Journal of Engineering Mechanics

It is meaningful to develop an accurate universal approach to solve the dynamical characteristic problem of a cable system combined with additional components used in real engineering. A segmented dynamic governing equation is presented for a taut shallow cable supported in the middle by a transverse component. Then, a universal frequency characteristic equation is proposed that considers all the influence factors, including the flexural rigidity, sagging, inclination angle, finite rigidity or damped boundary condition, and the intermediate supporting component. A general numerical solution is presented by giving an analytical derivative expression for the dynamic stiffness of the cable system. As a result, the modal parameters of an arbitrary complicated cable system can be obtained via the root of the equation. Finally, the accuracy of the proposed approach is verified using numerical cases, and its validity is also proved by applying it to case studies of several typical cable systems.

Using cross-ties to connect a vulnerable cable with its neighbor(s) and forming a cable network is a common countermeasure to suppress bridge stay cable vibrations. An effective design of cross-tie solution should provide an optimum combination of cross-tie installation location, stiffness, and number of cross-tie lines to maximize the network in-plane frequency and structural damping while minimizing the number of excited local modes. However, the mechanics associated with cable networks is not as simple as their geometrical appearance. In particular, the addition of an extra line of cross-ties to an existing cable network would considerably increase the complexity of its structural behavior. While the effects of cross-tie position and stiffness on network response have been investigated in some existing studies, that associated with the number of cross-tie lines is scarce. For better understanding of how the dynamic behavior of a group of cables would be influenced when interconnected by different number of cross-tie lines, the current study proposes an analytical model of cable networks consisting of two parallel main cables interconnected by multiple lines of flexible transverse cross-ties. A new parameter, the degree of mode localization (DML), is introduced to quantitatively evaluate the global nature of a network mode. The in-plane modal responses of two cables when interconnected respectively by one, two, and three lines of cross-ties are analyzed and compared. A parametric study is conducted to assess the impact of various system properties on the in-plane frequency and local mode excitation of networks containing different number of cross-tie lines.

A new sampling method on the basis of a distance index and spherical subset simulation is proposed in this paper, with which the samples of uncertain variables are equally generated in the possible domain of uncertain variables and the failure probability is estimated using the concept of conditional probability. Coupling with this new sampling method, two practical procedures are developed for estimating the failure probability: one is a coarse procedure for the analysis of ordinary problems and the other is a refined procedure for the analysis of critical problems. The accuracy and efficiency of the proposed sampling method and procedures for estimating the failure probability are demonstrated through a series of examples. The results show that the proposed approach is valid for general applications and can yield an accurate estimate of the failure probability. The accuracy and efficiency are not influenced by the distribution type of uncertain variables, correlation among uncertain variables, nonlinearity of the performance function, and dimension of uncertain variables.

This study investigates new dynamic scaling laws of geometrically distorted models in predicting the dynamic characteristics of a cantilever plate. The significance of this study is to provide new scaling laws and rules for selecting dynamic scaling laws, which guide the design of distorted models. By considering the size effect of different orders’ vibration, a governing equation and the method of sensitivity analysis are employed to establish dynamic scaling laws between the model and the prototype. Both approximate and accurate scaling laws are investigated and the processes for determining these scaling laws are summarized. After that, a commonly used titanium alloy plate is analyzed as a prototype to compare the accuracy of the approximate scaling laws and the accurate scaling laws. Finally, the applicability of these new scaling laws is validated by experimental data. The results indicate that, by using the new scaling laws, the distorted models can predict the characteristics of the titanium alloy plate prototype with good accuracy.

