International Journal of Structural Stability and Dynamics

This paper is concerned with the vibration of a heavy string tethered to a mass–spring system which is a model for tower crane or gantry crane. The governing equation of motion of the aforementioned problem is solved analytically and exact closed-form characteristic solutions for the natural frequencies are presented. These exact solutions would serve as benchmarks for models which may be more complex than the basic vibration problem considered. Moreover, we investigate the effect of the string-mass pendulum as a flexible dynamic vibration absorber. Such a problem is important in vibration control, and is investigated analytically for the first time. It is found that the effect of the bottom mass is to decrease the amplitude of the string in general. The effect of increased forcing frequency increases the number of nodal points on the string. In most cases, the amplitude of the top mass is reduced.

This paper presents the dynamic modeling of a piezolaminated plate considering geometrical nonlinearities. The piezo-actuator and piezo-sensor are connected via proportional derivative feedback control law. The Hamilton’s principle is used to extract the strong form of the equation of motion with the reflection of the higher order strain terms by means of the strain–displacement relationship of the von Karman type. Then the nonlinear partial differential equation (PDE) obtained is converted to a nonlinear algebraic equation by employing the combination of harmonic balance method and single-mode Galerkin’s technique. Finally, the vibration suppression performance and sensitivity of the dynamic response is evaluated for various control parameters and magnitudes of external disturbance.

Herein, the static and dynamic pull-in instabilities of nanotweezers and nanoswitches fabricated from conductive cylindrical nanowires are studied. A bilayer model based on the Gurtin–Murdoch surface elasticity and the consistent couple stress theory is developed to incorporate the coupled effects of surface energy and microstructure phenomenon. The differential quadrature method is employed to solve the nonlinear governing equation of the system. The effects of various parameters on the static and dynamic pull-in parameters and stability threshold of the nanostructures are demonstrated.

This paper studies the size-dependent dynamic behavior of electrostatically actuated microaccelerometers using the modified couple stress theory. The device is modeled as a cantilevered microbeam with an electrostatically actuated proof mass attached to its free end. The equation of motion is derived based on the Hamilton’s principle and solved both numerically (using the finite element and finite difference methods) and analytically (using the perturbation technique) and the dynamic response and pull-in instability of the device is studied. The results of these methods are compared and the source of error in the analytical results at high values of external acceleration is discussed. Furthermore, the results are compared with those evaluated based on the classical theory. It is found that for cantilevered accelerometers with a beam thickness of the order of the material length scale parameter, the classical theory gives a rough estimation of the dynamic response of the system. In this situation, the error of using the classical theory may change the prediction of the system behavior from unstable to stable.

A comparative study is carried out on the performance of various elastomeric and frictional base isolation (BI) systems in the vibration mitigation of structures subjected to underground blast induced ground motion (BIGM). The parametric sensitivities of the base isolated structures to variations in the design parameters of the isolators are examined for different intensities of blast input. Results indicate that substantial reductions in both the acceleration and displacement responses of the structure can be achieved by the different base isolators. Generally, the Electricite de France (EDF) base isolator produces higher peak response reductions. However, peak bearing displacements are also largest here. The pure friction (P-F), resilient-friction base isolator (R-FBI) and friction pendulum (FP) systems produce lower values of response reductions but peak bearing displacements as well as residual displacements of isolators are also low. The New Zealand (N-Z) system provides good response reductions with a low to moderate value of peak bearing displacement. The present study indicates how a proper selection of the type of BI system with suitable design parameters can mitigate structural vibration due to different intensities of BIGM and restrict the unwanted characteristics of large isolator displacement and its permanent deformation.

The nonlinear behavior of space structures has been researched by various authors using the total and updated Lagrangian formulations. In this paper, a corotated-updated Lagrangian (CR-UL) formulation is used for studying the postbuckling behavior of steel reticulated systems. This formulation is used since space truss elements contain large components of rigid body displacements. The global tangent stiffness is derived from the corotation (CR) principle and the local (natural) tangent stiffness is derived using the updated Lagrangian (UL) finite element formulation. A state determination procedure is used for including the inelastic behavior with mixed hardening. Here members are assumed to reach the material strength limit state, which is reasonable in large span space structures based on serviceability governed design, with no consideration made for member buckling. The effect of bolt slip in the member joints is included by using a sudden slip model under the service loads. The global nodal displacements and coordinates are updated based on the analytical model of the bolt slip displacement using a simple affine transformation. The effect of bolt slip on the global displacements and member forces has been studied and compared with the results of previous authors.

