International Journal of Structural Stability and Dynamics

In this study, the critical load and natural vibration frequency of Euler–Bernoulli single nanobeams based on Eringen’s nonlocal elasticity theory are investigated. Cantilever nanobeams with attached sprung masses were subjected to compressed concentrated and distributed follower forces. The parameter that determines the direction of nonconservative follower forces was given the positive and negative values, therefore, sub-tangential and super-tangential load were analyzed. The stability analysis is based on dynamical stability criterion and was carried out using a numerical algorithm for solving segmental nanobeams with many boundary conditions. The presented algorithm is based on the exact solutions of motion equations which are derived from equilibrium conditions for each separated segment of the nanobeam. Two comparison studies are conducted to ensure the validity and accuracy of the presented algorithm. The excellent agreement of critical load for Beck’s nano-column on Winkler foundation observed was confirmed as reported by other researchers. The effect of different values of the nonlocality parameter, tangency coefficient, spring stiffness coefficient, location of sprung mass and the greater number of attached sprung masses on a critical load of nanobeams compressed by nonconservative load are discussed. One of the presented results shows that significant differences between local and nonlocal theory appear when the beam subjected to follower forces loses its stability by flutter.

The optimal design of inertial amplifier base isolators (IABI) for dynamic response mitigation of multi-storey buildings subjected to base excitations has been studied in this paper. In order to achieve the closed-form expressions for optimal design parameters of IABI, $H_2$ optimization method has been employed. The effectiveness of the closed-form expressions for optimal design parameters was evaluated by determining the isolated structures’ frequency and time domain responses and comparing them to the corresponding responses obtained from equivalent uncontrolled structures. A numerical study employing the Newmark-beta method is conducted to obtain time-domain responses using near-field earthquake base excitation. The response reduction capacity (%) of the optimum inertial amplifier base isolator is compared to the response reduction capacity (%) of the optimum traditional base isolators, demonstrating that inertial amplifiers have increased the vibration reduction performance of traditional base isolators by 50% to 60%. All the outcomes from the study are mathematically accurate and also feasible for practical design purposes.

Due to different settlements of the base, failure of the foundation, etc., the rigid blocks may experience free-standing rocking on a flexible foundation with a slope under excitation. However, the rigid blocks free-standing on a foundation with a slope were not taken into account. A modified concentrated spring model is proposed to simulate the rocking of the asymmetric rigid blocks free-standing on a flexible foundation with a slope in this study. The rocking response of the free-standing rigid block on a flexible foundation with a slope under free vibration, one-sine pulse excitation, and earthquake motions is investigated. It reveals that the rocking response of a rigid block can be influenced by the slope of the flexible foundation and the slenderness of the block. The energy dissipated from the asymmetric block rocking is larger than the energy dissipated from the symmetric block.

The seismic performance of monopiled offshore wind turbine (OWT) structures was evaluated numerically. The aim was to analyze offshore wind farm sites on complicated layered seabed with high seismicity. Following pile soil analysis (PISA) model, three-dimensional (3D) numerical evaluations were undertaken for two separate locations under two independent seismic events. The effects of pile diameter, depth, site impact owing to transverse soil layering, uni-directional and multi-directional seismic loading and seismic acceleration magnitude are presented. Dynamic impedance depth variation and site response analysis via lateral displacement, lateral soil response and Fourier response amplitude are explored in frequency and time domain. In a seismic zone with stratified soil, pile diameter has a greater influence. Variations in soil profile affect wind turbine performance and seismic sensitivity. This research will give a strong platform for later studies to recommend a safe wind farm site based on simulation results.

The parametrically excited instability of the spatially periodic visco-elastomer sandwich plate with supported masses under quadrilateral longitudinal temporal harmonic excitations is studied. The improvability of the parametrically excited instability by periodic distribution parameters is explored. The direct eigenvalue analysis approach for solving the parametrically excited stability problem of the periodic sandwich plate system under longitudinal harmonic excitations is proposed. The spatial periodic distribution of facial layer thickness and core layer modulus of the sandwich plate is considered. The non-linear partial differential equations of longitudinal and transverse coupling motions of the periodic visco-elastomer sandwich plate with supported masses under biaxial longitudinal boundary excitations are derived. The longitudinal displacements of the sandwich plate are separated into two parts and the longitudinal boundary excitations relevant to symmetric part are incorporated into the sandwich plate system. Then the partial differential equations with boundary excitations are converted into parametrically excited system equations and further converted into ordinary differential equations with time-varying parameters, which describe the parametrically excited vibration with multi-mode coupling of the periodic sandwich plate system. The fundamental perturbation solution to the equations is expressed as the product of periodic and exponential parts based on the Floquet theorem. The ordinary differential equations with harmonic parameters are converted into a set of algebraic equations using the harmonic balance method. Then the parametrically excited instability of the periodic sandwich plate system is determined directly by matrix eigenvalues. The overall instability characteristics of parametrically excited vibration with multi-mode coupling of the system under longitudinal harmonic excitations are illustrated by numerical results on unstable regions. The parametrically excited instability can be improved by the spatially periodic distribution of geometrical and physical parameters. The proposed approach is applicable to general sandwich structures with spatial distribution parameters in multi-mode-coupling parametrically excited vibrations for overall instability analysis on continuous frequency band.

Viscous dampers mitigate the interstory drift ratios (IDRs) and peak floor accelerations (PFAs) of buildings subjected to earthquakes. This leads to a multi-objective optimization problem (MOOP) for a viscous damper placement along the building height to minimize IDRs and PFAs simultaneously. This paper proposes innovative methods to address the MOOP and compares those proposed methods to non-dominated sorting algorithm II (NSGA-II) through case studies. Subsequently, the meaning of solutions on the Pareto optimal front in future earthquake events is investigated. The case studies apply each method to a two-dimensional ten-story shear building and adopt four measures to evaluate the performance of searched solutions in multiple aspects. The results show that the proposed methods, by executing fewer number of time history analyses and with convergence comparable to that of NSGA-II, successfully offer improvement against NSGA-II in the aspect of productivity and diversity. As for understanding solutions on the Pareto front in future earthquake events, the knee point solution’s design, which proposed methods can arrive at or approach, successfully reduces both peaks IDR and PFA under 20 ground motions.

The warping effects may predominate in geometrically nonlinear analysis of open cross-section members. The formulation of conventional beam-column elements incorporating the warping effects is cumbersome due to the method considering the inconsistency between the shear center and centroid. To develop a concise warping element formulation, this paper presents a transformation matrix to integrate the inconsistent effects into the element stiffness matrix. The co-rotational (CR) method used to establish the element equilibrium conditions in the geometrically nonlinear analysis is adopted to simplify the element formulation and improve the efficiency of nonlinear analysis. A new beam-column element explicitly considering the warping deformation and the Wagner effects is derived based on the CR method and the Euler–Bernoulli beam theory. A detailed kinematic description is provided for considering large deflections and rigid body motions. Based on the mechanical characteristic, the coordinate and the rigid body motion transformation matrices are given. The secant relationship is developed to evaluate the element internal forces accurately and effectively in each iteration. Several verification examples are provided to validate the proposed method’s reliability and robustness. The verifications demonstrate that the proposed element leads to considerable computational advantages. The results of this paper are useful for future upgrading of frame analysis software with warping degrees-of-freedom (DOFs).