This paper introduces structural identification using expectation maximization (STRIDE), a novel application of the expectation maximization (EM) algorithm and approach for output-only modal identification. The EM algorithm can be used to estimate the maximum likelihood parameters of a state-space model. In this context, the state-space model represents the equation of motion for a linear dynamic system. STRIDE is an iterative procedure that uses Kalman filtering and Rauch-Tung-Striebel (RTS) smoothing equations to produce estimates of the unobserved states; these calculations are based on the observed data and prior estimates of the state-space parameters. With this information, the conditional likelihood of the model is maximized and the state-space parameters are updated at each iteration. Once an iteration meets user-prescribed convergence criterion, the algorithm ends—yielding maximum likelihood estimates (MLE) for the state-space model parameters. The modal properties of the structure are then extracted from these MLE. The performance of STRIDE is compared in detail with eigenvalue realization algorithm-natural excitation technique (ERA-NExT) and eigenvalue realization algorithm-observer Kalman filter identification of output-only systems (ERA-OKID-OO) identification algorithms in the analyses of ambient vibration data from the Northampton Street Bridge and Golden Gate Bridge, both collected using a dense wireless sensor network. A computational comparison shows that STRIDE provides a successful identification at a significantly lower model order than ERA-NExT, ERA-OKID-OO, or auto-regressive (AR), simultaneously requiring fewer cumulative floating point operations than ERA-OKID-OO in both applications.

The stiffness and strength of a composite structure formed by a slab and an underlying beam made of different materials strongly depends on the shear coupling at their interface, which in general is not perfect because of the compliance of the shear connectors. The proposed approach interprets the effects of this partial interaction by establishing an equivalence, in terms of stress and deflection, with a composite beam with perfect shear bonding, but with a slab of smaller effective width. The method relies upon the minimization of the strain energy functional within a restricted class of shape functions for the deformation, finding the best approximation intermediate between the two limit cases of frictionless sliding and perfect shear coupling. If the response of the connectors is linear elastic, a simple formula is reached to calculate the effective width of the slab as a function of the static scheme and of the mechanical and geometrical properties. If the response is nonlinear, as it is in practice, the effective width is found by solving an algebraic equation, whose coefficients also depend on the magnitude of the applied load. Comparisons with numerical experiments confirm the very good accuracy of the proposed approach.

The aim of the study is to investigate the influence of pore structure on acoustic absorption of porous asphalt concrete (PAC) and to obtain the optimum pore structure for achieving the maximum acoustic absorption capacity. The Zwikker and Kosten model for rigid-framed porous materials was implemented with transfer-matrix method to predict the acoustic absorption coefficient of PAC considering the idealized pore structure parameters (pore radius, pore length, and porosity). The predicted results were compared with experimental measurements reported in the literature, and the model was validated. Sensitivity analysis was conducted to evaluate the influences of pore structure parameters on acoustic absorption spectra of PAC. The results show that an increase in pore radius can reduce acoustic absorption. Increasing porosity results in a reduction of acoustic absorption but an increase in the frequency range where the maximum acoustic absorption occurs. Conversely, increasing pore length (as an indication of PAC layer thickness) causes the maximum absorption occurring in the lower frequencies. Simulated annealing (SA) algorithm was developed to determine the optimum pore structure for improving sound absorption performance of PAC considering different tire-pavement noise generation mechanisms. The application of acoustic absorption model along with the optimization algorithm provides a useful tool for guiding mix design of PAC in terms of acoustic performance.

This study examined the vibrations of a hinged-free nonlinear beam placed on a nonlinear elastic foundation. The authors found that specific combinations of an elastic modulus in the elastic foundation resulted in 1:3 internal resonances in the first and second modes of the beam. This prompted adding a dynamic vibration absorber (DVA) on the elastic beam in order to prevent internal resonance and suppress vibrations. When the DVA was placed at the free end of the beam, the boundaries were time dependent. Thus, a shifting polynomial function was used to convert the nonhomogeneous boundary conditions into homogeneous boundary conditions. The authors analyzed this nonlinear system using the method of multiple scales (MOMS). Fixed-point plots were also used to facilitate the observation of internal resonance. This made it possible to study the influence of nonlinear geometry and nonlinear inertia associated with the vibration of the elastic beam. The authors also examined the combination of optimal mass ratio and elastic modulus for the DVA in order to prevent internal resonance and achieve optimal damping effects. In the nonlinear beam investigated in this study, the placement of a DVA between $0.25l$ and $0.5l$ from the hinged end of the beam proved the most effective for damping; locations between $0.7l$ and $0.8l$ on the beam were ineffective. Finally, numerical methods and simple experiments were studied to compare the results from MOMS and demonstrate the effects of the DVA of this model.

