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Addition Formulas of Leaf Functions and Hyperbolic Leaf Functions

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Computer Modeling in Engineering & Sciences 2020年第5期123卷 441-473页

作者： kazunori shinohara Department of Mechanical Systems Engineering Daido UniversityNagoya457-8530Japan

Addition formulas exist in trigonometric ***-angle and half-angle formulas can be derived from these ***,the relation equation between the trigonometric function and the hyperbolic function can be derived using an imaginary *** inverse hyperbolic function arsinher(r)■ro 1/√1+t^(2)dt p1tt2 dt is similar to the inverse trigonometric function arcsiner(r)■ro 1/√1+t^(2)dt p1t2 dt,such as the second degree of a polynomial and the constant term 1,except for the sign−and+.Such an analogy holds not only when the degree of the polynomial is 2,but also for higher *** such,a function exists with respect to the leaf function through the imaginary number i,such that the hyperbolic function exists with respect to the trigonometric function through this imaginary *** this study,we refer to this function as the hyperbolic leaf *** making such a definition,the relation equation between the leaf function and the hyperbolic leaf function makes it possible to easily derive various formulas,such as addition formulas of hyperbolic leaf functions based on the addition formulas of leaf *** the addition formulas,we can also derive the double-angle and half-angle *** then verify the consistency of these formulas by constructing graphs and numerical data.

关键词： Leaf functions hyperbolic leaf functions lemniscate functions Jacobi elliptic functions ordinary differential equations nonlinear equations

Damped and Divergence Exact Solutions for the Duffing Equation Using Leaf Functions and Hyperbolic Leaf Functions

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Computer Modeling in Engineering & Sciences 2019年第3期118卷 599-647页

作者： kazunori shinohara Daido University 10-3 Takiharu-choMinami-kuNagoya 457-8530Japan

According to the wave power rule,the second derivative of a functionχ(t)with respect to the variable t is equal to negative n times the functionχ(t)raised to the power of 2n?*** the ordinary differential equations numerically results in waves appearing in the *** ordinary differential equation is very simple;however,waves,including the regular amplitude and period,are drawn in the *** this study,the function for obtaining the wave is called the leaf *** on the leaf function,the exact solutions for the undamped and unforced Duffing equations are *** the ordinary differential equation,in the positive region of the variableχ(t),the second derivative d^2χ(t)/dt^2 becomes ***,in the case that the curves vary with the time under the conditionχ(t)>0,the gradient dχ(t)/d constantly decreases as time *** is,the tangential vector on the curve of the graph(with the abscissa and the ordinate χ(t)changes from the upper right direction to the lower right direction as time *** the other hand,in the negative region of the variableχ(t),the second derivative d^2χ(t)/dt^2 becomes *** gradient d χ(t)/d constantly increases as time *** is,the tangent vector on the curve changes from the lower right direction to the upper right direction as time *** the behavior occurring in the positive region of the variable χ(t)and the behavior occurring in the negative region of the variableχ(t)alternately occur in regular intervals,waves appear by these *** this paper,I present seven types of damped and divergence exact solutions by combining trigonometric functions,hyperbolic functions,hyperbolic leaf functions,leaf functions,and exponential *** each type,I show the derivation method and numerical examples,as well as describe the features of the waveform.

关键词： Leaf functions hyperbolic leaf functions lemniscate functions jacobi elliptic functions ordinary differential equations duffing equation nonlinear equations

Lemniscate of Leaf Function

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Computer Modeling in Engineering & Sciences 2021年第1期126卷 275-292页

作者： kazunori shinohara Department of Mechanical Systems Engineering Daido University10-3 Takiharu-choMinami-kuNagoya457-8530Japan

A lemniscate is a curve defined by two foci,F_(1) and F_(2).If the distance between the focal points of F_(1)−F_(2) is 2a(a:constant),then any point P on the lemniscate curve satisfy the equation PF_(1)·PF_(2)=a^(2).Jacob Bernoulli first described the lemniscate in *** Fagnano discovered the double angle formula of the lemniscate(1718).The Euler extended the Fagnano’s formula to a more general addition theorem(1751).The lemniscate function was subsequently proposed by Gauss around the year *** insights were summarized by Jacobi as the theory of elliptic functions.A leaf function is an extended lemniscate *** formulas of leaf functions have been presented in previous papers;these included the addition theorem of this function and its application to nonlinear *** this paper,the geometrical properties of leaf functions at n=2 and the geometric relation between the angle θ and lemniscate arc length l are presented using the lemniscate *** relationship between the leaf functions sleaf_(2)(l)and cleaf_(2)(l)is derived using the geometrical properties of the lemniscate,similarity of triangles,and the Pythagorean *** the literature,the relation equation for sleaf_(2)(l)and cleaf_(2)(l)(or the lemniscate functions,sl(l)and cl(l))has been derived analytically;however,it is not derived geometrically.

