System In Physical Space Research Articles

Multi-type dynamic load identification algorithm in continuous system: A numerical and experimental study based on SSM-Newmark-β

Dynamic load identification based on structural responses is an important problem in the field of engineering and plays an important role in the condition assessment of mechanical structures. Current popular load identification methods such as the state-space method (SSM) and the Green's kernel function method (GKFM) are implemented on discrete systems with outstanding performance, but when dealing with complex continuous systems, there are some limitations such as low efficiency and inaccuracy. In this paper, a continuous system load identification algorithm based on SSM and Newmark-β is proposed for the first time. Using modal coordinate transformation and modal truncation methods, the number of infinite vibration differential equations of a continuous system in physical space are converted to a finite number of vibration differential equations in modal space, where the modal truncation order and the optimal layout of the sensors are combined by modal strain energy. The Newmark-β method in modal space is derived and thus combined with SSM to obtain a load identification model Y=HF called SSM-Newmark-β method, which reduces the size of the transfer matrix H. The solution time of the proposed algorithm is 0.38 s for continuous systems, which is rather shorter than that for discrete systems. Furthermore, the simulations show that it has better accuracy and noise immunity than SSM and GKFM in the identification of sinusoidal load, impact load, and random load. The effect of time step is also discussed which reveals that the larger time step has less effect on the proposed algorithm. An experimental study is carried out on a cantilever beam system. The result verifies that the SSM-Newmark-β algorithm has better accuracy in load identification for the continuous system. This research provides a new sight for the real-time identification of dynamic loads for complex structures.

A generalized elastic coordinate method for unconstrained structural dynamics

A generalized elastic coordinate method (GECM) is proposed for the vibrational (elastic) response analysis of unconstrained structural dynamics. Firstly, the generalized rigid body and elastic coordinates are defined to describe the overall motion of a discrete unconstrained structure. Secondly, the corresponding equations of motion for generalized elastic coordinates are established with a tiny computational cost, and the stiffness matrix is still sparse. Finally, the elastic deformation in physical space can be exactly caught by the proposed equations of motion after determining the rigid body modes and the coordinate system of the rigid body motion. Different from directly solving the original semi-positive definite system in physical space, in which the overall displacement can only obtain, and the direct modal projection, the modal truncation error problem can be effectively overcome based on the established positive definite system when the modal order reduction is carried out. In light of this, the modal truncation error correction of the elastic displacement for the transient time domain and steady-state frequency domain of unconstrained structures is directly realized, summed the above as GECM, and the validity and practicability are illustrated through the numerical examples.

Spin 1/2 one‐ and two‐particle systems in physical space without eigen‐algebra or tensor product

Under the spin–position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra substitutes the vector–matrix spin model built on the Pauli spin operator. The standard quantum operator‐state spin formalism is replaced with vectors transforming by proper and improper rotations in the same 3D space—isomorphic to the space of Pauli matrices. In the single‐spin case, the novel spin 1/2 representation (1) is Hermitian, (2) shows handedness, (3) yields all the standard results and its modulus equals the total spin angular momentum , (4) formalizes irreversibility in measurement, and (5) permits adaptive imbedding of the 2D spin space in 3D. Maximally entangled spin pairs (1) are in phase and have opposite handedness, (2) relate by one of the four basic improper rotations in 3D: plane reflections (triplets) and inversion (singlet), (3) yield the standard total angular momentum, and (4) all standard expectation values for bipartite and partial observations follow. Depending on whether proper and improper rotors act one—or two—sided, the formalism appears in two complementary forms, the “spinor” or the “vector” form, respectively. The proposed scheme provides a clear geometric picture of spin correlations and transformations entirely in the 3D physical orientation space.

