International Journal of Structural Stability and Dynamics

The dynamical model of multiple honeycomb plates connected by hinges, including the thermal–structural coupling effect, is investigated in this paper. Under the assumption of small deformations and strains, the classical plate theory is used to establish the dynamical model of the honeycomb plate. The Chebyshev polynomial is adopted to describe the deformation of the plate and the linear torsional spring to represent the elastic hinge. Using the Rayleigh–Ritz method, the characteristic equation of the honeycomb sandwich structure is derived, from which the natural frequencies are obtained. Considering the thermal effect of the plate, the thermal–structural coupling dynamical equation is obtained. The thermal conduction in the thickness direction is calculated by the finite difference method. The present model is validated by comparing with the result generated by an equivalent orthotropic plate model established by the finite element (FE) software MSC Patran. The response analysis reveals the important effect of the metal skin and the hinge stiffness on the dynamic characteristics of the honeycomb sandwich structure. Numerical simulations reveal thermal–structural coupling features for the multi-honeycomb-plate structure from the perspective of the change in dynamic characteristics and the distribution of the temperature gradient. The thermal–structural coupling calculation method adopted herein can be used to solve the thermal conduction of the plate. It serves as the theoretical method for analyzing the dynamical behavior of the solar panel subjected to the solar heat.

In this study, a simple and unified process is established for transient vibration analysis of functionally graded material (FGM) sandwich plates in thermal environment. The temperature field, considered constant in the plane, is distributed along the thickness with uniform, linear and nonlinear profiles. For the material properties, both temperature and position dependence are taken into account. A further refined zigzag plate theory accounting for partitioned transverse displacements and piecewise-continuous in-plane displacements is developed within the framework of Hamilton’s principle including thermal effects. Appropriately and simplicity representation of the deformation states is provided in the governing equations. A spectral analysis technique, namely, method of reverberation ray matrix (MRRM), is employed to calculate the transient vibration responses of FGM sandwich plates with general boundary conditions and arbitrary external loadings. The artificial spring technology and the equivalent wave source vector are introduced to improve the numerical stability and parametric adjustability of MRRM. The accuracy, flexibility and efficiency of the proposed process are discussed using many numerical examples. On this basis, the effects of the boundary parameters, FGM gradient index, core-to-facesheet thickness ratio, thermal properties and external loadings on the transient vibration behaviors of FGM sandwich plates are thoroughly investigated.

Small-caliber steel core projectiles fired by light weapons pose a great threat to metal structures. Coating with polyurea (PU) is a potential option to improve the anti-penetration performance of metal structures. In this work, we carried out numerical simulations to clarify the dynamic characteristics of PU-coated ASTM1045 steel plates subjected to oblique penetration by 5.8-mm small-caliber steel core projectiles. The failure modes, dynamic response process, energy absorption characteristics, and comprehensive protection effects of target plates with different coating positions and thicknesses during the penetration process were compared and analyzed. The result showed that coating with a certain thickness of PU could enhance the protection ability of the steel plate against the oblique penetration of projectiles. In contrast to the results obtained from experiments in which the projectile penetrated the composite plate normally, when the PU coated both sides, the effect of improving the oblique penetration resistance of the steel plate was the best. The effect was lowest with a PU layer only on the back face. This study provides a reference for strengthening the bulletproof performance of various systems, including steel structures, weapons, and vehicles.

This paper presents a new approach for analyzing the free vibration of thin plates with arbitrary piecewise smooth curvilinear contour under various boundary conditions. It can also be applied to plates with cracks. This approach is based on the transformation of energy integral expressions and the domain decomposition technique. Furthermore, boundary conditions are modeled by using linear springs to restrain the plate edges. For obtaining the expressions of energy integral, the arbitrarily shaped domain of integration is divided into several trapezoid domains with curved sides by a set of parallel lines passing through the intersection points of contour curve segments. Then, Jacobi orthogonal polynomials are introduced as the admissible functions, so that the repeated integrals in the energy expressions are reduced to definite integrals analytically. At this point, the calculation method of the energy functional is determined by the equation forms of the curve segments of the plate contour. When the equations of the curve segments allow the integrands to have analytic primitive functions, the energy functional has an analytical solution. Otherwise, the Gauss–Legendre method is used to obtain the numerical solution. Accordingly, the arbitrarily shaped plate with cracks is decomposed into several arbitrarily shaped subdomains based on the cracks. Each subdomain is handled according to the above procedure. The continuity conditions at the interconnecting interfaces of the subdomains are realized by linear springs. The plate without or with crack is modeled by setting the spring stiffness to infinity or 0. The accuracy of the proposed method is verified by comparing the obtained results with the published results. Furthermore, the vibration characteristics of plates with various shapes, such as astroid-shaped plates and cracked elliptical plates, are investigated. These new results can serve as benchmarks for further studies on the vibration of plates.

Dynamic analysis of functionally graded size-dependent annular nano-plate is the main concern in this study. To obtain the vibrational behavior of this plate, the stress-driven nonlocal integral elasticity, as well the strain gradient theory were used in conjunction with the classical plate theory. The resulting equilibrium equations were solved using the generalized differential quadrature rule (GDQR) and the influences of various parameters such as; size-effect parameter, material heterogeneity index, the aspect ratio of the inner to outer radii, and the effects of different boundary conditions were investigated on the vibrational behavior of the nano-plate, based on different types of boundary conditions. Results indicate that the natural frequencies increase with an increase in the heterogeneity index $n$ and the increase in size-effect parameter shows a similar effect in both models. Additionally, for the simply supported and free-edge boundary conditions (for both edges), as well as the free and knife-edges, and simply supported-free edges, the strain gradient theory predicts higher values of frequency ratios as $L_c$ was increased. Similar results were obtained for the remaining types of boundary conditions, with a higher sensitivity to $L_c$, provided the stress-driven model is used. This behavior can be interpreted as the sensitivity of the nano-plate to $L_c$ that is manifested by the use of the stress-driven model for the prediction of vibrational behavior of the nano-plate.

This paper introduces a new rigid finite element method (RFEM) formulation for dynamic analysis of plates. In RFEM, a flexible body is divided into several rigid elements which are interconnected by spring and damping elements. Mainly, RFEM has been used to model systems with beam-like slender components, such as ropes and cables, and few RFEM formulations were developed to model plates and shells. In this study however, by means of the Timoshenko beam theory and cuboid rigid elements, a novel RFEM formulation is developed to model flexible flat plates with generic geometries of the surface, considering large deformation. For this purpose, an RFEM formulation is presented for straight beams with rectangular cross-section by means of the Timoshenko beam theory. Next, this formulation is expanded to model flexible rectangular plates with uniform thickness and then, it is elaborated on how to model non-rectangular plates with uniform thickness using only cuboid elements and consequently, the development of the proposed RFEM formulation is completed. After investigating various case studies, the competence of the proposed formulation is evaluated thoroughly. The results of RFEM came on a proper agreement with the FEM results in a way that the maximum difference between these results in dynamic analysis was about 3%.

The propagation of transition waves in multi-stable mechanical systems can be effectively harnessed in various fields, such as mechanical signal communication, mechanical diodes, and energy absorption. In this work, the propagation of transition waves in a one-dimensional (1D) bistable mass-spring chain is systematically studied. The underlying physical mechanism for the formation and propagation of transition waves is clarified, and the influences of some crucial factors, such as the pumped momentum, stiffness of the connecting springs, viscous damping, number of masses, and asymmetry of the double-well potential, on the propagation of transition waves are discussed in detail. As a result, the parameter space for achieving the robust propagation of transition waves through the whole chain is presented. This study is expected to be beneficial for the control of transition waves and design of novel devices used for mechanical signal transmission.

We present the results of a series of experiments, which study the effect of the fluid layer height, viscosity and free surface waves on the vibration damping of a thin rectangular plates interacting with a fluid. The suppression technique is based on the shunt circuit connected to the piezoelectric elements. The possibility of using the previously proposed mathematical formulation and approach for calculating the optimal values of the parameters of a RL-circuit in systems with hydrodynamic dissipation is estimated. The experimental results presented confirm its reliability. It has been demonstrated that the efficiency of vibration damping of a single plate structure changes insignificantly with increasing height of the fluid layer except for some interval. At a small amount of the liquid, the waves on its free surface disturb the piezoelectric element reducing its efficiency. Using as an example an assembly of two parallel plates damping of “in-phase” and “out-of-phase” modes has been shown using one location of piezoelement.

Many studies on structural control have been done in recent decades to enhance the safety and serviceability of high-rise structures or towers against earthquakes and severe winds. Because most structures have an unbalanced layout, when they are exposed to an earthquake, they undergo torsion effects, which exacerbate the structural reaction. Also, such structures might be built on soft soil, where the influence of the Soil–Structure Interaction (SSI) would be significant. Thus, taking into account the SSI effect, a mathematical model is developed in this study to determine the seismic performance of an irregular multi-story structure with Active Tuned Mass Dampers (ATMDs) at the top floor. The results were produced utilizing MATLAB/SIMULINK software using the proposed hybrid Shallow Neural Network (SNN) technology and Shuffled Shepherd Optimization (SSO). The seismic response of 40-story asymmetric project buildings is studied using this model. The findings showed that using ATMDs on the higher floors of 40-story structures on soft soil reduced the produced structural reflexes. When compared to the Particle Swarm Optimization (PSO) and Ant Lion Optimization (ALO) algorithms, the suggested technique outperforms them both.

Cracks have a significant impact on the stability of rotating machinery. However, most studies focus on rotating machinery with only one crack. This paper discusses the influence of two cracks on the stability of a flywheel rotor-bearing system. In this study, the dynamic models of vertically placed flywheel rotor-bearing system with two open cracks and two breath cracks are established using the finite element method (FEM). Floquet theory is used to calculate the stability of the system and the influence of depth and positions of cracks are analyzed. The results show that breathing cracks cause more unstable regions than open cracks, and the range of rotating speeds over which the rotor is unstable increases with increasing crack depth. In addition, it is observed that when the crack locations are adjacent, the unstable region will become very large, covering most of the crack depth range and speed range, making the rotor extremely unstable. Besides, the bearing stiffness causes an offset in the unstable regions, whereas the damping influences the instability value of the rotor.

For high-rise buildings subjected to typhoon or earthquake actions, the excitations are likely non-stationary, which inevitably violates the stationary assumption that is generally adopted by conventional modal identification methods. Under such a condition, conventional modal identification methods may not be applicable, and their performances need to be evaluated. To this end, the performances of seven widely used modal identification algorithms for structural modal estimation under non-stationary excitations are evaluated via a numerical simulation study. Then, three methods with good performance are selected to evaluate their applicability and accuracy for field measurements involving non-stationary excitations. From the comparative study, a time–frequency domain method with the best performance among these seven methods is employed to investigate the structural dynamic properties of a 509-m-tall skyscraper under typhoon and earthquake excitations. Based on the reliable modal estimates, the relationships between the modal properties with response amplitude and environmental temperature are presented and discussed. This paper aims to identify the effective methods for accurate estimation of structural modal parameters based on non-stationary structural responses and investigate the structural dynamic properties of high-rise buildings under typhoon and earthquake excitations.

Based on the moving-window correlation coefficient of signals, a damage detection method is proposed for bridge structures. The signals collected by two sensors during the vehicle crossing the bridge are intercepted as windowed pair time series, and the damage index is defined based on the correlation of them. The damage vector is composed of damage indices from the beginning to end according to the moving direction of the window, and the damage location can be determined by the peak information of all the damage vectors which are obtained by different sensor pairs. First, the damage detection method and corresponding detection steps are introduced. Then, the proposed method is validated by numerical simulation, and the influence of moving window length, moving step, the number of sensors, deviation of vehicle parameters and road-surface roughness on damage localization are discussed, respectively. Finally, the proposed method is validated by experiments using a two-axis vehicle and a steel–concrete composite beam. The results show that the proposed method can effectively identify the damage location. High-pass filtering of the raw data to remove trend items and wavelet noise reduction can significantly improve the accuracy of damage detection, and can accurately locate the damage in the presence of road-surface roughness. The damage detection result is not sensitive to vehicle parameter deviation, and the damage location can still be accurately identified when the vehicle weight or speed deviates 50% from the vehicle parameters in the reference data. In addition, the proposed method can make full use of the damage information between sensors, and can accurately identify the damage location with limited sensors. The number of sensors can be flexibly determined considering both accuracy and economy.

The purpose of this study is to analyze the nonlinear vibration behavior of two-layer bi-material beams by using the Euler beam theory and Timoshenko beam theory. It is assumed that material properties satisfy a power law distribution along the thickness direction. The differential quadrature (DQ) method in conjunction with an iterative algorithm is employed to solve the nonlinear governing equations for two-layer bi-material beams. Numerical results are presented to show the influence of Young’s modulus ratio and thickness ratio on nonlinear frequency ratio–amplitude curves of two-layer bi-material beams. It is observed that the nonlinear frequency ratio–amplitude curves are unsymmetrical with the hinged end because of bending-extension coupling effect in two-layer beams. It is also observed that the hinged–hinged two-layer beams may occur the softening-spring nonlinearity when the amplitude of oscillation is small. This softening-spring nonlinearity is dependent on the thickness ratio, Young’s modulus ratio, vibration amplitude, layer number and boundary condition. The greater the difference of material properties between the two layers is, the more obvious the softening-spring nonlinearity becomes.

This paper presents research on the modal damping and frequency response of functionally graded fiber-reinforced composite cylindrical shells considering the internal damping. Based on the Love shell theory and energy approach, the dynamical equations of cylindrical shells are established. In the process of variable separation, the Haar wavelet series and trigonometric functions are respectively to represent the axial and circumferential modes. Based on the microscopic damping prediction method and multi-cell model of hybrid materials, the equivalent damping and elastic characteristics of composite materials are determined. Then the damping and frequency response characteristics are solved by the complex modulus method. The present analysis is validated by comparing the results with those in the literature and finite element simulation. The effects of fiber content and distribution, lamination and geometry configuration on damping and frequency response properties are further analyzed. The analysis show that the damping decreases monotonically with the increase of fiber volume fraction. The damping behaviors may be improved by changing the fiber distribution type and stacking sequence. Increasing the internal damping of composites can obviously reduce the vibration amplitude in the resonance region, especially in the high frequency range.

Deep sedimentary basins often increase the intensity of ground motions, but this effect is not considered explicitly in most codal provisions. The effect of basin amplification on structures to the fragility level is significant to study. For the first time, the effect of basin amplification on Steel Moment Resisting Frames (SMRF) is presented as a function of the basin material and geometry. This paper evaluates the effect of basin material, basin depth, and basin width on Peak Ground Velocity (PGV), Spectral Acceleration (Sa), and fragility of 4, 8, 12, and 20 story steel structures using synthetic ground motions simulated in SPECFEM3D. It has been found that the variation in basin width and impedance ratio can increase the spectral acceleration by a factor of 4 and 2.5, respectively. The response of SMRF is computed by incremental dynamic analysis, and fragility curves are derived for the collapse limit state. Results of fragility analysis reveal that SMRF structure is more fragile to variation in impedance contrast between basin-bedrock. It has been observed from the results that the collapse intensity measure for impedance ratio variation is 40% and 19% lesser on average than the width and depth variation, respectively. Comparison between the present fragility analysis results and HAZUS fragility parameters indicates that the vulnerability of structure located in the basin is underestimated in its current provisions, and the SMRF would need to increase its strength two times to account for basin amplification.

Axially loaded micro/nano-beams supported on foundations are extensively applied in micro/nano-electro-mechanical systems. This paper deals with the problems of free vibration, buckling and dynamical stability of Timoshenko micro/nano-beam supported on Winkler–Pasternak foundation subjected to a follower axial periodic load. Based on Hamilton’s principle, the governing equations of the system are derived in conjunction with nonlocal strain gradient and Timoshenko theory. The transition parameter is introduced to describe the follower direction of axial load during the deformation of the micro/nano-beam. Employing the weighted residual method, the variational consistency boundary conditions (BCs) can be derived according to the governing equations. Using differential quadrature method (DQM), the governing equations are discretized and numerical solutions of the natural frequencies, critical buckling load and instability region are obtained. Numerical examples are performed to verify present solutions by those available in the literature. Significant effects of the transition parameter and variational consistency BCs are revealed on the free vibration, buckling and dynamical stability of the axially loaded micro/nano-beam. The present analysis is of significance to axially-loaded micro/nano-beam mechanical system, especially for determination of the direction of follower axial force.