International Journal of Structural Stability and Dynamics

The aim of the present paper is to study the thermoelastic damping of a micro-beam resonator in the context of the generalized thermoelasticity theory with three-phase-lag (TPL). The thermoelastic damping of the micro-beam resonator is obtained by the Laplace transform procedure as well as by the finite-sine Fourier transformation. The vibration responses of deflection and thermal moment are obtained for the micro-beams with simply supported and isothermal ends. Initially, the analytic solution is obtained for the amplitudes of deflection and thermal moment. It was observed that both amplitudes are attenuated and the vibration frequency is increased with the three-phase-lag. The effects of phase-lags on the deflection and thermal moment are obtained and evaluated by comparing the present numerical results with the corresponding results based on the theory of thermoelasticity of type GN-III. It was observed that higher values of deflection and thermal moment of the resonator are obtained for the TPL when compared with those of the GN-III model. It was also found that these properties are size-dependent.

A direct eigenvalue analysis approach for solving the stability problem of periodically supported beams with multi-mode coupling vibration under general harmonic excitations is developed based on the Floquet theorem, Fourier series and matrix eigenvalue analysis. The transverse periodic supports are considered for improving the parametrically excited stability of beams under longitudinal periodic excitations. The dynamic stability of parametrically excited vibration of the beam with transverse spaced supports under longitudinal harmonic excitations is studied. The partial differential equation of motion of the beam with spaced supports under harmonic excitations is given and converted into ordinary differential equations with time-varying periodic parameters using the Galerkin method, which describe the parametrically excited vibration of the beam with coupled multiple modes. The fundamental solution to the equations is expressed as the product of periodic and exponential components based on the Floquet theorem. The periodic component and periodic parameters are expanded into Fourier series, and the matrix eigenvalue equation is obtained which is used for directly determining the parametrically excited stability. The dynamic stability of parametrically excited vibration of the beam with spaced supports under harmonic excitations is illustrated by numerical results on unstable regions. The influence of the periodic supports and excitation parameters on the parametrically excited stability is explored. The parametrically excited stability of the beam with multi-mode coupling vibration can be improved by the periodic supports. The developed analysis method is applicable to more general period-parametric beams with multi-mode coupling vibration under various harmonic excitations.

Tuned liquid damper (TLD) as an economical passive damper has gained importance because of its efficiency in suppressing the undesirable motion of a structure due to devastating earthquakes when it is rigidly attached to the structure. This phenomenon has been studied previously, but mostly limited to rectangular- or cylindrical-shaped TLD. The present study is aimed at determining the potential of the sloped bottom tuned liquid damper to suppress the unwanted vibration of the structure subjected to earthquake ground motion. Three different earthquake ground motions characterized by low-, intermediate- and high-frequency contents are selected for the dynamic analysis of the TLD–structure coupled system. A parametric study on the sloped bottom TLD and its interaction with the sustaining structural system is conducted. The structural equations, which are coupled with fluid equations, are solved by the Newmark-$\beta$ method with average acceleration, while the fluid equations are solved using velocity potential-based finite element method. The liquid domain in the TLD is comprised of a combination of three-node triangular and four-node quadrilateral elements. The result shows the reduction in structure response is significant with less amount of water in sloped bottom TLD rather than rectangular TLD.

A new nonlinear model based on the absolute nodal coordinate formulation (ANCF) and the nonlocal elasticity theory is proposed to investigate the single-layered graphene sheets (SLGSs) impacted by nanoparticles. The geometrical definition of SLGSs is described by using the ANCF thin plate element, and the strain energy is expressed by using the nonlocal theory. The Lennard–Jones pair potential is adopted to model the van der Waals (vdW) force between SLGSs and nanoparticles. The impact dynamics of the system is simulated in multibody framework by using the generalized-alpha numerical integration method. The impact response of the gold atom–SLGSs system is simulated to validate the performance of the proposed model. Three impact dynamic simulations are conducted to investigate the influence of nanoparticles on the impact dynamics of SLGSs. The results show that the coupling of SLGSs vibration and vdW force led to the amplitude inconsistence of $Z$-position for nanoparticles.

