Kinematic and Static Solutions for Beam Column with Nonlinear Springs Using the Extended Linear Matching Method

In this paper, the kinematic and static solutions for solving the static response of the beam column with nonlinear springs are presented by adopting the extended linear matching method (LMM). The extended LMM can be used to predict the displacement response of the beam-column system consisting of perfectly plastic and strain-softening materials. It is found that the kinematic solution generated by the extended LMM demonstrates a monotonic decrease for perfect plastic materials with certain restrictions on the yield surface. The potential energy of the system is proved to decrease with iterations for both perfect plastic and strain-softening materials if the loading multiplier remains constant. The extended LMM method is then applied to analyse the response of the pile system in a 3-leg offshore platform. An incremental procedure is recommended to determine the peak load for the soil exhibiting strain-softening. A displacement-control approach is used with the loading multiplier obtained from the variation of the potential energy. Good convergence of the method is obtained.

Constitutive Modeling of the Densification Behavior in Open-Porous Cellular Solids

The macroscopic mechanical behavior of open-porous cellular materials is dictated by the geometric and material properties of their microscopic cell walls. The overall compressive response of such materials is divided into three regimes, namely, the linear elastic, plateau and densification. In this paper, a constitutive model is presented, which captures not only the linear elastic regime and the subsequent pore-collapse, but is also shown to be capable of capturing the hardening upon the densification of the network. Here, the network is considered to be made up of idealized square-shaped cells, whose cell walls undergo bending and buckling under compression. Depending on the choice of damage criterion, viz. elastic buckling or irreversible bending, the cell walls collapse. These collapsed cells are then assumed to behave as nonlinear springs, acting as a foundation to the elastic network of active open cells. To this end, the network is decomposed into an active network and a collapsed one. The compressive strain at the onset of densification is then shown to be quantified by the point of intersection of the two network stress-strain curves. A parameter sensitivity analysis is presented to demonstrate the range of different material characteristics that the model is capable of capturing. The proposed constitutive model is further validated against two different types of nanoporous materials and shows good agreement.

Semi-Analytical Model to Predict the Elastic Post-buckling Response of Axially Compressed Cylindrical Shells with Tailored Distributed Stiffness

This study introduces an approximate analytical model to predict the post-buckling response of cylinders with tailored nonuniform distributed stiffness. The shell's wall thickness, and thus its stiffness, is tailored so as to obtain multiple controlled elastic local buckling events when the cylinder is subjected to uniform axial compression. The proposed model treats cylinder segments of different stiffness as individual panels and combines their response by considering them as connected linear or nonlinear springs. The governing equations for the panels are formulated using von Karman's theory and solved by Galerkin's approximate method for a predefined radial deformation. Radial deformation functions are used to improve the model's accuracy and results show that the model's accuracy increases significantly with the number of considered radial functions. The model's predicted axial response for different cylinders are compared to results from experiments on 3D printed samples. Results indicate that this model accurately predicts the order of the buckling events while the buckling forces from the model are higher than those measured experimentally.

Analysis of Two-Dimensional Nonlinear Sloshing in a Rectangular Tank by Using a Concentrated Mass Model

Major problems can occur when liquid sloshes in a tank, such as occurs in liquid storage tanks during an earthquake, and this is an important engineering problem to address. To analyze this phenomenon, semi-analytical methods such as the perturbation method, the multimodal method, and the finiteelement method are generally used. However, semi-analytical methods involve quite complicated equations, and the finite-element method involves many degrees of freedom when the tank is large. In this paper, a nonlinear numerical model with relatively few degrees of freedom is established for vertical and horizontal two-dimensional nonlinear sloshing in a rectangular tank excited horizontally. The model comprises concentrated masses of liquid connected by nonlinear springs and dampers. The connecting springs have characteristics based on the static and dynamic pressures of the liquid. In addition, a method is proposed for reducing the number of degrees of freedom in the two-dimensional model. The natural frequencies, modes, and frequency responses are then compared among the concentrated-mass model, theoretical calculations, and experimental results. Good agreement was achieved among them, thus demonstrating the validity of the model.

Frequency-Adaptable Tuned Mass Damper Using Metal Cushions

A frequency-adaptable tuned mass damper (FATMD) using metal cushions as tuneable stiffness components is presented. The dynamic properties of the cushions with respect to stiffness and damping are investigated experimentally in this context. The natural frequency of the experimental FATMD is found to be dependent on the precompression of the metal cushions, which behave like nonlinear springs, yielding an adjustable frequency range from 67 to 826 Hz. As the precompression is increased, the stiffness increases while the damping characteristics decrease, the effect of which was quantified using a viscous mass damper model as a first approximation. Measurements have been carried out under five different excitation amplitudes to investigate the amplitude dependency of the resonance frequency. The FATMD was largely unaffected by changes in input amplitude. It was concluded that metal cushions show great potential for use in FATMDs, surpassing the utility of elastomers, especially with respect to their temperature stability.

Nonlinear vibration of a lumped system with springs-in-series

The paper deals with the dynamics of a lumped mass mechanical system containing two nonlinear springs connected in series. The external harmonic excitation, linear and nonlinear damping are included into considerations. The mathematical model contains both differential and algebraic equations, so it belongs to the class of dynamical systems governed by the differential–algebraic system of equations (DAEs). An approximate analytical approach is used to solve the initial value problem for the DAEs. We adopt the multiple scales method (MSM) that allows one to obtain the sufficiently correct approximate solutions both far from the resonance and at the resonance conditions. The steady and non-steady resonant vibrations are analyzed by employing the modulation equations of the amplitudes and phases which are yielded by the MSM procedure.

Analysis of RC Deep Beams Considering the Shear Deformations and Bar-concrete Interaction

In this paper, reinforced concrete (RC) deep beams (DBs) have been analyzed numerically and a new approach is proposed to the nonlinear numerical modeling of such structural members. The effect of shear deformations and the interaction between reinforcing steel bar and concrete are considered in modeling and analysis. In order to consider the effect of shear deformations, the Timoshenko beam theory has been applied to formulate the analysis method. In the modeling, the RC DB is divided into several sub-elements which are composed of concrete and reinforcing steel bars. Individual degrees of freedom have been assigned to each reinforcing steel bar. Thus, each reinforcing steel bar is able to slip relative to its surrounding concrete and the bond effect is simulated by nonlinear springs. To consider the interaction between reinforcing steel bar and concrete, the concrete segment acts as a beam element, and each reinforcing steel bar acts as a truss element. The reliability of this method has been confirmed by comparing the obtained results from the numerical analysis and the results of the experimental pushover test.

Performance of An Electromagnetic Energy Harvester with Linear and Nonlinear Springs under Real Vibrations

The introduction of nonlinearities into energy harvesting in order to improve the performance of linear harvesters has attracted a lot of research attention recently. The potential benefits of nonlinear harvesters have been evaluated under sinusoidal or random excitation. In this paper, the performances of electromagnetic energy harvesters with linear and nonlinear springs are investigated under real vibration data. Compared to previous studies, the parameters of linear and nonlinear harvesters used in this paper are more realistic and fair for comparison since they are extracted from existing devices and restricted to similar sizes and configurations. The simulation results showed that the nonlinear harvester did not generate higher power levels than its linear counterpart regardless of the excitation category. Additionally, the effects of nonlinearities were only available under a high level of acceleration. The paper also points out some design concerns when harvesters are subjected to real vibrations.