Towards a Unified Single Analysis Framework Embedded with Multiple Spatial and Time Discretized Methods for Linear Structural Dynamics

We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple subdomains.This is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework.In the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange multiplier.However,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the subdomains.By selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given simulation.The method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great flexibility.The accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for general linear dynamics through numerical examples.

Structural Dynamics of 3-Dimethylamino-2-methyl-propenal in S2（ππ^＊） State

The photophysics of 3-dimethylamino-2-methyl-propenal （DMAMP） after excitation to the S2 （ππ^＊） electronic state was studied using the resonance Raman spectroscopy and complete active space self-consistent field method calculations. The transition barriers of the ground state tautomerization reactions between DMAMP and its three isomers were determined at B3LYP/6-311＋＋G（d,p） level of theory. The vibrational spectra were assigned. The A- band resonance Raman spectra were obtained in acetonitrile with excitation wavelengths in resonance with the first intense absorption band to probe the structural dynamics of DMAMP. The B3LYP-TD computation was carried out to determine the relative A-band resonance Raman intensities of the fundamental modes, and the result indicated that the vibronic-coupling existed in Franck-Condon region. Complete active space self-consistent field （CASSCF） calculations were carried out to determine the excitation energies of the lower-lying singlet and triplet excited states, the conical intersection points and the intersystem crossing points. The A-band short-time structural dynamics and the corresponding decay dynamics of DMAMP were obtained by analysis of the resonance Raman intensity pattern and CASSCF computations. It was found that a sudden de-conjugation between C1=O6 and C2=C3 occurred at the Franck-Condon region of the S2（ππ^＊） state, while the enhancement of the conjugation interaction between C3 and N（CH3）2, and between C1 and C2 evolutions shortly after the wavepacket leaves away the Pranck-Condon region via the excited state charge redistribution. The de-conjugation interaction between C1=O6 and C2=C3 made the rotation of C3=N（CH3）2 group around the C2-C3 bond much easier, while the enhanced conjugation between C1 and C2, and between C3 and N（CH3）2 made the rotation around the C1-C2 bond and C3-N5 more difficult. It was revealed that the initial structural dynamics of DMAMP was predominantly towards the CI-I（S2/S0） point, while the opportunities towards either CI-2（S2/S0） or CI-3（S2/S0） point were negligible. Two decay channels of DMAMP from S2,FC（ππ^＊） to So or Tl,min via various CIs and ISCs were proposed.

Structural Dynamics of Phenyl Azide in Light-Absorbing Excited States： Resonance Raman and Quantum Mechanical Calculation Study

The excited state structural dynamics of phenyl absorbing S2（A＇）, S3（A＇）, and S6（A＇） states were troseopy and complete active space self-consistent and the UV absorption bands were assigned on azide （PhN3） after excitation to the light studied using the resonance Raman specfield calculations. The vibrational spectra the basis of the Fourier transform （FT）- Raman, FT-infrared measurements, the density-functional theory computations and the normal mode analysis. The A-, B-, and C-bands resonance Raman spectra in cyclohex- ane, acetonitrile, and methanol solvents were, respectively, obtained at 273.9, 252.7, 245.9, 228.7, 223.1, and 208.8 nm excitation wavelengths to probe the corresponding structural dynamics of PhN3. The results indicated that the structural dynamics in the S2 （A＇）, S3（A＇）, and S6（A＇） states were significantly different. The crossing points of the potential energy surfaces, S2S1（1） and S2S1（2）, were predicted to play a key role in the low-lying excited state decay dynamics, in accordance with Kasha＇s rule, and NT=N8 dissociation. Two decay channels initiated from the Franck-Condon region of the S2（A＇） state were predicted： the radiative S2,min→S0 radiative decay and the S2→S1 internal conversion through the crossing points S2S1 （1）/S2S1（2）.