The thermo-electro-mechanical nonlinear vibration of circular cylindrical nanoshells on the Winkler–Pasternak foundation is investigated. The nanoshell is made of functionally graded piezoelectric material (FGPM), which is simulated by the nonlocal elasticity theory and Donnell’s nonlinear shell theory. The Hamilton’s principle is employed to derive the nonlinear governing equations and corresponding boundary conditions. Then, the Galerkin’s method is used to obtain the nonlinear Duffing equation, to which an approximate analytical solution is obtained by the multiple scales method. The results reveal that the system exhibits hardening-spring behavior. External applied voltage and temperature change have significant effect on the nonlinear vibration of the FGPM nanoshells. Moreover, the effect of power-law index on the nonlinear vibration of the FGPM nanoshells depends on parameters such as the external applied voltage, temperature change and properties of the Winkler–Pasternak foundation.

This paper presents the field tests and vibration performance assessment of two long-span floors with tuned mass dampers (TMDs). The floors considered are made of steel beams and concrete slabs, as part of a gymnasium with composite floors spanning 36 m in each direction and equipped with 30 TMDs. Operational modal analysis based on ambient acceleration measurements is performed to extract the modal parameters of the floors. Ambient vibration tests were conducted at three stages of construction for each floor, namely (i) after the concrete slab was completed, (ii) after one layer over the concrete slab was added, and (iii) after the flooring (surfacing) was fully finished. The effects of the layers making up the flooring system and of the TMDs on the dynamic properties of the floors are studied. The finite element models of the floors are validated using the identified modal parameters. The effects of natural frequency of TMDs on the dynamic properties of the floors are investigated using the validated model. Finally, the effects of flooring on the vibration serviceability of the two floors are studied with TMDs in operation, when the floors were subjected to crowd-induced rhythmic loading, from which the efficiency of TMDs is assessed numerically. The results show that the coupled vibrations of the two floors with TMDs turned off occur in the first two modes, while the natural frequencies of the floors decrease with the addition of layers. The TMDs in operation break the first mode of the floor into two modes with similar mode shapes, resulting in smaller vibration response and larger damping ratios, which vary with the natural frequency of TMDs. Also, the wood flooring significantly increases the human-induced vibration of the floor, while the plastic flooring shows basically no effect.

This paper focuses on the aeroelastic vibration energy harvesting performance of a wing panel. A nonlinear mathematical model of fluid-structure-electric coupling field was established based on the aeroelastic vibration equation and piezoelectric equation. Numerical analysis was performed to explore the influences of the airflow velocity and the piezoelectric material structural parameters on both the dynamic response and the energy harvesting performance. A small experimental wind tunnel and several prototypes of energy harvesters of the wing panel were designed and fabricated. The experimental results show that the vibration amplitude and output power of the wing panel increase with the airflow velocity; the average output power first increases until it attains the maximum values, and then decreases with the increase of the dimensionless length ($L_{\mathit{\text{p}}}$/$L_{\mathit{\text{b}}})$ and the thickness of the piezoelectric patch. It shows that the theoretical and experimental results are in good agreement. The experimental optimal output power is 3mW at the airflow velocity of 12m/s, and the piezoelectric patch length, width and thickness of 40, 20 and 0.2mm, respectively. This work provides an effective theoretical and experimental basis for studying energy harvesting and vibration control of airfoil aircrafts.

For a super high-speed elevator running in a hoistway, it will encounter air flows at high speed. The transverse force and pitching moment generated by the air intensify the transverse vibration of the elevator. In this paper, by fully considering the guide rail excitation and air disturbance, the transverse vibration of a super high-speed elevator under different working conditions is examined. Based on the Lagrange principle, a four degree-of-freedom (DOF) model is adopted for the transverse vibration of the elevator. Combined with computational fluid dynamics (CFD), the effects of various parameters corresponding to different working conditions on the aerodynamic forces acting on the transverse surfaces (the surfaces facing the guide rail) of the car is analyzed. Finally, the Newmark-$\beta$ method is employed to analyze the effect of air disturbances on the transverse vibration acceleration of the car under different working conditions. The results show that when the car is symmetrically positioned, the aerodynamic characteristics on both transverse surfaces of the car also appear to be symmetric. The operating speed and the distance between the car’s transverse surface and the hoistway wall (DCH) have a minor effect on the transverse vibration of the car, and the car is basically in a state of forced balance in the transverse direction. However, once the car deviates from the symmetric position, the balance will be violated, and the transverse resultant force and moment of the car will increase with the increase in the deviation amount. Among all these factors, the influence of the rotation angle on the elevator’s vibration acceleration is the most significant.