The objective of this paper is to develop a finite element modeling procedure that is accurate for tackling vehicle–track interaction problems. This procedure enables us to compute the transient response of the vehicle when it accelerates over the track from rest and to investigate the applicability of using the vehicle response for identifying the foundation stiffness variation of railway tracks. To this end, a left half-infinite element, a general element subjected to a moving vehicle, other general elements under no vehicle, and a right half-infinite element were assembled to simulate an infinite beam on a viscoelastic foundation subjected to a moving vehicle. The system governing equations were solved by the Newmark average acceleration method to obtain the responses of rail and vehicle. First, a proper model discretization was investigated by comparing finite element results with available analytical solutions to constantly moving load, mass, or vehicle problems. Next, the dynamic response of the vehicle was explored when the vehicle accelerated from rest along the track. It was found that the initial response of the vehicle was influenced by boundary conditions in the model where the vehicle started to accelerate. Finally, the dynamic responses of the vehicle passing a healthy track and damaged tracks where foundation stiffness loss occurs were simulated. The results showed that the changes in the acceleration response of the unsprung mass of the vehicle due to the foundation stiffness loss can be used as an effective indicator for detecting the damage location, level and extent.

The modal analysis of rotating cantilevered rectangular Mindlin plates with variable thickness is studied. The Ritz method is used to derive the governing eigenfrequency equation by minimizing the energy functional of the plate. The admissible functions are taken as a product of the Chebyshev polynomials multiplied by the boundary functions, which enable the displacements and rotational angles to satisfy the geometric boundary conditions of the plate. The Chebyshev polynomials guarantee the numerical robustness, while the Ritz approach provides the upper bound of the exact frequencies. The effectiveness of the present method is confirmed through the convergence and comparison studies. The effects of the dimensionless rotational speed, taper ratio, aspect ratio and thickness ratio on modal characteristics are investigated in detail. The frequency loci veering phenomenon along with the corresponding mode shape switching is exhibited and discussed.

This paper studies the vibration of a nonlinear 3D-string fixed at both ends and supported by a nonlinear elastic foundation. Newton’s second law is adopted to derive the equations of motion for the string resting on an elastic foundation. Then, the method of multiple scales (MOMS) is employed for the analysis of the nonlinear system. It was found that 1:3 internal resonance exists in the first and fourth modes of the string when the wave speed in the transverse direction is $a_2\approx 101.5$ and the elasticity coefficient of the foundation is $k_y=9{\pi }^4$. Fixed point plots are used to obtain the frequency responses of the various modes and to identify internal resonance through observation of the amplitudes and mode shapes. To prevent internal resonance and reduce vibration, a tuned mass damper (TMD) is applied to the string. The effects of various TMD masses, locations, damper coefficients ($g_s$), and spring constants ($f_s$) on overall damping were analyzed. The 3D plots of the maximum amplitude (3D POMAs) and 3D maximum amplitude contour plots (3D MACPs) are generated for the various modes to illustrate the amplitudes of the string, while identifying the optimal TMD parameters for vibration reduction. The results were verified numerically. It was concluded that better damping effects can be achieved using a TMD mass ratio $m_D=0.3$–0.5 located near the middle of the string. Furthermore, for damper coefficient $g_s=0.9$, the use of spring constant $f_s=9$–13 can improve the overall damping.

Based on the dynamic theory of flexible multi-body systems, a nonlinear dynamic model is established of a long shaft rotor system with a stabilized elastic bearing located along the shaft at an arbitrary position by the generalized Hamilton’s principle. Lower-order polynomials are adopted to construct the Ritz basis for investigating the first two vibration frequencies and the critical rotational velocity, as well as the optimal stabilized position of the elastic bearing. The critical rotational velocity and optimal stabilized position of the elastic bearing are also verified by the finite element method. The results obtained by the two methods agree well. Then, the post-buckling and the nonlinear vibration responses of the system fluctuating at the rotational velocity are investigated. The present study indicates that critical rotational velocity exists for the long shaft rotor system with stabilized elastic bearing. Once the rotational velocity exceeds the critical value, the system’s trivial equilibrium state losses its stability by pitchfork bifurcation. The optimal stabilized position of the elastic bearing for the long shaft rotor system is located at 73% length of the shaft from the pinned end. When in the supercritical state, the system changes to different vibration modes with local period-1 solutions and global period-2 solutions around the post-buckling position due to fluctuation of the rotational velocity. Furthermore, the global period-2 vibration may evolve to the almost periodic motion as the fluctuation frequency varies. This study provides a theoretical basis for understanding the geometrical nonlinear effect and vibration modes of the long shaft rotor system working in the supercritical state.

Excessive floor vibrations in slender structural systems due to human activity are becoming more prevalent. This may result in serviceability problems such as discomfort to occupants and even subsequent public panic. This paper describes the experimental and analytical studies on the vibration performance of a long-span pre-stressed cable RC truss (PCT) floor system, along with an extensive comparison between the present results and the current vibration design criteria used in the USA and China. The dynamic responses of this floor system under heel-drop, falling-into-seats, and jumping loads were obtained through on-site tests. The test results show good agreement in natural frequencies of the PCT floor system with others, but there are obvious differences in peak accelerations and damping ratios. A method based on the classical plate theory was adopted to determine the fundamental frequency of the system. Dynamic magnification factors (DMFs) under different loads were calculated using the inversion technique and then compared with the results available from others. Some of the conclusions achieved may be incorporated into the structural design of the system of concern to improve safety and serviceability. They can also serve as the basis for developing the relevant design guideline.

