Purpose
To protect patients from RF heating in MRI scan, this work proposes an accurate and patient‐specific whole‐body specific absorption rate (SAR) characterization method based on an equivalent ...circuit model. Compared to the standard pulse energy method defined in NEMA MS 8‐2016, this method avoids the complexity of integrating flux loops and has the potential to be easily implemented in MRI scanners.
Theory and Methods
In this study, we use an equivalent parallel circuit to model the power distribution on the transmit coil and subject. The coil and subject equivalent resistances are fitted by the frequency response functions of reflection coefficient and are thereafter used to calculate the power ratio between them. To assess the accuracy of this method, we measured the subject absorbed power of 2 phantoms and 5 volunteers and compared it with the standard pulse energy method with flux loops.
Results
The resistances, resonant frequencies, and quality factors of the transmit coil are fitted with the equivalent circuit model in both unloaded and loaded conditions. Whole‐body SAR of 5 volunteers is measured at 2 different landmarks. In addition, the relationship between SAR and the working frequencies of the transmit coil is measured and analyzed. The subject absorbed power measured by the proposed method demonstrates good accuracy (RMS error and maximum error of 3.77% and 9.47%, respectively) relative to the flux loop method.
Conclusion
The equivalent circuit model‐based method enables individualized, accurate, and simplified SAR characterization for clinical applications and research with moderate implementation complexity.
Adding particles to mechanical elements can reduce their vibrations. Both the particles and the mechanical elements interrelate in a highly complex manner, thereby influencing the energy dissipation ...of the mechanical elements. The particle damping is extremely nonlinear, and the energy dissipation mechanism in such a granule–structure interaction system has scarcely been examined. This study aims to investigate the dynamic behavior and energy dissipation mechanism for a mass–spring–damper–slider system with a particle damper. A simple but robust energy method was first proposed to explore the energy dissipation mechanism, and a two-way coupled model of the discrete element method (DEM) and multi-body dynamics (MBD) was employed to analyze the complex interaction system. Three numerical benchmark tests and free vibration experiments for the system with a particle damper were conducted to validate the proposed energy method and the adopted coupled DEM–MBD model. Results show that the coupled DEM–MBD simulations reasonably agree with the corresponding experiments. The validated coupled model was subsequently employed to calculate the distribution of system energy, and to explore the effect of contact properties on the energy dissipation of the system during the free vibration process. In the mass–spring–damper–slider system with a particle damper, the damping effect resulting from particles is essentially caused by the contact forces generated when the particles make contact with the hollow box. The induced contact forces act as resistance forces to the hollow box, always do negative work, and suppress the motion of the hollow box. The energy loss of the particles primarily occurs through contact friction and contact damping when the particles are hit by the hollow box. Contact properties, such as friction and restitution coefficients, exhibit a negligible effect on the dynamic behavior of the hollow box, but substantially affect the distribution of energy dissipation in the particular system.
This paper is devoted to the analysis of an n-dimensional model which describes thermoviscoelastic materials. With careful use of the standard energy method, we obtain the global existence and ...asymptotic decay of solutions for n≥1, provided that the initial data are smooth and sufficiently small in L2-Sobolev space.
In this paper, we investigate the general decay rate of the solutions for a class of fractional Laplace viscoelastic equations in the whole space
ℝn,n≥1$$ {\mathbb{R}}^n,n\ge 1 $$, given by
...utt−Δu+u−∫0tg(t−s)(−Δ)αu(s)ds=0,$$ {u}_{tt}-\Delta u+u-{\int}_0^tg\left(t-s\right){\left(-\Delta \right)}^{\alpha }u(s) ds=0, $$
with
0<α<1$$ 0<\alpha <1 $$ and
g$$ g $$ satisfying
g′(t)≤−η(t)g(t)$$ {g}^{\prime }(t)\le -\eta (t)g(t) $$. We prove the existence of a solution formula then use the energy method in the Fourier space to establish a general decay result which depends on
α$$ \alpha $$ and
η$$ \eta $$. We also present three illustrative examples by the end.
Cogging torque can cause the torque ripple and noise of machines and reduce the machine control accuracy. The analytical calculation method of cogging torque has always been a hot research topic in ...the field of machine. Conventional energy method is usually adopted to compute the cogging torque. Recently, a novel energy method is proposed. To reveal the fundamental difference and respective merits of these two energy methods, this paper first derives the analytical models of cogging torque in homopolar inductor machines (HIMs) considering the leakage fluxes of the stator slots by the two energy methods. Based on the derived analytical models, the cogging torque production mechanisms expressed by the two energy methods are analyzed and compared from the viewpoint of air-gap field modulation principle. The cogging torque computed by the two energy methods is all produced by the interactions of the air-gap magnetic fields modulated by the harmonics of the air-gap magnetomotive force (MMF) and air-gap permeance. However, due to the difference in the approaches of solving the air-gap magnetic field energy density, the novel energy method takes into account more harmonics of the air-gap MMF and air-gap permeance. Furthermore, the computational accuracy and complexity of the two energy methods are analyzed and compared based on the analytical calculations and three-dimensional (3-D) finite element analysis (FEA) for the cogging torque in a 48-slot/4-pole (48S4P) permanent magnet (PM) HIM and a 45-slot/6-pole (45S6P) field winding HIM. Compared with the conventional energy method, the novel energy method has higher accuracy, but is more complex. Finally, a prototype of the 48S4P PM HIM is manufactured. The results of analytical calculation, 3-D FEA and comparison are verified by experiments.