A model is proposed to represent nonstationary fluctuating winds based on the concept of instantaneous power spectrum representation and amplitude modulation to model the fluctuating winds with time-varying mean wind speed. This results in the nonstationary fluctuating winds at a point to be characterized by a power spectral density function with a frequency modulation; it is proposed and shown that the frequency modulation can be assigned based on a time transformation defined through a dimensionless distance traveled by the winds that is calculated using the mean wind speed. In essence, nonstationary fluctuating winds are obtained by mapping the stationary fluctuating winds through a nonlinear time transformation and by applying an amplitude modulation. The proposed model is employed to simulate nonstationary winds for parametric investigation of the peak displacement of linear and nonlinear inelastic single-degree-of-freedom systems. It is shown that a structure designed by neglecting ductility capacity and/or for stationary winds of 10 to 60 min has an unaccounted capacity to sustain nonstationary winds with a maximum mean wind speed that can be much greater than that for stationary winds. The use of the proposed model to represent the incoherent nonstationary fluctuating wind fields is also explored. An illustrative example focused on the fluctuating downburst winds at a few points within the downburst wind field is presented.

The present paper deals with the reflection of three-dimensional plane waves at a traction-free boundary of a self-reinforced medium under initial stresses. The analytical expressions of all three phase velocities of quasi-compressional (qP), quasi-shear (${\mathrm{qS}}_1$ and ${\mathrm{qS}}_2$) waves in three dimensions under initial stresses have been obtained. The closed form expressions for the amplitude ratios of reflection coefficients of the three quasi waves in a self-reinforced medium in terms of the phase velocity, propagation vector, initial stresses, and the stiffness coefficients of the medium have also been obtained. The variations of reflected coefficients with the angle of incidence have been carried out numerically, and the results are given in the form of graphs.

Frequency domain analysis of a dynamical system yields the response spectral density. There are many spectral fatigue methods for evaluating the mean fatigue damage from a stress spectrum, but they are only approximate. The only accurate method is to simulate the time history from the spectrum, succeeded by rainflow counting. However, this procedure is time-consuming because of the need for numerous realizations to achieve statistical convergence, making it incompatible with the high efficiency of frequency domain analysis. To overcome the slow convergence rate of conventional Monte Carlo simulation (MCS), this paper proposes an efficient simulation approach, which to date, appears to be the first of its kind for such an application. The proposed approach reduces the variance of the fatigue damage samples by invoking the technique of importance sampling, and entails only the coefficient of variation (CoV) of the damage to construct the importance sampling density. The CoV can be estimated initially using an analytical approach, and subsequently updated adaptively. The proposed approach is implemented on a diversity of spectral shapes, and is found to provide a substantial computational advantage over MCS.

An exact solution is established pertaining to the problem of undamped free vibration of a thin circular plate resting on a Winkler foundation with variable subgrade modulus. The solution is performed by applying the infinite power series method. Moreover, the solution procedure is demonstrated through an illustrative example, wherein the general frequency equation is derived for two different boundary conditions. The correctness of the solution is also verified using results available in the literature. Finally, it is shown that the proposed method of solution is directly applicable to the more-general problem of circular plates on a variable-modulus Pasternak-type foundation.

