading, and thermal/mechanical boundary conditions on arch’s dynamic buckling temperature.

With the development of wind power energy, the steel-concrete hybrid tower has been gradually popularized as the onshore tall wind turbine tower. To avoid the resonant response that brings violent damage to the wind turbine tower, the fundamental frequency of the hybrid tower must be carefully analyzed. This study develops a closed-form solution of the fundamental frequency of the hybrid tower, where the abrupt changes of cross-section and material properties, the effect of prestressing, and the mass and rotary inertia of the wind turbine are taken into account. It provides an effective way to obtain the fundamental frequency in the preliminary design of the hybrid tower. The effectiveness of the proposed solution is validated by comparing it with the results of finite element analysis, showing good agreement. By using the proposed solution, a parametric analysis is conducted to investigate the variation rules of the fundamental frequency to the design parameters. It indicates that with the variation of the proportion of the concrete/steel segments, the correlations between the fundamental frequency and the design parameters also change significantly. The parametric analysis conducted herein may provide instructive guidelines to adjust the parameters in the preliminary design of the hybrid tower.

Sandwich composite structures may have a significant variation in their dynamic behavior due to the uncertain preconditions of the manufacturing processes, material properties, geometry, etc. Therefore, quantifying and modeling such variability in the dynamic behavior of sandwich composite structures is a necessity. In this study, free vibration analysis is carried out for a glass-fiber reinforced plastic (GFRP) sandwich composite plate. The natural frequencies are obtained by taking into account various uncertainties involved in preparing the sandwich composite plate. The Kolmogorov–Smirnov (KS) and Anderson–Darling (AD) goodness-of-fit (GOF) tests are performed for the quantification of the uncertainty of the natural frequencies. The appropriate probabilistic distribution describing the variability of the vibrational response is recommended. The knowledge of the uncertainty of dynamic responses might help to control the quality of the manufacturing process, as well as for the reliability study of the sandwich composite structures.

In terms of the heavy load and low viscosity operation conditions of the marine rim-driven thruster (RDT), a novel Magnetic Liquid-double-suspension Elastic-supported Thrust Bearing (MLETB) is designed. The MLETB combines the structural features of the Rubber-supported Water-lubricated Thrust Bearing (RWTB) and Permanent Magnet Bearing (PMB). To investigate the axial stiffness and damping of the bearing, the dynamic model of MLETB incorporating a multi-layer structure is developed. Simulation indicates that the dynamic performance of the MLETB is close to that of the RWTB, but the load capacity of the MLETB is better. Besides, the load is not the most important factor to affect the dynamic performance. The parameter identification method is proposed to analyze the experiment results based on the water-lubricated bearing test rig, which show that the MLETB has a dilemma between the load capacity and dynamic performance that its stiffness and damping will be seriously affected by the specific rubber structure.

This study investigates the axisymmetric postbuckling of functionally graded graphene platelets reinforced composite (FG-GPLRC) annular plates resting on nonlinear elastic medium in thermal environment. Five kinds of graphene platelets (GPLs) distribution patterns including $U$-pattern, $X$-pattern, $O$-pattern, $A$-pattern, and $V$-pattern have been considered. The nonlinear equilibrium equations and associated boundary conditions are obtained based upon the Mindlin plate theory. The governing equations are solved via the generalized differential quadrature method (GDQM). Afterwards, the direct iterative method is implemented to accomplish postbuckling loads using the buckling mode deflection. In order to confirm the accuracy of the present model, comparisons between our data with those published in the available literature are put forth. Eventually, this paper emphasizes the impact of diverse parameters such as geometrical parameters of the structure, GPLs patterns and their geometric, GPLs weight fraction, boundary conditions, elastic medium’s parameters and temperature change on the buckling and postbuckling response of nanocomposite annular plates. It can be found that elastic medium overshadows the applicability of distribution patterns and weight fraction of GPLs.

This paper aims to present the exact closed-form solutions for the free vibration of double-beam systems composed of two parallel beams connected by an arbitrary number of discrete elastic supports. The general solutions of the mode shapes of the double-beam system are derived employing the Laplace transform method from a perspective of the entire domain of beams without enforcement of any segmentation. A unified strategy applied to various boundary conditions is proposed to determine the independent constants involved in the general solutions, as well as the frequency equation. Numerical calculations are performed to verify the present solutions by comparing the results from the previous literature and finite element simulation, and to discuss the effects of support parameters (stiffness, location, and number) on the modal characteristics of the double-beam system in detail. Outcomes show that the support location plays a pivotal role in regulating the modal characteristics of the double-beam system; for each-order mode, there are one or more potential optimal positions to maximize the effect of the elastic support. The mode veering phenomenon is detected as the support parameters change. It is highlighted that, by introducing an amplitude similarity index, the proximity degree for the mode shapes of the two beams influenced by the support parameters can be evaluated quantitatively. The present analysis is greatly helpful to the optimal design, health monitoring, and vibration control of the double-beam system.

Vibration-based global damage detection based on updating of finite element (FE) model by targeting the modal measurements is a significant area of interest in structural health monitoring (SHM). In a typical modal testing setup, the measured mode shapes have missing components against various degrees of freedom (DOFs) due to the limitation in the number of sensors available. In this context, a novel Gibbs sampling approach is proposed for updating of FE model incorporating model reduction (MR) to facilitate the global-level detection of structural damages from incomplete modal measurements. In addition to the ease with similar sizes of analytical and experimental mode shapes, the proposed Gibbs sampling approach (for updating the reduced order FE model in the Bayesian framework) has some important advantages like: (A) no need for consideration of system mode shapes as parameters (unlike needed in the typical Gibbs sampling approach) thereby having a significant reduction in the number of parameters, (B) non-requirement of mode matching with consequent reduction in computation time to a significant extent. A generalized formulation is presented in this work providing the scope for incorporating measurements from multiple sensor setups. Moreover, formulations are adapted to incorporate multiple sets of data/measurements from each setup targeting the epistemic uncertainty. Finally, validation is carried out with both numerical (truss structure and building structure) and experimental (laboratory building structure) exercises in comparison with the typical Gibbs sampling approach having a full-sized model. The proposed approach is observed to be evolved as a computationally efficient technique with satisfactory performance in FE model updating and global damage detection.