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The study compares the impact of two different pedagogical approaches in police training by assessing the knife defense performance of German police recruits against different types of knife attacks. Linear or nonlinear – which pedagogical approach leads to more efficient knife defense performance?

A total of 20 German state police recruits (w = 5, m = 15) were assigned to linear and nonlinear groups. The linear and nonlinear groups' performance on knife defense was assessed in a pretest, after a three-week training intervention in a posttest and eight weeks thereafter in a retention test, utilizing a mixed-method design (Sendall et al., 2018).

Quantitative data on knife defense performance suggest a lastingly better performance of the nonlinear group: in the retention test, participants of the nonlinear group were hit less (p = 0.029), solved the attack faster (p = 0.044) and more often (81.8%) than participants of the linear group (55.6%). In contrast, qualitative data reveal that, despite of evidence for a high level of perceived competence, the nonlinear teaching of knife defense skills has been accompanied by considerable uncertainties, affected by the lack of techniques and the focus on principles and operational parameters only.

It is the first study assessing the impact of different pedagogical approaches in police training. For the practice of police trainers, the results provide empirical orientations for an evidence-based planning of and reflection on pedagogical demands within their training (Mitchell and Lewis, 2017).

The purpose of this paper is to describe the structure of nonlinear dampers and the dynamic equations, and nonlinear realization principles and optimize the parameters of nonlinear dampers. Using the finite element method to analyze the seismic performance of the frame structure with shock absorber.

The nonlinear shock absorber was installed in a six-storey reinforced concrete frame structure to study its seismic performance. The main structure was designed according to the eight degree seismic fortification intensity, and the time history dynamic analysis was carried out by Abaqus finite element software. EL-Centro, Taft and Wenchuan seismic record were selected to analyze the seismic response of the structure under different magnitudes and different acceleration peaks.

Through the principle study and parameter analysis of the nonlinear shock absorber, combined with the finite element simulation results, the shock absorption performance and shock absorption effect of the nonlinear energy sink (NES) nonlinear shock absorber are given as follows: first, the damping of the NES shock absorber is satisfied, and the linear spring stiffness and nonlinear stiffness of the shock absorber are based on the relationship k1=kn×kl2, so that the spring design length is fixed, and the linear stiffness of the shock absorber can be obtained. The nonlinear shock absorber has the characteristics of high rigidity and frequency bandwidth, so that the frequency is infinitely close to the frequency of the main structure, and when the mass of the shock absorber satisfies between 0.056 and 1, a good shock absorption effect can be obtained, and the reinforced concrete with the shock absorber is obtained. The frame structure can effectively reduce the seismic response, increase the natural vibration period of the structure and reduce the damage loss of the structure. Second, the spacer and each additional shock absorber have a small difference in shock absorption effect. After the shock absorber parameters are accurately calculated, the number of installations does not affect the shock absorption effect of the structure. Therefore, the shock absorber is properly constructed and accurately calculated. Parameters can reduce costs.

New shock absorbers reduce earthquake-induced damage to buildings.

The purpose of this paper is to make a theoretical comprehensive efficiency evaluation of a nonlinear analysis method based on the Woodbury formula from the efficiency of the solution of linear equations in each incremental step and the selected iterative algorithms.

First, this study employs the time complexity theory to quantitatively compare the efficiency of the Woodbury formula and the LDLT factorization method which is a commonly used method to solve linear equations. Moreover, the performance of iterative algorithms also significantly effects the efficiency of the analysis. Thus, the three-point method with a convergence order of eight is employed to solve the equilibrium equations of the nonlinear analysis method based on the Woodbury formula, aiming to improve the iterative performance of the Newton–Raphson (N–R) method.

First, the result shows that the asymptotic time complexity of the Woodbury formula is much lower than that of the LDLT factorization method when the number of inelastic degrees of freedom (IDOFs) is much less than that of DOFs, indicating that the Woodbury formula is more efficient for local nonlinear problems. Moreover, the time complexity comparison of the N–R method and the three-point method indicates that the three-point method is more efficient than the N–R method for local nonlinear problems with large-scale structures or a larger ratio of IDOFs number to the DOFs number.

This study theoretically evaluates the efficiency of nonlinear analysis method based on the Woodbury formula, and quantitatively shows the application condition of the comparative methods. The comparison result provides a theoretical basis for the selection of algorithms for different nonlinear problems.

The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of general shape. This method is used to investigate the effects of thickness, geometry of various shapes, boundary conditions and material properties on the large deformation analysis of Mindlin plates.

Nonlinear analysis of plates based on Mindlin theory is presented. The equations are derived by the Von-Karman assumption and total Lagrangian formulations. Newton-Raphson method is applied to achieve linear equations from nonlinear equations. Simple HP-cloud method is used for the construction of the shape functions based on Kronecker-δ properties, so the essential boundary conditions can be enforced directly. Shepard function is utilized for a partition of unity and complete polynomial is used as an enrichment function.

The suitability and efficiency of the simple HP-cloud method for the geometrically nonlinear analysis of thin and moderately thick plates is studied for the first time. Large displacement analysis of various shapes of plates, rectangular, skew, trapezoidal, circular, hexagonal and triangular with different boundary conditions subjected to distributed loading are considered.

This paper shows that the simple HP-cloud method is well suited for the large deformation analysis of Mindlin plates with various geometries, because it uses a set of a few arbitrary nodes placed in a plate of general shape. Moreover the convergence rate of the proposed method is high and the cost of solving equations is low.

