Journal of Engineering Mechanics

This paper presents an experimental study and theoretical analysis on the penetration behavior of a tungsten-alloy long-rod projectile into a concrete target with an impact velocity ranging from 900 to $\mathrm{1,700}\mathrm{m}/\mathrm{s}$. Different penetration regimes are investigated in the experiment in order to have a better understanding of the penetration mechanism of tungsten-alloy projectiles with different impact velocities. The state of the projectiles during penetration and damage parameters of residual projectile and targets are analyzed. Penetration models during abrasion and deforming stages are modified by taking into account of the coupling effects of abrasion, deforming, and shape evolution. Furthermore, the model during the eroding penetration stage is improved to describe the penetration process by considering shape evolution and deforming characteristics of the projectiles. Finally, the improved models are validated against the corresponding experimental results. The results indicate that the crater depth, diameter, and volume of a target are proportional to the impact velocity and impact kinetic energy, separately. The abrasion and deformation of the projectile have a great influence on its penetration process, which cannot be ignored. The calculated depth of penetration (DOP) with different velocities is well-correlated with the experimental results. Residual projectile after erosion penetration still has a greater penetration ability to the concrete target and contributes a larger proportion in the penetration depth.

This work presents an experimental study performed to investigate the effect of the size of the specimen on the fracture response of geometrically similar concrete notched beams. To the best of the authors’ knowledge, this study is the largest of its kind and includes beams of five different sizes. Twenty-eight beams were tested using a three-point bending (TPB) test setup designed according to draft guidelines. Five depths $D$, namely, 75, 150, 250, 500, and 1,000 mm, were considered, and the width $b$ was kept constant and equal to 150 mm for all specimens. A new setup is proposed for large specimens. Load responses, peak loads, failure modes, fracture energy, and size-effect analysis are presented and discussed.

In this paper, a meshless method for analyzing the elastodynamic behavior of two-dimensional problems is introduced. The nonsingular method of fundamental solutions (NMFS) is combined with the method of particular solutions. To overcome singularities arising from point-shaped sources, a technique known as the boundary distributed source (BDS) method is used, which involves distributing sources across disks centered on the boundary. The NMFS is regarded as a mesh-free boundary method due to source point independence to the neighboring source details. The dual reciprocity method (DRM) with a suitable approximation is used to obtain the particular solution corresponding to the nonhomogeneous inertial term; moreover, added benefits of eliminating domain integration and readiness for computer algorithms anchor desirability. Cautious investigation of solutions to various numerical examples using DRM reinforces reliability and accuracy. Finally, the study comprehensively examines factors such as the number of collocation points, internal points, the radius of the circular disk, and the time-step size to assess their impact on achieving convergence.

Based on the principle of parallel connection of positive and negative stiffness structures, a new quasizero stiffness (QZS) isolation device is proposed in which the negative stiffness structure is designed by a nonlinear precompressed spring system. The mechanical model of the device is dimensionless, and the parameter conditions required to achieve QZS at the static equilibrium position are derived. The agreement between the theoretical mechanical model and the experimental mechanical model of the device is further verified by static experiments. The dynamic model of the QZS system is investigated by using the approximate analytical and numerical methods of nonlinear vibration, which reveals the influence of the device parameters on its nonlinear dynamic characteristics and vibration isolation performance. Shaking table test were conducted to compare and analyze the dynamic response characteristics and isolation performance of the QZS system with the equivalent linear system. The results showed that the new device can effectively extend the isolation frequency range, reduce the isolation amplitude, and have good isolation performance.

This paper presents the application of nonlinear Bayesian filtering–based system identification (SI) methods when employed to estimate the parameters of stochastic fractional dynamic systems. The objective is to demonstrate the capabilities and limitations of time-domain stochastic filtering–based SI for systems endowed with fractional derivative elements when the estimation is performed under different operating conditions. The conditions include measured forcing inputs (input-output identification), stochastic/unmeasured forcing inputs (output-only identification), and different types of measurements and levels of measurement noise, in the context of both linear and hysteretic fractional oscillators. The accuracy and estimation error of three methods was studied, namely, the unscented Kalman filter, the ensemble Kalman filter, and the particle filter. Baseline results that can be applied to the modeling, identification, and control of fractional structural and mechanical systems are provided. It is shown that nonlinear Bayesian filtering methods have the capability to accurately estimate the response and parameters of fractional oscillators, and that the coefficient and order of fractional elements are observable/identifiable from output response measurements.

The variational asymptotic method (VAM) was used to analyze the deformation behavior of bidirectional functionally graded material (FGM) beams under transverse loading. Gradation was provided in the longitudinal as well as along the transverse direction of the beam. A number of gradation models available in the literature of FGMs were considered to derive the closed-form analytical solutions for various field variables, including Timoshenko-like shear deformations. A bidirectionally graded cantilever beam with a point load at the end was considered to verify the analytical results against finite-element analysis (FEA) solutions. Further, verification of the analytical results was also done against the available results in the literature for varied loading and boundary conditions. Application of VAM to this problem resulted in simpler governing equations and associated boundary conditions, thereby enabling closed-form analytical solutions without considering any ad hoc or a priori assumptions.

A finite element is developed for a piezoelectric beam theory whose displacement varies according to the Timoshenko assumption, and the electric potential varies quadratically through each piezoelectric patch thickness. The application of Gauss’s law to patches in the sensing mode is treated as a constraint in order to eliminate electric degrees of freedom from the weak form of the problem and, thus, formulate a two-node element with the same degrees of freedom as its purely mechanical counterpart (i.e., two displacements and one rotation per node). As a result, the element can be easily included in any computer program by simply replacing the existing purely mechanical element with this piezoelectric one. Since the approximation space is the same as that of the general homogeneous solution of the piezoelectric beam theory, the element enjoys the superconvergence property and is completely free of locking. Simple numerical tests on linear static problems are presented to demonstrate the ability of the element to give exact nodal values for the displacements, rotations, and reactions, irrespective of the mechanical and electrical loadings applied and mesh used. Also, the ability of a postprocessing scheme, which is set up to recover the exact sensing voltages at the nodes, is demonstrated. The element is further employed in shape-control problems.

Wind-induced vibration has become increasingly prominent for long-span bridges. Flutter instability, as a type of divergent vibration, is a key component in the wind resistance investigation of long-span bridges. Based on the principle of instantaneous power balance (IPB) of the flutter critical state of bridge girders, an algorithm for predicting the flutter critical wind speed of long-span bridges was proposed by utilizing a nonlinear optimization strategy. For the bending–torsional coupling two-dimensional (2-D) motion system, the contribution of the wind-induced self-excited and structural elastic forces of the 2-D bridge section to the energy of the system was revealed to be dependent on some key parameters, such as reduced frequency, wind speed, amplitude ratio, and phase lag between vertical and torsional motions. Therefore, according to the principle of IPB during the critical flutter state, the prediction of flutter onset wind velocity can be transformed into an extreme value optimization problem of the IPB objective function. The feasibility and accuracy of the IPB algorithm were verified by comparing them with those obtained from segmental model wind tunnel tests and previous 2-D flutter prediction algorithms. Compared with the traditional methods characterized by force balance, the proposed method clearly and quantitatively presents the contribution relationship among multiple self-excited aerodynamic components on the flat plate and bridge section while flutter occurs; the method first evaluates the flutter critical state as an alternative algorithm from an energy perspective.