SENSITIVITY ANALYSIS BASED ON LANCZOS ALGORITHM IN STRUCTURAL DYNAMICS

The sensitivity calculating formulas in structural dynamics was developed by utilizing the mathematical theorem and new definitions of sensitivities. So the singularity problem of sensitivity with repeated eigenvalues is solved completely. To improve the computational efficiency, the reduction system is obtained based on Lanczos vectors. After incorporating the mathematical theory with the Lanczos algorithm, the approximate sensitivity solution can be obtained. A numerical example is presented to illustrate the performance of the method.

PGA and structural dynamics input motion at a given site

The computation of the representative ground motions,to be used as input for the dynamic analyses of a struc- ture at a particular site,can be approached by several methods.The choice of the approach depends on two factors:the da- ta available and the type of problem to be solved.This paper reports the experience of the authors in approaching a specific case study:the Southern Memnon Colossus,located in Luxor,Egypt.The results are of interest when the hazard analysis estimation in developing countries and the safeguard of cultural heritage are concerned.Monuments have to be treated as important structures,due to their historical and economical value.Hence,standard procedures of probabilistic seismic haz- ard analysis for the seismic classification of common buildings have to be disregarded.On the other hand,the consequences of the collapse of a monument are not comparable to those related to structures such as nuclear power plants and large dams, for which the deterministic seismic hazard analysis provides a straightforward framework for evaluation of the worst case ground motions.An'intermediate'approach,which requites a lower amount of input data with respect to the deterministic one,is adopted.Its stochastic component can eapture significant eharacteristics of earthquakes,primarily the frequency contents which depend on the magnitude(often referred to as the earthquake scaling law).

Ultrafast Infrared Spectroscopic Study of Microscopic Structural Dynamics in pH Stimulus-Responsive Hydrogels

Hydrogels show versatile properties and are of great interest in the fields of bioelectronics and tissue engineering.Understanding the dynamics of the water molecules trapped in the three-dimensional polymeric networks of the hydrogels is crucial to elucidate their mechanical and swelling properties at the molecular level.In this report,the poly(DMAEMA-co-AA)hydrogels were synthesized and characterized by the macroscopic swelling measurements under different pH conditions.Furthermore,the microscopic structural dynamics of pH stimulus-responsive hydrogels were studied using FTIR and ultrafast IR spectroscopies from the viewpoint of the SCN-anionic solute as the local vibrational reporter.Ultrafast IR spectroscopic measurements showed the time constants of the vibrational population decay of SCN-were increased from 14±1 ps to 20±1 ps when the pH of the hydrogels varied from2.0 to 12.0.Rotational anisotropy measurements further revealed that the rotation of SCNanionic probe was restricted by the three-dimensional network formed in the hydrogels and the rotation of SCN-anionic probe cannot decay to zero especially at the pH of 7.0.These results are expected to provide a molecular-level understanding of the microscopic structure of the cross-linked polymeric network in the pH stimulus-responsive hydrogels.

A time integral formulation and algorithm for structural dynamics with nonlinear stiffness

A newly-developed numerical algorithm, which is called the new Generalized-α （G-α） method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zero- stable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.

HOMOTOPY SOLUTION OF THE INVERSE GENERALIZED EIGENVALUE PROBLEMS IN STRUCTURAL DYNAMICS

The structural dynamics problems,such as structural design,parameter identification and model correction,are considered as a kind of the inverse generalized eigenvalue problems mathematically.The inverse eigenvalue problems are nonlinear.In general,they could be transformed into nonlinear equations to solve.The structural dynamics inverse problems were treated as quasi multiplicative inverse eigenalue problems which were solved by homotopy method for nonlinear equations.This method had no requirements for initial value essentially because of the homotopy path to solution.Numerical examples were presented to illustrate the homotopy method.

Review on the Theories and Applications of Dynamic Condensation and Component Mode Synthesis Methods in Solving FEM-based Structural Dynamics

The rapid development of modern science,technology,and industrialization has promoted the birth of more large and complex engineering structures.When the finite element(FE)method is used for dynamic analysis of these structures,such as high-rise buildings,aircraft,and ships,the structural FE models often contain millions of degrees of freedom.This will lead to great hardware and computing costs,which is often unacceptable in the engineering field.Therefore,many FE model reduction technologies have been developed,among which dynamic condensation and component mode synthesis are the most widely used methods.This paper reviews the historical processes and general theoretical framework of these two main categories of FE model reduction technologies and briefly summarizes the latest applications of these methods in the engineering field.Current bottlenecks in dynamic condensation and component mode synthesis methods,as well as solutions found in literature,are also briefly discussed.Finally,this paper gives a conclusion and brief prospects for future research.This review aims to comprehensively introduce the two most widely used methods of FE model reduction technologies and hopes to provide suggestions and guidance for developing new model reduction technologies.

Steroid hormone receptors and prostate cancer： role of structural dynamics in therapeutic targeting

Steroid hormone receptors （SHRs） act in cell type- and gene-specific manner through interactions with coregulatory proteins to regulate numerous physiological and pathological processes at the level of gene regulation. Binding of steroid receptor modulator （SRM） ligand leads to allosteric changes in SHR to exert positive or negative effects on the expression of target genes. Due, in part, to the fact that current SRMs generally target ligand binding domain （LBD）/AF2 and neglect intrinsically disordered （ID） N-terminal domain （NTD）/AF1, clinically relevant SRMs lack selectivity and are also prone to the development of resistance over time. Therefore, to maximize the efficacy of SHR-based therapeutics, the possibility of developing unique modulators that act to control AF1 activity must be considered. Recent studies targeting androgen receptor＇s （AR＇s） ID AF1 domain for the castration-resistant prostate cancer has provided the possibility of therapeutically targeting ID NTD/AF1 surfaces by allosteric modulations to achieve desired effects. In this review article, we discuss how inter- and intra- molecular allosteric regulations controlled by AR＇s structural flexibility and dynamics particularly the ID NTD/AF1 is an emerging area of investigation, which could be exploited for drug development and therapeutic targeting of prostate cancer.

Structural ensemble dynamics based closure model for wall-bounded turbulent flow

Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics （SED）, which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations （DNS）. Computational results show that the new closure model reproduces accurately the solution of the original Navier-Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions.

An Educational GUI-Based Software for Dynamic Analysis of Framed Structural Models

This paper introduces a new version of the open-source educational software, LESM (Linear Elements Structure Model), developed in MATLAB for structural analysis of one-dimensional models such as frames, trusses, and grillages. The updated program includes dynamic analysis, which incorporates inertial and damping effects, time-dependent load conditions, and a transient solver with multiple time integration schemes. The software assumes small displacements and linear-elastic material behavior. The paper briefly explains the theoretical basis for these developments and the reorganization of the source code using Object-Oriented Programming (OOP). The updated Graphical User Interface (GUI) allows interactive use of dynamic analysis features and displays new results such as animations, envelope diagrams of internal forces, phase portraits, and the response of degrees-of-freedom in time and frequency domain. The new version was used in a structural dynamics course, and new assignments were elaborated to improve students’ understanding of the subject.

A strategy for lightweight designing of a railway vehicle car body including composite material and dynamic structural optimization

Rolling stock manufacturers are finding structural solutions to reduce power required by the vehicles,and the lightweight design of the car body represents a possible solution.Optimization processes and innovative materials can be combined in order to achieve this goal.In this framework,we propose the redesign and optimization process of the car body roof for a light rail vehicle,introducing a sandwich structure.Bonded joint was used as a fastening system.The project was carried out on a single car of a modern tram platform.This preliminary numerical work was developed in two main steps:redesign of the car body structure and optimization of the innovated system.Objective of the process was the mass reduction of the whole metallic structure,while the constraint condition was imposed on the first frequency of vibration of the system.The effect of introducing a sandwich panel within the roof assembly was evaluated,focusing on the mechanical and dynamic performances of the whole car body.A mass saving of 63%on the optimized components was achieved,corresponding to a 7.6%if compared to the complete car body shell.In addition,a positive increasing of 17.7%on the first frequency of vibration was observed.Encouraging results have been achieved in terms of weight reduction and mechanical behaviour of the innovated car body.