Super304H steel is a new fine-grained austenitic heat-resistant stainless steel developed in recent years, and it is widely used in high temperature section superheater and reheater tubes of ultra-supercritical thermal power units’ boiler. Currently intergranular corrosion (IGC) has occurred in a few austenitic stainless steel tubes in ultra-supercritical units and led to boiler leakage. The purpose of this paper is to find a nondestructive method to quickly and easily detect IGC of austenitic stainless steel tube.

This paper uses the nonlinear characteristics of ultrasonic propagation in steel tube to detect the IGC of Super304H tube.

The experimental results show that the nonlinear coefficient generally increases sensitively with the degree of IGC; hence, the nonlinear coefficient can be used to assess IGC degree of tubes, and the nonlinear coefficient measurement method is repeatable for the same tube.

A theory of how IGC would affect the ultrasonic signals and lead to a nonlinear response needs further research.

A nondestructive method to quickly and easily detect IGC is provided.

Using ultrasonic nonlinear coefficient to assess IGC degree of tubes is a new try.

This paper provides a new way to test IGC.

The purpose of this study is to address the nonlinear oscillations of single-crystal silicon micro-electromechanical systems (MEMS) accelerometers subjected to mechanical excitation.

The nonlinear behavior was detected and analyzed by using experimental, analytical and numerical approaches. Piezoelectric shaker as a source of mechanical excitation and differential laser Doppler vibrometer in combination with a micro system analyzer were used in the experimental effort. Two types of devices considered included nonencapsulated samples and samples encapsulated in nitrogen gas compressed between two glasses. Numerical and analytical investigations were conducted to analyze the nonlinear response. A novel method has been suggested to calculate the nonlinear parameters. The obtained experimental, numerical and analytical results are in good agreement.

It has been found that the nonlinearity leads to a shift in frequencies and generates higher harmonics, but, most importantly, reveals new phenomena, such as the jump and instability of the vibration amplitudes and phases.

It has been shown that under the constant excitation force, the MEMS device can work in both linear and nonlinear regions. The role of the beat phenomenon has been also addressed and discussed. It has been found that the attributes of the nonlinear response are strongly dependent on the level and duration of the excitation. It is concluded that the nonlinear response of the systems is strongly dependent on the level of the excitation energy. It has been also concluded that larger quality factors are able to enhance dramatically the nonlinear effects and vice versa.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

This paper aims to present an approach for calibrating the numerical models of dynamical systems that have spatially localized nonlinear components. The approach implements the extended constitutive relation error (ECRE) method using multi-harmonic coefficients and is conceived to separate the errors in the representation of the global, linear and local, nonlinear components of the dynamical system through a two-step process.

The first step focuses on the system’s predominantly linear dynamic response under a low magnitude periodic excitation. In this step, the discrepancy between measured and predicted multi-harmonic coefficients is calculated in terms of residual energy. This residual energy is in turn used to spatially locate errors in the model, through which one can identify the erroneous model inputs which govern the linear behavior that need to be calibrated. The second step involves measuring the system’s nonlinear dynamic response under a high magnitude periodic excitation. In this step, the response measurements under both low and high magnitude excitation are used to iteratively calibrate the identified linear and nonlinear input parameters.

When model error is present in both linear and nonlinear components, the proposed iterative combined multi-harmonic balance method (MHB)-ECRE calibration approach has shown superiority to the conventional MHB-ECRE method, while providing more reliable calibration results of the nonlinear parameter with less dependency on a priori knowledge of the associated linear system.

This two-step process is advantageous as it reduces the confounding effects of the uncertain model parameters associated with the linear and locally nonlinear components of the system.

The purpose of this paper is to aim to an application of element of the theory of differential geometry for building the state space transformation, linearizing nonlinear dynamic system into a linear form.

It is assumed that the description of nonlinear electric circuits with concentrated parameters or electromechanical systems is given by nonlinear system of differential equations of first order (state equations). The goal is to find transformation which leads nonlinear state equation (written in one coordinate system) to the linear in the other – sought coordinate system.

The necessary conditions fulfilled by nonlinear system undergoing linearization process are presented. Numerical solutions of the nonlinear equations of state together with linearized system obtained from direct transformation of the state space are included (transformation input – the state of the nonlinear system).

Application of first order exact differential forms for determining the transformation linearizing the nonlinear state equation. Simple linear models obtained with the use of the linearizing transformation are very useful (mainly because of the known and well-mastered theory of linear systems) in solving of various practical technical problems.

The purpose of this paper is to investigate nonlinear vibrations of triple-walled carbon nanotubes buried within Pasternak foundation carrying viscous fluids.

Considering the geometry of nanotubes, the governing equations were initially derived using Timoshenko and modified couple stress theories and by taking into account Von-Karman expressions. Then, by determining boundary conditions, type of fluid motion, Knudsen number and, ultimately, fluid viscosity, the principal equation was solved using differential quadrature method, and linear and nonlinear nanotube frequencies were calculated.

The results indicated that natural frequency is decreased as the fluid velocity and aspect ratio increase. Moreover, as the aspect ratio is increased, the results converge for simple and fixed support boundary conditions, and the ratio of nonlinear to linear frequencies approaches. Natural frequency of vibrations and critical velocity increase as Pasternak coefficient and characteristic length increase. As indicated by the results, by assuming a non-uniform velocity for the fluid and a slip boundary condition at Kn = 0.05, reductions of 10.714 and 28.714% were observed in the critical velocity, respectively. Moreover, the ratio of nonlinear to linear base frequencies decreases as the Winkler and Pasternak coefficients, maximum deflection of the first wall and characteristic length are increased in couple stress theory.

This paper is a numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid.