International Journal of Structural Stability and Dynamics

Laminated plates are loading-bearing components that are generally connected to flexible pads and exhibit complicated mechanical responses. To investigate the geometrically nonlinear transient responses of a laminated plate with flexible pad supports, a varied constraint reaction model and a systematic numerical procedure are presented in this paper. The flexible pad supports of the plate were treated as viscoelastic boundary conditions, wherein the strip-type pad per unit length was modeled as a cantilever beam. The nonlinear Kelvin–Voigt model was developed to simulate the nonlinear viscoelastic behaviors of the flexible pads. The dynamically varied constraint reactions generated by the viscoelastic supports, which depend upon the displacement and velocity of the nodes along the plate edge, were determined by the deflection and slope equations of the beam theory used, and they were applied on the plate edges by using the nonlinear load functions. Thus, the dynamical responses of the laminated plate with viscoelastic supports were obtained. Numerical results show that the present method can effectively treat the geometrically nonlinear transient response of the laminated plate with viscoelastic supports, and it is essential to consider the effects of non-ideal boundary conditions in the nonlinear transient analysis.

The majority of the existing damage diagnostic techniques are based on linear models. Changes in the state of the dynamics of these models, before and after damage in the structure based on the vibration measurements, are popularly used as damage indicators. However, the system may initially behave linearly and subsequently exhibit nonlinearity due to the incipience of damage. Breathing cracks that exhibit bilinear behavior are one such example of the damage induced due to nonlinearity. Further many real world structures even in their undamaged state are nonlinear. Hence, in this paper, we present a nonlinear damage detection technique based on the adaptive Volterra filter using the nonlinear time history response. Three damage indices based on the adaptive Volterra filter are proposed and their sensitiveness to damage and noise is assessed through two numerically simulated examples. Numerical investigations demonstrate the effectiveness of the adaptive Volterra filter model to detect damage in nonlinear structures even with measurement noise.

The continuously variable transmission (CVT) is one of the prevailing automotive transmissions. Nowadays, the most popular design is Van Doorne's CVT with single metal pushing V-belt. However, it is only applicable to low-power passenger cars because of its low torque capacity. To overcome this limitation of traditional single-belt Van Doorne's CVT, this research proposes a novel parallel Van Doorne's dual-belt CVT system which can be applied to heavy-duty vehicles. As the first attempt, an analytical model for both torque capacity and power efficiency based on effective radii instead of traditional working radii for the single-belt CVT is developed for this novel CVT system, and this newly developed model is experimentally validated. Evaluation result reveals that the new analytical model based on effective radii is more accurate than that based on working radii. Experimental and simulation results show that the proposed dual-belt CVT system can greatly improve the torque capacity as compared with the single-belt CVT. Moreover, the newly proposed analytical model can provide a foundation for further study of multi-belt CVTs.

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z${}^{\prime }$Y${}^{\prime }$X${}^{\prime }$. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

We present an analytical procedure for the exact, explicit construction of Euler–Bernoulli beams with given values of the first $N$ buckling loads. The result is valid for pinned–pinned (P–P) end conditions and for beams with regular bending stiffness. The analysis is based on a reduction of the buckling problem to an eigenvalue problem for a vibrating string, and uses recent results on the exact construction of Sturm–Liouville operators with prescribed natural frequencies.

This paper presents experimental, analytical and numerical investigations about the flexural behavior of glass fiber reinforced polymer (GFRP) pultruded panels for footbridge decks. The analyzed panels, made of isophthalic polyester and E-glass fibers, comprise a multicellular thin-walled cross-section with panel-to-panel vertical snap-fit connections at their lateral edges. As part of a comprehensive study about the mechanical and structural behavior of this type of footbridge decks, the experimental study presented here addresses: (i) the mechanical characterization of the laminated material, and (ii) the quasi-static flexural behavior of the panels for both service and failure conditions. The experimental data obtained is used to validate and assess the accuracy of three-dimensional shell finite element (FE) models and analytical formulae. Particular focus is given to the serviceability and failure performance of the panels, in terms of their deformability and susceptibility to buckling phenomena, respectively. Regarding the serviceability behavior, the results obtained in this study demonstrate the importance of duly specifying the shear coefficient of the multicellular cross-section on Timoshenko beam theory, in order to obtain accurate deflection predictions. In terms of failure performance, both the flexural tests and the analytical formulae indicate that the local buckling of the compressive flanges seems to have triggered the collapse of the tested panels, thus limiting their load carrying capacity. The geometrically nonlinear FE analyses allowed understanding in further depth the ultimate behavior of the panels, providing further insights about their failure mechanisms.

This study proposes a single degree of freedom nonlinear oscillator to model the lateral movement of the body center of mass of a pedestrian walking on a flat rigid surface. Experimentally recorded ground reaction force of a dozen of pedestrians in the lateral direction is used to develop the model. In detail, the hardening and softening effects are observed in the stiffness curve as well as higher odd harmonics are present in the frequency spectrum of the lateral force signals. The proposed oscillator is a modification of the Rayleigh and the Van der Pol oscillators with additional nonlinear softening and hardening terms. To obtain an approximation of the limit cycle of the oscillator and its stability, two methods are studied: the energy balance method and the Lindstedt–Poincare perturbation technique. The experimental force signals of pedestrians at four different walking speeds are used for the identification of the values of the model parameters. The results obtained from the proposed model show a good agreement with the experimental ones.

This paper introduces a new shell element formulation and investigates the buckling behavior of thin-walled beams composed of fiber-reinforced polymer composite-laminates, which is a primary design concern for thin-walled beams composed of fiber-reinforced polymer composite-laminates due to their slenderness. Although global buckling behavior can be captured using beam-column type two-node simple finite element formulations, shell-type more sophisticated elements are needed in order to be able to capture the effects due to cross-sectional deformations. Pursuit of an efficient shell element formulation continues to date and in this study, a new flat rectangular shell element formulation is developed for the buckling analysis of thin-walled composite-laminated members. The plate component of the shell is locking-free and based on the twist-Kirchhoff theory. For the membrane component of the shell element, variational formulation employing drilling degrees of freedom is adopted. Convergence studies were presented to illustrate the numerical performances of the element. A broad class of problems including distortional as well as global buckling cases were solved and compared with solutions from the literature to validate the use of the developed shell element for the buckling analysis of thin-walled composite-laminated members.

Dynamic stochastic stability of a two-degree-of-freedom gyroscopic system under bounded noise parametric excitation is studied in this paper through moment Lyapunov exponent and the largest Lyapunov exponent. A rotating shaft subject to stochastically fluctuating thrust is taken as a typical example. To obtain these two exponents, the gyroscopic differential equation of motion is first decoupled into Itô stochastic differential equations by using the method of stochastic averaging. Then mathematical transformations are used in these Itô equation to obtain a partial differential eigenvalue problem governing moment Lyapunov exponents, the slope of which at the origin is equal to the largest Lyapunov exponent. Depending upon the numerical relationship between the natural frequency and the excitation frequencies, the gyroscopic system may fall into four types of parametric resonance, i.e. no resonance, subharmonic resonance, combination additive resonance, and combination differential resonance. The effects of noise and frequency detuning parameters on the parametric resonance are investigated. The results pave the way to utilize or control the vibration of gyroscopic systems under stochastic excitation.

Modern slender structures such as long-span floors and cantilever stands are sensitive to jumping-induced vibrations. A conventional deterministic Fourier series model for the human jumping load may overestimate a structure's responses in resonance condition. This paper suggests a power spectral density (PSD) function for the individual jumping load, which was treated as a narrowband stationary stochastic process. Experiments were conducted on individual jumping loads resulting in 334 records from 73 subjects. Statistical analysis of the records led to experimental PSD curves on which a symmetrical bilinear function was suggested. The proposed PSD function is centered on the given jumping frequency and its integer multiples. The function's parameters were determined by equating the total energy of the proposed PSD with that of the experimental PSD. Application of the proposed PSD for predicting a floor's peak response via the stochastic vibration theory was then presented. The predictions for an experimental floor model subjected to individual jumping were compared with the measured peak responses. The comparisons demonstrated that the proposed PSD function was applicable for predicting the floor's response to individual jumping. Finally, the framework for calculating crowd-induced structure vibrations using the suggested PSD was also discussed.

In this paper, the free vibration analysis of non-uniform rotating Euler–Bernoulli beam is carried out. It is assumed that the beam has exponentially decaying circular cross-section. In order to solve the problem, the differential transform method (DTM) is utilized. Based on our knowledge, we claim that the recurrence relation presented herein is an elaborate recurrence relation which has been obtained for ordinary differential equations. Non-dimensional natural frequencies of the beam are obtained and tabulated for different values of the beam parameters such as taper ratio and rotating speed. Furthermore, the finite element method (FEM) is employed to solve the problem. Comparison of the results obtained by DTM and FEM indicates the accuracy of proposed solutions.

In 2004, Yang and co-workers proposed the extraction of bridge frequencies from the dynamic response of a moving test vehicle [Y. B. Yang, C. W. Lin and J. D. Yau, Extracting bridge frequencies from the dynamic response of a passing vehicle, J. Sound Vib. 272 (2004) 471–493] and verified the technique by a field test [C. W. Lin and Y. B. Yang, Use of a passing vehicle to scan the bridge frequencies — An experimental verification, Eng. Struct. 27(13) (2005) 1865–1878]. This technique was extended to construction of mode shapes [Y. B. Yang, Y. C. Li and K. C. Chang, Constructing the mode shapes of a bridge from a passing vehicles: A theoretical study, Smart Struct. Syst. 13(5) (2014) 797–819] and damage identification of bridges. It was referred to as the indirect method for bridge measurement because no vibration sensors are needed for installation on the bridge, but it only requires one or few vibration sensors on the test vehicle. When compared with the conventional direct method that relies fully on the response of the bridge fitted with vibration sensors, the advantage of the indirect method is clear: mobility, economy, and efficiency. Over the past years, many research studies were conducted along the lines of the indirect method for bridge measurement. Significant advances have been made on various aspects of application. This paper represents a state-of-the-art review of the related research works conducted worldwide. Comments and recommendations will be made at proper places, while concluding remarks including future research directions will be presented at the end of the paper.

The research reported herein follows the increased interest in buckling-induced functionality for novel materials and devices with a focus on cylindrical shells as a suitable structural prototype. The paper proposes the concept of using patterned thickening patches on the surface of cylindrical shells to modify and control their elastic postbuckling response. Cylindrical shells with non-uniform thickness distributions (NTD) were fabricated through 3D printing to understand rules for pattern designs and then tested under loading-unloading cycles. Strategic thickening patches act as governing imperfections that modify the response type, the number, the location and the sequence of the localized buckling events. The use of patterned thickening patches and their layout provides diverse design opportunities for a desired elastic postbuckling response and can be potentially used in design materials and structures with switchable functionalities.

An energy-based solution is developed for the lateral torsional buckling (LTB) analysis of wooden beams with flexible mid-span lateral bracing offset from section mid-height and subjected to uniformly distributed or mid-span point load. The study shows that such beams are prone to two potential buckling modes; symmetric or anti-symmetric. The symmetric mode is shown to govern the capacity of the beam for low bracing stiffness while the anti-symmetric mode governs the capacity when the bracing stiffness exceeds a threshold value. Using the present formulation, the threshold bracing stiffness required to suppress the symmetric mode and maximize the critical moments is directly obtained by solving a special eigenvalue problem in the unknown bracing stiffness. The technique thus eliminates the need for trial and error in standard solutions. A parametric study is conducted to investigate the effect of bracing height, load height, and bracing stiffness on the critical moments. A large database of runs is generated and used to develop simple expressions for determining the threshold bracing stiffness required to maximize the elastic LTB resistance.

Tuned mass dampers (TMDs) have been widely used to suppress or absorb vibration. Optimum tuning of the TMD parameters using metaheuristic algorithms demands numerous numerical analyses which is a tedious and time-consuming task. Recent advances in data processing systems have attracted great attention towards the creation of intelligent systems to evolve models in engineering applications. The present paper implements the least squares support vector machine (LS-SVM) to build up models which predict the optimum TMD parameters. The performance of the proposed models is largely dependent on the quantity and the accuracy of databases used for training the models. Therefore, a wide-range numerical tuning of the TMD system, attached to a single-degree-of freedom (SDOF) main system, is done using a novel metaheuristic algorithm, called the cuckoo search (CS), to obtain the tuning frequency and damping ratio of the TMD system for a main system subjected to three types of excitations: external white-noise force, harmonic base acceleration and white-noise base acceleration. The superior performance of the LS-SVM models in prediction of optimum TMD parameters is proved in comparison to other studies in the literature. Furthermore, it is found that the optimum TMD parameters are not influenced by the predominant frequency of the filtered white-noise excitation.

Collapse of transmission towers due to downbursts is often initiated by local failure of key structural members, while the local failure of key structural members is related to local material and geometrical nonlinearities. This paper presents a multi-scale finite element (FE) model for the failure analysis of transmission towers under downburst-induced wind loading. The potential local failure areas of the tower are modeled by shell or solid elements, and the remaining parts by beam elements. In this way, the failure of the tower can be accurately simulated on the one hand and the computational effort can be reduced on the other hand. This paper first introduces how to determine the downburst-induced wind loading on transmission towers. Both the conventional beam and multi-scale FE models of the transmission tower are then developed and used in the failure analysis. A comparison of the failure results obtained by the two FE models show that the multi-scale FE model can effectively simulate the stress concentration of angle members around the bolt connections and the cross-section plastic collapse of key structural members, leading to a different failure pattern for the tower from the conventional FE method. It is suggested that the multi-scale FE model should be used for better accuracy in the failure analysis of transmission towers under downburst loading.

In this study, nonlinear dynamics and vibrations of a mass, spring and damper system with constant and variable velocities have been investigated. One end of the large-sag cable is fixed and the other one can be varied using different heights with respect to the first end. The oscillator can be accelerated by the tangential component of the weight force. The governing equations of motion are derived with regard to the mutual influence of the cable movement and vertical motion of attached mass. The Galerkin’s method is employed in the displacement field in conjunction with the average acceleration method in the time domain to solve the governing equations. The parametric study is performed on the vertical movement of the oscillator, the displacement of the cable and the velocity of the moving oscillator.