ACG-TypeMethod for InverseQuadratic Eigenvalue Problems in Model Updating of Structural Dynamics

In this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matrices M,D and K for the quadratic pencil Q(λ)=λ^(2)M+λD+K,so that Q(λ)has a prescribed subset of eigenvalues and eigenvectors.This method can determine the solvability of the inverse eigenvalue problem automatically.We then consider the least squares model for updating a quadratic pencil Q(λ).More precisely,we update the model coefficient matrices M,C and K so that(i)the updated model reproduces the measured data,(ii)the symmetry of the original model is preserved,and(iii)the difference between the analytical triplet(M,D,K)and the updated triplet(M_(new),D_(new),K_(new))is minimized.In this paper a computationally efficient method is provided for such model updating and numerical examples are given to illustrate the effectiveness of the proposed method.

Structural,Electrical,and Lithium Ion Dynamics of Li2MnO3 from Density Functional Theory

The layered Li2MnO3 is investigated by using the first-principles calculations within the GGA and GGA-t-U scheme, respectively. Within the GGA4-U approach, the calculated intercalation voltage （ranges from 4,5 V to 4.9 V） is found to be in good agreement with experiments. From the analysis of electronic structure, the pure phase Li2MnO3 is insulating, which is indicative of poor electronic-conduction properties. However, further studies of lithium ion diffusion in bulk Li2MnO3 show that unlike the two-dimensional diffusion pathways in rock salt structure layered cathode materials, lithium can diffuse in a three-dimensional pathway in Li2MnO3, with moderate lithium migration energy barrier ranges from 0.57 to 0.63 e V.

Solid-state NMR spectroscopy at ultrahigh resolution for structural and dynamical studies of MOFs

To characterize the structure and dynamics of metal--organic frameworks(MOFs)indepth at the molecular level,it is necessary to pursue high-resolution solid-state magic angle spinning(MAS)nuclear magnetic resonance(NMR)spectroscopy.Spectral resolution is usually affected by the quality of materials and various experimental conditions,of which magic angle(MA)accuracy is a crucial determinant.The current industrial criteria for MA calibration based on the common standard of KBr were found insufficient in guaranteeing optimal resolution MAS NMR for highly ordered MOFs.To drive towards higher-resolution MAS NMR spectroscopy,we propose_a calibration protocol for more accurate MA with a higher-precision criterion based on 79Br MAS NMR of KBr,where the linewidth ratio of the fifth-order spinning sideband to the central band of KBr should be less than 1.00.As a result,ultrahigh-resolution 13C cross-polarization(CP)MAS NMR of MOF-5 is achieved with minimal linewidths as low as 4 Hz,and therefore MOF-5 can be used as a new standard convenient for verifying MA accuracy and also optimizing 13c CP conditions.Maintaining high-precision MA under variable temperature(VT)was found challenging on certain commercial MAS NMR probes,as was systematically investigated by VT NMR using KBr and MOF-5.Nevertheless,ultrahigh-resolution MAS NMR spectroscopy with stable MA under VT is employed to reveal fine structures and linker dynamics of a series of Zn-based MOFs with highly regulated structures.The ultrahigh-resolution NMR methodcan be generally applied to study a broad range of MOFs and other materials.