Modal space neural network compensation control for Gough-Stewart robot with uncertain load

This paper investigates the motion control of a Stewart parallel robot with uncertain load. The external disturbances caused by load can trigger dynamic coupling among six degree-of-freedoms and have a significant impact on control precision. In practice, the dynamic parameters of load is difficult to be precedent identified and the robot with load is a multi-input multi-output(MIMO) system in physical space, which makes the dynamic coupling problem difficult to solve effectively and the high-performance control is hard to achieve. In this paper, the dynamic effect of the load is first analyzed. Then a novel motion control method, modal space neural network compensation control, is designed with the aim of reducing the effect of the load disturbances. This controller implements the neural network to compensate for the load disturbances. In addition, the modal space control theory is introduced to realize the independent control of each control channel. The feasibility of the proposed controller is evaluated in numerical simulations. Results reveal that the proposed control method gives exceptional tracking performance and dynamic coupling suppression capability.

Transition paths of marine debris and the stability of the garbage patches.

We used transition path theory (TPT) to infer "reactive" pathways of floating marine debris trajectories. The TPT analysis was applied on a pollution-aware time-homogeneous Markov chain model constructed from trajectories produced by satellite-tracked undrogued buoys from the National Oceanic and Atmospheric Administration's Global Drifter Program. The latter involved coping with the openness of the system in physical space, which further required an adaptation of the standard TPT setting. Directly connecting pollution sources along coastlines with garbage patches of varied strengths, the unveiled reactive pollution routes represent alternative targets for ocean cleanup efforts. Among our specific findings we highlight: constraining a highly probable pollution source for the Great Pacific garbage patch; characterizing the weakness of the Indian Ocean gyre as a trap for plastic waste; and unveiling a tendency of the subtropical gyres to export garbage toward the coastlines rather than to other gyres in the event of anomalously intense winds.

Modal decomposition method for response spectrum based analysis of nonlinear and non-classically damped systems

Abstract A novel inelastic modal decomposition method for random vibration analysis in alignment with contemporary aseismic code provisions (e.g., Eurocode 8) considering non-classically damped and nonlinear multi degree-of-freedom (MDOF) systems is developed. Relying on statistical linearization and state-variable formulation the complex eigenvalue problem considering inelastic MDOF structural systems subject to a vector of stochastic seismic processes is addressed. The involved seismic processes are characterized by power spectra compatible in a stochastic sense with an assigned elastic response uniform hazard spectrum (UHS) of specified modal damping ratio. Equivalent modal properties (EMPs) of the linearized MDOF system, namely equivalent pseudo-undamped natural frequencies and equivalent modal damping ratios are provided. To this aim, each mode of vibration is assigned with a different stationary random process compatible with the excitation response spectrum adjusted to the corresponding equivalent modal damping ratio property. Next, an efficient iterative scheme is devised achieving convergence of the equivalent modal damping ratios and the damping premises of the excitation response spectrum corresponding to each mode of the system. Subsequently, the stochastically derived forced vibrational modal properties of the structure are utilized together with the appropriate mean response elastic UHS for determining peak nonlinear responses in modal coordinates. The modal participation factors are determined for the complex-valued mode shapes and generalized square-root-of-sums-squared (SRSS) is employed as the modal combination rule for determining the peak total responses of the system in physical space. The pertinency and applicability of the proposed framework is numerically illustrated using a three-storey bilinear hysteretic frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear response time-history analysis (RHA) involving a large ensemble of stationary Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed methodology in a Monte Carlo-based context.

Lagrangian solutions for the semi-geostrophic shallow water system in physical space with general initial data

Lagrangian solutions for the semi-geostrophic shallow water system in physical space with general initial data

On the Semi-geostrophic System in Physical Space with General Initial Data

In order to accommodate general initial data, an appropriately relaxed notion of renormalized Lagrangian solutions for the Semi-Geostrophic system in physical space is introduced. This is shown to be consistent with previous notions, generalizing them. A weak stability result is obtained first, followed by a general existence result whose proof employs said stability and approximating solutions with regular initial data. The renormalization property ensures the return from physical to dual space; as consequences we get conservation of Hamiltonian energy and some weak time-regularity of solutions.