The cables of the long-span bridge are usually featured as ultra-low frequency, hence making the acceleration unable to accurately capture the information, e.g. damping ratios, for assessing the cable state assessment and mitigating the excessive structural vibration. The displacement was approved to be more sensitive to the low-frequency vibration than the acceleration. However, there is still a lack of effective method to accurately monitor the long-term displacements of bridge cables using reference-free methods. To address this issue, this paper develops a novel acceleration-based approach for monitoring the long-term displacements of the cables of long-span bridges. In the monitoring scheme, recursive least squares method is utilized to conduct baseline correction in the time domain integration of acceleration. An adaptive band-pass filtering method considering cable vibration characteristics is used to eliminate noise, thus avoiding the difficulty of selecting the cut-off frequency by experience in traditional methods. A numerical test of an analytical cable model and a field experiment of the hanger of a full-scale suspension bridge are applied to the applicability and robustness of the developed method. Result shows that adaptive band-pass filter considering the vibration characteristics is suitable for estimating the displacements of the cables. The estimated displacements using the developed method agree well with the background truth in both time and frequency domains.

In this study, nonlinear vibration and stability of a pipe conveying fluid, with axially moving supports, immersed in an external fluid is studied. The equation of motion is derived with the aid of the Newtonian method via employing the Euler–Bernoulli beam theory and plug flow assumption. Considering the stretching effect, the nonlinear equation of motion is obtained, and it is discretized via the Galerkin method. Afterward, the stability of the system is investigated using two different approaches, and their results are compared. Numerical simulations show the system has complex dynamic behavior. To unveil the dynamics of the system, various analysis techniques such as bifurcation diagram of Poincaré map, phase portrait, power spectrum, and time trajectories are used. Limit cycle, period-n, quasi-periodic, and chaotic regime are observed. It is found that pipe can flutter around the trivial solution or post-buckling equilibrium points. Moreover, the influences of some system parameters on the chaotic behavior of the pipe are discussed.

The thickness configuration effect on natural frequency and critical speed of spinning variable-thickness cylindrical shells is investigated in this paper. Based on Love’s thin shell theory, the eigenfrequency equation is derived by employing the Rayleigh–Ritz method in conjunction with Chebyshev polynomials, considering the effects of Coriolis and centrifugal forces due to rotation. Seven types of thickness configurations and various classical boundary conditions are taken into account. Backward and forward wave frequencies, the critical speed, and the mode shapes of the spinning variable-thickness cylindrical shells are solved. Results show that the thickness configuration not only changes circumferential wave number corresponding to the lowest natural frequency, but also affects the critical speed. However, the influence of thickness configuration on mode shapes of the shell is not obvious. The stronger the boundary constraints, the more obvious effect of slope of thickness variation on the critical speed of spinning cylindrical shells.

This paper presents a novel strategy for indirectly identifying the natural frequency of a bridge via multiple sensors on an ordinary vehicle. It does not require specifically designed cars or multiple cars as the excitation sources, as many earlier studies have used, but only one normal vehicle, providing practicability. A signal processing method incorporating cross-spectrum estimation can extract the bridge frequency among complex and varied frequency components in the vehicle spectrogram. The bridge natural frequency as a common vibration component among different sensor responses is identified as a clear peak that occurs in the cross-spectrum. The methodology is validated by an experimental study using a steel beam and a scale truck model with an engine to construct the vehicle–bridge interaction system. With this approach, the first mode frequency of the bridge is successfully identified under various bridge conditions. In addition, the performance of the proposed strategy in bridges with and without road roughness is discussed, and the influence of vehicle weight on the success rates of frequency identification is also confirmed.

This study explored the disparities in bending, buckling, and vibration results of ideal and non-ideal functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) beams. The smooth and continuous profiles of material distributions of ideal FG-GPLRC beams were modified for making the controlling tracks to produce two different forms of non-ideal FG-GPLRC beams which had in-and out-stepwise distributions of material constituents across the beam’s thickness. The Halpin–Tsai model and the rule of mixture were used to predict the effective material properties of the nanocomposite beams. The closed-form solution possessing less time of computation was provided for predicting the mechanical behavior of the beams, and it was validated for accuracy by comparing with the results of the Ritz method. The study’s results suggest that non-ideal beams with an out-stepwise distribution of material constituents have a better dispersion of reinforcing nanomaterials than in-stepwise distribution. Therefore, the results of the beams with an out-stepwise distribution are closer to those of ideal beams than with in-stepwise distribution.