Capturing the non-equilibrium state in light–matter–free-electron interactions through ultrafast transmission electron microscopy

Ultrafast transmission electron microscope(UTEM) with the multimodality of time-resolved diffraction, imaging,and spectroscopy provides a unique platform to reveal the fundamental features associated with the interaction between free electrons and matter. In this review, we summarize the principles, instrumentation, and recent developments of the UTEM and its applications in capturing dynamic processes and non-equilibrium transient states. The combination of the transmission electron microscope with a femtosecond laser via the pump–probe method guarantees the high spatiotemporal resolution, allowing the investigation of the transient process in real, reciprocal and energy spaces. Ultrafast structural dynamics can be studied by diffraction and imaging methods, revealing the coherent acoustic phonon generation and photoinduced phase transition process. In the energy dimension, time-resolved electron energy-loss spectroscopy enables the examination of the intrinsic electronic dynamics of materials, while the photon-induced near-field electron microscopy extends the application of the UTEM to the imaging of optical near fields with high real-space resolution. It is noted that light–free-electron interactions have the ability to shape electron wave packets in both longitudinal and transverse directions, showing the potential application in the generation of attosecond electron pulses and vortex electron beams.

Exploring the Limits of a Deflection-Based Method for the Estimation of Dynamic Stress in Beams

Estimation of the dynamic stress in structures,such as beams and plates,has previously been made using the relationship between stress and velocity spatial maxima based on far-field assumptions.This paper presents a method for the estimation of dynamic stress in a beam using Euler–Bernoulli beam theory,where deflection data from a grid of measurement points on the surface of the beam is used to estimate the dynamic bending stress in the structure.The limitations of the method are investigated via response data provided by a numerical model of a freefree beam.A nondimensional wavenumber analysis is used to determine the number of points required for an accurate estimate of stress.Beams with a range of material and geometric parameters are modeled in order to explore the limits of the estimation method,and parameters representative of several real-world materials are used to assess the suitability of the method for practical applications.

Practice on Gravity-1 Rocket Dynamic Characteristics Design

Since the Dongfeng-2 missile, full-vehicle modal testing has been established as an indispensable part of the development and testing of rocket and missile models. However, as rockets have been developed larger, the cost and duration of such tests have significantly increased, magnifying their impact on model development. This article follows the process of the modal testing practice of the Gravity-1 rocket, reviewing and summarizing the design process of the rocket's dynamic characteristics. Initially, the article introduces common modeling techniques for launch rockets, including the mass-beam model and the hybrid element model. It then discusses the relationship between the structural dynamics model of the launch rocket and modal testing, aiming to reduce testing costs through refined structural dynamics modeling methods. Subsequently, the article describes the dynamic characteristics design process of the Gravity-1 carrier rocket, categorizes structural parameters, and studies how the selection of structural parameters affects the predicted dynamic characteristics of the rocket. Finally, it elaborates on the design of the modal testing scheme and the dynamic characteristics design based on the test data.

Seismic response of a mid-story isolated structure considering SSI in mountainous areas under long-period earthquakes

At present,there is not much research on mid-story isolated structures in mountainous areas.In this study,a model of a mid-story isolated structure considering soil-structure interaction(SSI)in mountainous areas is established along with a model that does not consider SSI.Eight long-period earthquake waves and two ordinary earthquake waves are selected as inputs for the dynamic time history analysis of the structure.The results show that the seismic response of a mid-story isolated structure considering SSI in mountainous areas can be amplified when compared with a structure that does not consider SSI.The structure response under long-period earthquakes is larger than that of ordinary earthquakes.The structure response under far-field harmonic-like earthquakes is larger than that of near-fault pulse-type earthquakes.The structure response under near-fault pulse-type earthquakes is larger than that of far-field non-harmonic earthquakes.When subjected to long-period earthquakes,the displacement of the isolated bearings exceeded the limit value,which led to instability and overturning of the structure.The structure with dampers in the isolated story could adequately control the nonlinear response of the structure,effectively reduce the displacement of the isolated bearings,and provide a convenient,efficient and economic method not only for new construction but also to retrofit existing structures.