A symmetric substructuring method for analyzing the natural frequencies of conical origami structures

Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness.

A substructure approach for analyzing pile foundation and soil vibrations due to train running over viaduct and its validation

An efficient computational approach based on substructure methodology is proposed to analyze the viaduct-pile foundation-soil dynamic interaction under train loads.Thetrain-viaductsubsystemissolvedusingthe dynamic stiffness integration method,and its accuracy is verified by the existing analytical solution for a moving vehicle on a simply supported beam.For the pile foundation-soil subsystem,the geometric and material properties of piles and soils are assumed to be invariable along the azimuth direction.By introducing the equivalent stiffness of grouped piles,the governing equations of pile foundation-soil interaction are simplified based on Fourier decomposition method,so the three-dimensional problem is decomposedintoseveraltwo-dimensionalaxisymmetricfinite element models.The pile foundation-soil interaction model is verified by field measurements due to shaker loading at pile foundation top.In addition,these two substructures are coupled with the displacement compatibility condition at interface of pier bottom and pile foundation top.Finally,the proposed train-viaduct-pile foundation-soil interaction model was validated by field tests.The results show that the proposed model can predict vibrations of pile foundation and soil accurately,thereby providing a basis for the prediction of pile-soil foundation settlement.The frequency spectra of the vibration in Beijing-Tianjin high-speed railway demonstrated that the main frequencies of the pier top and ground surface are below 100 and 30 Hz,respectively.

Numerical Analysis of a Gravity Substructure for 5 MW Offshore Wind Turbines Due to Soil Conditions

In order to increase the gross generation of wind turbines, the size of a tower and a rotor-nacelle becomes larger. In other words, the substructure for offshore wind turbines is strongly influenced by the effect of wave forces as the size of substructure increases. In addition, since a large offshore wind turbine has a heavy dead load, the reaction forces on the substructure become severe, thus very firm foundations should be required. Therefore, the dynamic soil-structure interaction has to be fully considered and the wave forces acting on substructure accurately calculated. In the present study, ANSYS AQWA is used to evaluate the wave forces. Moreover, the substructure method is applied to evaluate the effect of soil-structure interaction. Using the wave forces and the stiffness and damping matrices obtained from this study, the structural analysis of the gravity substructure is carried out through ANSYS mechanical. The structural behaviors of the strength and deformation are evaluated to investigate an ultimate structural safety and serviceability of gravity substructure for various soil conditions. Also, the modal analysis is carried out to investigate the resonance between the wind turbine and the gravity substructure.

Velocity plus displacement equivalent force control for real-time substructure testing

This paper employs a velocity plus displacement（V＋D）-based equivalent force control（EFC） method to solve the velocity/displacement difference equation in a real-time substructure test. This method uses type 2 feedback control loops to replace mathematical iteration to solve the nonlinear dynamic equation. A spectral radius analysis of the amplification matrix shows that the type 2 EFC-explicit, Newmark-β method has beneficial numerical characteristics for this method. Its stability limit of Ω = 2 remains unchanged regardless of the system damping because the velocity is achieved with very high accuracy during simulation. In contrast, the stability limits of the central difference method using direct velocity prediction and the EFC-average acceleration method with linear interpolation are shown to decrease with an increase in system damping. In fact, the EFC-average acceleration method is shown to change from unconditionally stable to conditionally stable. We also show that if an over-damped system with a damping ratio of 1.05 is considered, the stability limit is reduced to Ω =1.45. Finally, the results from an experiment with a single-degree-of-freedom structure installed with a magneto-rheological（MR） damper are presented. The results demonstrate that the proposed method is able to follow both displacement and velocity commands with moderate accuracy, resulting in improved test performance and accuracy for structures that are sensitive to both velocity and displacement inputs. Although the findings of the study are promising, additional test data and several further improvements will be required to draw general conclusions.

Vibration suppression of composite panel with variable angle tow design and inerter-based nonlinear energy sink

This study investigates the vibration transmission and suppression of a laminated composite panel with variable angle tow(VAT)designs and an attached inerter-based passive nonlinear energy sink.Based on analytical and numerical methodologies,the substructure technique is used to obtain a steady-state dynamic response and the results are verified by experimental and analytical methods.It is demonstrated that fiber orientation has a significant impact on the natural frequencies.The dynamic responses and energy transmission path characteristics are determined and evaluated by forced vibration analysis.The main vibration transmission paths inside the structure are displayed using power flow density vectors.It is demonstrated that the dynamic responses of the plate can be changed considerably by using various fiber placement schemes and passive suppression devices.In addition,it is indicated that the vibration transmission paths are significantly influenced by the tailored fiber angles for improved dynamic performance.Our investigation enhances the understanding of enhanced vibration suppression designs of variable-stiffness composite plates with attached passive devices.

An Iterative Domain Decomposition Algorithm for the Grad(div)Operator

This paper describes an iterative solution technique for partial differential equations involving the grad(div)operator,based on a domain decomposition.Iterations are performed to solve the solution on the interface.We identify the transmission relationships through the interface.We relate the approach to a Steklov-Poincare operator,and we illustrate the performance of technique through some numerical experiments.