In this work, the nonlinear flexural behavior of laminated carbon/epoxy composite panels is investigated numerically using a generalized nonlinear mathematical model based on two higher-order shear deformation midplane kinematics and Green-Lagrange type geometrical nonlinearity. The exact flexural behavior of the laminated panel is computed by considering all the nonlinear higher order terms in the present mathematical model. The nonlinear governing equations are obtained using variational principles and discretized through suitable finite-element steps. The desired nonlinear responses are computed numerically using the direct iterative method. The proposed nonlinear models have been validated by comparing the responses with those available in published literature and the experiment (three-point bend test) as well. In addition, the linear and nonlinear flexural responses of the laminated carbon/epoxy flat panel are also computed using ANSYS 13.0 simulation finite element analysis package. Finally, the efficacy and applicability of the proposed models have been checked by solving some numerical examples for different geometrical parameters (thickness ratio, aspect ratio, curvature ratio, and constraint condition) and discussed in detail. The practical importance of the proposed nonlinear higher-order theory for the laminated structure is highlighted by comparing the linear and nonlinear responses with experimental (three-point bend test) and simulation results.

To reasonably determine the limit equilibrium zone width, a coal pillar was simplified as a half-infinite load-bearing beam while its weak floor rock mass was assumed to be a continuous elastic foundation according to the mechanical characteristics of the coal pillar. This paper develops the Winkler elastic foundation beam model of a coal pillar under high bearing pressure using the elastic foundation beam analytic method. Furthermore, the deflection, diversion, bending moment, and shear force at any interface of the coal pillar are studied based on a mechanical model of the coal pillar under different bearing pressures. A theoretical calculation formula for the width of the limit equilibrium zone of the coal pillar is put forward under conditions where a shear slip appears on the elastic–plastic interface of the coal pillar. The results show that the limit equilibrium zone width of the coal pillar is closely related to the buried depth of the roadway, volumetric weight of the overburden, the stress concentration factor, the width of the elastic zone, the elastic characteristic value of the floor, the lateral pressure coefficient, the cohesive force, and the internal friction angle on the elastic-plastic interface of the coal pillar. Taking an 850–875 m section of the transport gateway of the 13503 face in a Wangcun coal mine as an example, the theoretical limit equilibrium zone width of the coal pillar is calculated after the other parameters were determined. On this basis, the deformation and failure of the coal pillar in a range of 6 m is tested using a borehole scope. The theoretical width of the limit equilibrium zone of the coal pillar is almost consistent with the results of the field test.

A new type of concrete, named metaconcrete, has been developed for the attenuation of shock waves induced by dynamic excitation. Inspired by the metamaterials used for the manipulation of electromagnetic and acoustic waves, this new metamaterial for the mitigation of shock waves utilizes the activation of resonance within engineered inclusions. Metaconcrete replaces the standard stone and gravel aggregates of regular concrete with spherical inclusions consisting of a heavy core coated in a compliant outer layer. Finite-element analyses of metaconcrete slabs for the case of purely elastic constituents reveal trapping of the supplied energy within the inclusions and a reduction in mortar stress, indicating the presence of resonance behavior within the aggregates. Mortar is, however, a brittle material and the fracture properties under dynamic loading should also be considered. Thus, the models used in the elastic analyses are extended by incorporating brittle fracture through the use of an eigenerosion scheme, which erodes elements satisfying an energy-based fracture criterion. The effect of different fracture parameters on the performance of the slab is investigated through parametric studies, looking at the change in slab behavior caused by various aggregate geometry and material configurations. These studies indicate that mechanical energy is captured by the aggregates, reducing the transmission of energy through the slab, the extension of the zone damaged by fracture, and the longitudinal stress within the mortar matrix. The understanding gained from these analyses incorporating fracture characteristics will enable more informed design of metaconcrete aggregates for dynamic loading applications, such as blast shielding and impact protection.

Modeling of water flow in the propagating cracks plays an important role in the stability analysis of concrete dams. The water pressure within concrete cracks is a function of water permeability of the crack. In this paper, a partially saturated finite-element algorithm is used for numerical modeling of water pressure within a propagating cohesive crack. In order to calculate fracture opening along the crack path suitably, a trilinear cohesive law is considered to describe mechanical behavior of the fracture process zone. The zero-thickness cohesive interface elements are used to capture the mixed-mode fracture behavior in tension and compression. On the basis of the experimental data, it is shown that a unified formula for natural fractures permeability can suitably describe the permeability of a propagating crack in both cases of slow and fast loading rates.