•The analytical models of TVMS for profile-shifted spur gears are established.•The positive shift decreases the TVMS so that it causes stronger vibrations in the gear system.•The negative shift ...increases the TVMS so that it weakens vibrations in the gear system.•The positive compound shift decreases TVMS and increases the vibration.•The negative compound shift leads to TVMS rising and significantly reducing vibration.
Nowadays, profile shift is one of the most powerful techniques to achieve high-performance spur gear transmission system. Although this technique has been widely used in industry, its influence on time-varying meshing stiffness (TVMS) and dynamic characteristics is still unclear. This paper presents a novel analytical model of TVMS for profile-shifted spur gears. The modification coefficient and transition curve revise the proposed model. Afterward, numerical simulations are carried out to analyze individual and compound shifts based on a six-degree of freedom gear model. For individual shifts, the positive shift can decrease the gear tooth's stiffness and TVMS so that it causes stronger vibrations in the gear system. On the contrary, the negative shift can improve the gear tooth's stiffness and TVMS, thereby mitigating the gear system's vibration. For compound shift, S0-gearing poses a slight impact on TVMS, but an unneglectable effect on dynamic characteristics. Besides, the S-gearing with the positive compound shift can decrease TVMS and increase vibration. In contrast, the S-gearing with the negative compound shift leads to TVMS rising and significantly reducing vibration. The insightful findings derived from the study can help engineers and manufacturers better understand the operation performance and dynamic features of profile-shifted spur gears.
In this paper, two coupled and decoupled dissipative finite difference schemes with high‐order accuracy are proposed for solving the dissipative generalized symmetric regularized long wave equations. ...Dissipation of the discrete energy of scheme with different parameters is discussed. A priori estimate, existence and uniqueness of numerical solutions, convergence with O(τ2+h4) and stability of the schemes are proved by the discrete energy method. Numerical examples are given to support the theoretical analysis.
In this work we prove the exponential stability for a laminated beam consisting of two identical layers of uniform density, which is a system closely related to the Timoshenko beam theory, taking ...into account that an adhesive of small thickness is bonding the two layers and produce the interfacial slip. It is assumed that the thickness of the adhesive bonding the two layers is small enough so that the contribution of its mass to the kinetic energy of the entire beam may be ignored.
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•A novel variable stiffness pneumatic artificial muscle based on origami is proposed.•Geometric configurations during the actuation are obtained by kinematic analysis ...model.•Quasi-static characteristic analysis model is developed based on the energy method.
A novel variable stiffness axial expansion pneumatic artificial muscle based on hexagonal origami is proposed. Based on the presented assumptions, a kinematic analysis model of the pneumatic artificial muscles is presented, and the changes in crease angles, air cavity volume and geometric configurations of the pneumatic artificial muscles during the actuation process are obtained. The equivalent elastic modulus of the hyperelastic material is obtained by fitting the stress-strain curve. The stress state of the crease is simplified as the pure bending model of a straight beam, and the rotational stiffness of the crease is formulated. Based on the energy method, a quasi-static characteristic analysis model of the pneumatic artificial muscles is developed. The pressure-displacement curve under the unloading state and the output force-displacement curve under the loading state are calculated. The variable stiffness characteristics of the pneumatic artificial muscles are evaluated. Compared with the experimental and numerical simulation results, the analysis models are verified. The work will provide analysis models for the mechanical design and force-displacement control of this type of pneumatic artificial muscles.
We present a well-posedness and stability result for a class of nondegenerate linear parabolic equations driven by geometric rough paths. More precisely, we introduce a notion of weak solution that ...satisfies an intrinsic formulation of the equation in a suitable Sobolev space of negative order. Weak solutions are then shown to satisfy the corresponding energy estimates which are deduced directly from the equation. Existence is obtained by showing compactness of a suitable sequence of approximate solutions whereas uniqueness relies on a doubling of variables argument and a careful analysis of the passage to the diagonal. Our result is optimal in the sense that the assumptions on the deterministic part of the equation as well as the initial condition are the same as in the classical PDEs theory.
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