Aimed at its elegance, the rigid-body-based procedure for geometric nonlinear analysis is extended to including the plastic-hinge concept for elasto-plastic analysis of framed structures. To this end, the rigid body test for initially stressed elements is first briefed, followed by derivation of the tangent stiffness of the 2D elasto-plastic beam element using the initial and full yield surfaces to consider gradual yielding of the cross-section. Of theoretical importance, the tangent and geometric stiffnesses are jointly tested by the rigid body rule for initially stressed elements. The above concepts are contained in the global and local strategies, respectively, for tracing the load–deflection curves and for performing the trial-and-error iterations. The former can deal with the formation of multi plastic hinges, in addition to multi-critical points, whereas the latter is strongly rooted in the rigid body rule and thus is free of fictitious forces (source of slow convergence). The accuracy and efficiency of the solutions obtained are confirmed by comparison with the existing ones. In conclusion, the procedure proposed in its entity makes the elasto-plastic analysis simpler and faster. The more complicated the problem is, the greater the saving in computation time using the proposed procedure. Since only minimal mathematical operations are required, this procedure has the potential of being widely accepted by structural engineers in routine analysis.

In conventional seismic design, the structure is often assumed to be fixed at the base. However, this assumption does not reflect reality. Furthermore, if the structure has close neighbors, the adjacent structures will alter the response of the structure considered. Investigations on soil–structure interaction and structure–soil–structure interaction have been performed mainly using numerical models. The present work addresses the dynamic response of adjacent single-degree-of-freedom models on a laminar box filled with sand. Impulse loads and simulated ground motions were applied. The standalone condition was also studied as a reference case. Models with different fundamental frequencies and slenderness were considered. Results from the impulse tests showed that the top displacement of the models with an adjacent structure was reduced compared with that of the standalone case. Changes in the fundamental frequency of the models due to the presence of an adjacent model were also observed. Results from ground motions showed amplification of the maximum acceleration and the top displacement of the models when both structures have a similar fundamental frequency.

Significant differences between the predicted and measured dynamic response of 3D rigid foundations on multi-layered soils in the time domain were identified due to the existence of uncertainties, which makes the issue a complicated one. In this study, a numerical method was developed to determine the dynamic responses of 3D rigid surfaces and embedded foundations of arbitrary shapes that are bonded to a multi-layered soil in the time domain. First, the dynamic stiffness matrices of the rigid foundations in the frequency domain are calculated via integral domain transformation. Secondly, a dynamic stiffness equation for rigid foundations in the time domain is established via the mixed variables formulation, which is based on the discrete dynamic stiffness matrices in the frequency domain. The proposed method can be applied to the treatment of systems with multiple degrees of freedom without losing the true information that concerns the coupling characteristics. Numerical examples are presented to demonstrate the accuracy of the proposed method for predicting the horizontal, vertical, rocking, and torsional vibrations. Further, a parametric study was carried out to provide insight into the dynamic behavior of the soil–foundation interaction (SFI) while considering soil nonhomogeneity. The results indicate that the elastic modulus of the soil has a significant impact on the dynamic responses of the rigid foundation. Finally, a numerical example of a rigid foundation resting on a six-layered, semi-infinite soil demonstrates that the proposed method can be used to deal with multi-layered media in the time domain in a relatively easy way.