To investigate the elastic buckling behavior of self-anchored suspension bridges subjected to proportionally increasing dead loads, a new stability procedure is proposed based on the deflection theory. For this purpose, a finite element buckling analysis is performed using the initial state solution based on the unstrained length method (ULM) (Ref. ). The finite element solutions are compared with those by the deflection theory. It is shown that both the main girder and tower of the self-anchored suspension bridge are under compression, but their fundamental buckling modes are tower-dominant. Importantly, it is observed that local buckling within the main girder supported by hangers occurs without any geometric change of the main cable, in the higher buckling modes of the self-anchored suspension bridge.

The vibration analysis of composite pipes with internal wall defects due to erosion-induced surface degradation is investigated. The surface defects are treated as discontinuities. The geometry of the discontinuity is permitted to vary within the cross-section both in the angular and radial directions, and to occupy any length of the pipe span. A B-spline wavelet-based finite element method (BWFEM) that takes advantage of the localization properties of wavelets is invoked; thus utilizing its effectiveness in modeling of crack problems and local damages. The composite pipe was treated as beam elements that obey the Euler–Bernoulli beam theory. Unlike the conventional finite element method (FEM), the developed BWFEM uses fewer elements without compromising the accuracy. Numerical simulations are performed to demonstrate the accuracy and efficiency of the developed element through comparison with available results in the literature, as well as results obtained using ANSYS. Some benchmark solutions are obtained for the composite pipe with internal surface defects of different geometries.

A hybrid analytical and numerical method is presented for the mid-frequency vibration analysis of a class of plate structures with discontinuities based on the concept of structural partitioning. The type of structures considered includes rectangular plates with internal property discontinuity, homogeneous but non-rectangular plates, or built-up structures composed of rectangular homogenous plates with complex joints. Compared with the conventional finite element (FE) method, the present method has the advantage of high accuracy and high efficiency in the analysis of mid-frequency vibration of the structures of concern. The main idea of the proposed approach is to divide the whole structure into uniform rectangular plate regions and other non-rectangular regions. The vibration behavior of the rectangular regions is accurately and efficiently described by analytical wave solutions so that the FE modeling for these regions is not necessary. The other non-rectangular regions are modeled by the conventional FE method. The analytical waves used to describe the rectangular regions are obtained by the symplectic method, thereby avoiding the limitation of the conventional analytical method in dealing with plates having two opposite edges simply supported. By enforcing the displacement continuity and force equilibrium at the connection interfaces, the dynamic coupling is established between the rectangular regions described in terms of the analytical waves and the regions modeled by FEs. Furthermore, the hybrid solution formulation for the mid-frequency vibration of the entire structure is proposed. The high accuracy and efficiency of the present method are demonstrated by several numerical examples, with the effect of element size of the FE regions investigated. Finally, the applicability of the proposed method is analyzed.

A simply supported reinforced concrete (RC) beam only experiences sagging moment under static loads while it might experience both sagging and hogging moments under impact loads due to the inertial effect. In order to investigate inertial effect on the impact behavior of RC beam, a numerical model is developed by using the finite element code LS-DYNA. The strain rate effect of the material is considered in the numerical model. The numerical model is calibrated with the testing results of drop weight impact on RC beams available in the literature. The numerical results show that the prediction is better than some other researchers’ predictions in terms of peak impact force and peak deformation. In addition, inertial effect is quantitatively evaluated by the peak impact force and the peak hogging moment. The relationship between the peak hogging moment and the peak impact force of the beam is investigated by conducting parametric studies with regard to various net spans, impact masses and impact velocities. The empirical formulae are then proposed to predict the peak impact force and the peak hogging moment. The predications by the proposed empirical formulae are compared with the testing results and the predicted results by other formulae available in the literatures.

Design guidelines for implementing viscous dampers to buildings have been broadly included in seismic design codes worldwide. Although the relationship between the damping coefficient of viscous dampers and the added damping ratio to the structure has been theoretically studied, the process of distributing the damping coefficient onto each story of a building has not been regulated by the codes. For practical applications, some distribution methods have been previously proposed. However, no comparison has been made between these proposed methods considering the controllability and design economy. In this paper, two search methods based on the genetic algorithms (GAs) are adopted to examine the optimal distribution of damping coefficients. The results are then compared with a variety of existing distribution methods. A comparison is made for the distribution methods assuming the same added damping ratio for the structure. Three two-dimensional frames are adopted in the comparison: a regular moment frame, a moment frame with a soft-story, and a setback building. The results indicated that similar seismic response reduction can be achieved by using different distribution methods if the supplemental damping ratio is the same, while the optimal story damping coefficient can be obtained by using the proposed optimization method. Moreover, the “story shear strain energy to efficient stories” (SSSEES) method, among others, offers advantages in terms of seismic reduction efficiency, economical design, and practical application simplicity.