On Lagrangian Solutions for the Semi-geostrophic System with Singular Initial Data

We show that weak (Eulerian) solutions for the semi-geostrophic system in physical space exhibiting some mild regularity in time cannot yield point masses in dual space. However, such solutions are physically relevant to the model. Thus, we discuss a natural generalization of weak Lagrangian solutions in the physical space to include the possibility of singular measures in dual space. We prove existence of such solutions in the case of discrete measures in dual space. We also prove that weak Lagrangian solutions in physical space determine solutions in the dual space. This implies conservation of geostrophic energy along the Lagrangian trajectories in the physical space.

Adaptive numerical advection. The coordinate transformation equation method

In many hydrodynamical applications, advection is the most important dynamical process. Advected quantities typically develop greatly disparate spatial scales because of the inherent non-linearity of advection. A method is outlined how to tackle this process numerically. The basic idea of the coordinate transformation equation (CTE) method is to introduce a moving coordinate system in physical space before applying any discretisation. This keeps the problem of discretisation separate from the problem of adaptation. In the new coordinate system, which changes in time, the effects on the numerical representation of the advection terms are twofold. Firstly, the advection is with respect to a relative velocity between coordinates and flow, which is arranged to be less than the absolute velocity, leading to a less restrictive stability criterion for the explicit time stepping compared to the Courant condition. Since the relative velocity is smaller than the absolute velocity, this also leads to a decrease in the importance of the non-linear advection term in comparison with other terms in the equation being solved, and therefore to a decrease in numerical errors from advection. Secondly, a smoothing of the spatial gradients of the quantities to be advected decreases the diffusion due to the discretisation, especially if monotonic (but therefore diffusive) discretisation schemes are used. Illustrations of the applicability and accuracy of the method are given, using comparisons with the results of other advection techniques and analytical solutions of linear advection problems, i.e., problems in which the velocity field is given, in one and two dimensions, including rarefaction and compression waves. The remaining illustrations are of non-linear problems, in which the velocity field is solved for as part of the problem. In such problems the CTE is coupled non-linearly to the equations of motion. However, the main shortcoming of the method is the large computing time required to solve the CTE system.

Sideband evolution of a complex Ginzburg-Landau equation: a three-dimensional dynamical system and its resulting new aperiodic attractor

The temporal evolution of a resonant sideband system, obtained from a nonlinear evolution equation of Ginzburg-Landau type, is studied. In the phase space of an associated three-dimensional dynamical system, a non-trivial attractor is discovered within certain parameter ranges. The present attractor differs from well-known non-trivial attractors of either Lorenz or Silnikov type in that it does not result from homoclinic bifurcation, but rather relates to the break-down of heteroclinic cycles and the creation of global non-planar limit cycles, and results from the motion of stable and unstable manifolds of three global limit cycles. It shares however some common features of bifurcating sequences: a stable non-planar limit cycle → an aperiodic attractor → a pair of spiral sinks, which in an asymptotic state correspond respectively to periodic, chaotic, or steady modulation of the sideband wave system in physical space.

流れ計算のための航空機外郭と物理空間の計算格子

For the purpose of numerical analysis of threedimensional compressible steady flow around an airplane, it is necessary to find quantitatively local positions of an out surface of the airplane and local directions of the surface in a rectangular computational grid system in physical space. The out surface of airplane is made up of many elements of small triangular planes. The local positions of the out surface in the grid system are determined by local intersections of axes of the grid with these triangular planes. Directions of the triangular planes are substituted for the local directions of the out surfaces. Using these results, views of the out surface of airplane are drawn in sheets of paper.

Spatial Mapping as a Method for Observing Classroom Art Instruction

on classifying the verbal behaviors of teachers. Yet in art classrooms, many significant teacher-student exchanges occur within a spatial usage context. Spatial usage, a facet of nonverbal behavior, is a fundamental aspect of instruction that involves the arrangement of physical space, patterns of travel, and the kinds and durations of behaviors that take place. The rationale for studying the spatial dimensions of teaching stems from the work of various researchers. Hall (1977) stated that physical space systems subtly influence the form and content of communications taking place in classrooms. Sommer (1969) conducted numerous studies in classrooms and showed