The present paper concentrates on the active control of the static bending and dynamic response of a functionally graded piezoelectric material (FGPM) plate subjected to thermo-electro-mechanical loads. Using the first-order shear deformation theory and Hamilton’s principle, the equation of motion for the FGPM plate is deduced. Based on the smart properties of piezoelectric ceramic, the active control of the static bending and vibration of the FGPM plate is studied by the mechanical load feedback, velocity feedback and LQR control methods in thermal environment. The effects of load parameter, temperature, volume fraction index and feedback control gain on the static bending and dynamic response of the FGPM plate are examined in detail. The simulation results show that the present control method can largely improve both the static and dynamic stability of the FGPM plate.

This paper investigates the lateral buckling of simply supported nonprismatic I-beams with axially varying materials by a novel finite element formulation. The material properties of the beam are assumed to vary continuously through the axis according to the volume fraction of the constituent materials based on an exponential or a power law. The torsion governing equilibrium equation of the simply supported beam with free warping is numerically solved by employing the power series approximation. To this end, all the mechanical properties and displacement components are expanded in terms of the power series to a known degree. Then the shape functions are obtained by representing the deformation shape of the axially functionally graded (AFG) web and/or flanges tapered thin-walled beam in a power series form. At the end, new $4\times 4$ elastic and buckling stiffness matrices are exactly determined from the weak form expression of the governing equation. Three comprehensive examples each of axially nonhomogeneous and homogeneous tapered beams with doubly symmetric I-sections are presented to evaluate the effects of different parameters such as axial variation of material properties, tapering ratio and load height parameters on the lateral buckling strength of the beam. The numerical outcomes of this paper can serve as a benchmark for future studies on lateral-torsional critical loads of AFG beams with varying I-sections.

Principal component analysis (PCA) has been successfully applied in structural dynamics in recent years. However, it is usually used as a black-box, resulting in a gap between the application aspect and the physics essence of the problem. Thus a physical interpretation of PCA is necessary, along with further investigation, especially on the mechanism involved. This paper provides a physical meaning of the PCA by the theoretical analysis and numerical experiment on the vibration of a 1D string. Conditions that make the interpretation feasible were identified. The theoretical derivation and numerical simulation results indicate that the PCA gives a good estimation of the modal participation ratio in terms of energy, and the principal component coefficient (PCC) can be used to estimate the structural modes. The physical interpretation gives a new perspective on how the current methods work while providing the possibility of further application of the PCA related methods to structural dynamic problems.

A footbridge is a structure designed for pedestrians or animals to cross roads, water or railways, safely. Modern ones are designed as slender and light structures to be more aesthetic and economic, but may lack enough stiffness and damping that might produce excessive vibrations under service conditions, overpassing comfort limits for users and compromise structural integrity. This work presents the synthesis of a nonlinear optimal control strategy for reducing vibrations in footbridges by means of using magnetorheological dampers. The proposed optimal controller considers both, the footbridge linear dynamics and the damper nonlinear dynamics, as the complete system to be controlled. For analysis purposes, the continuous structure of a footbridge is conveniently idealized as an $N$-degrees-of-freedom discretized model, such that it can be handled as an $N$-order system. Parameters from an actual footbridge are used to propose a discretized model system of 11 translational degrees of freedom and to analyze the system response as a case study. The dynamical response involves displacement, velocity and acceleration for different number of pedestrians crossing in groups. The investigation rests on comparing the structural response over time for two different conditions: with no control device installed and with one magnetorheological damper installed at the span center. Results obtained with the use of the proposed optimal controller show to be an effective way of reducing the structural motion response.

Operation safety of high-speed trains is dependent on their vibration characteristics, which vary with bridge deformation. This paper studies the influence of bridge pier settlement and girder creep camber, which are two typical types of long-term bridge deformation, on the vibration of high-speed trains. To this end, an analytical approach is presented to link the bridge deformation with railway track deformation; the track deformation is used to analyze the vibration of the CRH2 high-speed train in China. The vibration analysis results are validated using the in-situ measurement data. The present study shows that bridge pier settlement greatly affects the vertical acceleration, derailment coefficient and wheel unloading rate of the high-speed train; incorporating bridge girder camber aggravates the vibration of the train–bridge system. The threshold of bridge pier settlement is suggested to be 11.1mm for trains moving at 350km/h with regard to the code-specified vibration limit. This study has significant implications for the design and operation of high-speed railways.