关键词： Geometry lemniscate of Bernoulli leaf functions lemniscate functions Pythagorean theorem triangle similarity

Swimmer simulation using robot manipulator dynamics under steady water

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Natural Science 2010年第9期2卷 959-967页

作者： kazunori shinohara 不详

To help swimmers improve, we have developed a computational swimming model using underwater manipulator dynamics. We formulate the equations of the underwater manipulator dynamics using the fluid drag, which is proportional to the square of the velocity. We construct a swimming model consisting of several links based on these equations. The distance traveled by the optimal swimming motion is derived using the model. The input parameters are the joint torques. The arm and leg positions in the model are determined from the joint torques. The force transmitted from the water to the manipulator is defined to be the action force, and the force transmitted from the manipulator to the water is defined to be the reaction force. This reaction force is defined to be the propulsion force. By combining the propulsion force generated by the arms and legs and the frictional drag with respect to the body we can calculate the distance traveled. To optimize the propulsion, which depends on the swimmer’s motion, a variational approach using the Lagrange function is applied. We can use the model to simulate 2D pseudo-backstroke motion. Our model has a lower cost than other techniques in the literature, because it does not require computational fluid dynamics (CFD). The swimmer velocity calculated by our model agrees quite closely with the results in the literature. The model qualitatively captures the movement of an actual swimmer.

关键词： Sports Engineering Swimmer Robot Manipulator Dynamics Optimal Trajectory Adjoint Variable Method Euler–Lagrange Equation Fluid Drag Force Variational Method

Optimal Trajectory of Underwater Manipulator Using Adjoint Variable Method for Reducing Drag

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Open Journal of Discrete Mathematics 2011年第3期1卷 139-152页

作者： kazunori shinohara 不详

In order to decrease the fluid drag on an underwater robot manipulator, an optimal trajectory method based on the variational method is presented. By introducing the adjoint variables, which are Lagrange multipliers, we formulate a Lagrange function under certain constraints related to the target angle, target angular velocity, and dynamic equation of the robot manipulator. The state equation (the partial differentiation of the Lagrange function with respect to the state variables), adjoint equation (the partial differentiation of the Lagrange function with respect to the adjoint variables), and sensitivity equation (the partial differentiation of the Lagrange function with respect to torques) can be derived from the stationary conditions of the Lagrange function. Using the state equation, we can calculate the state variables (angles, angular velocities, and angular acceleration) at every time step in the forward time direction. These state variables are stored as data at every time step. Next, by using the adjoint equation, we can calculate the adjoint variables by using these state variables at every time step in the backward time direction. These adjoint variables are stored as data at every time step. Third, the sensitivity equation is calculated by using both the state variables and the adjoint variables. Finally, the optimal trajectory of the manipulator is obtained using the sensitivities. The proposed method is applied to the problem of two-link manipulators. It can obtain the optimal drag reduction trajectory of the manipulator under the constraints mentioned above.

关键词： Robot Manipulator Dynamics Optimal Trajectory Adjoint Variable Method Euler-Lagrange Equation Fluid Drag Force Calculus of Variations

Evaluation of Fatigue Life of Semiconductor Power Device by Power Cycle Test and Thermal Cycle Test Using Finite Element Analysis

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Engineering（科研） 2010年第12期2卷 1006-1018页

作者： kazunori shinohara Qiang Yu 不详

To accurately predict the fatigue life of a power device, a fatigue life evaluation method that is based on the power cycle is presented in terms of an algorithm based on a combination of electrical analysis, heat analysis, and stress analysis. In literature, the fatigue life of power devices has been evaluated on the basis of the thermal cycle. This cycle is alternately repeated within a range from a high temperature to a low temperature. In an actual operating environment, however, a power device works in a power cycle that consists of being switched ON and OFF. To accurately predict the fatigue life cycle of a device, then, the evaluation should take account of this important aspect of the power cycle. To verify the utility of the evaluation method presented in this study, the results for a power cycle based on the combined use of electrical analysis, heat analysis, and stress analysis are compared to the results based on the thermal cycle, as found in the literature. Our conclusion is that the fatigue life cycle as estimated by the thermal cycle test is higher than that estimated by the power cycle.

关键词： Power Electronics Power Modules Reliability Damage Simulation Technology Solder Joint Fatigue Crack Propagation Mechanical Stress

Dynamic Contact Problem for Slide Hinge

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Open Journal of Applied Sciences 2012年第4期2卷 82-86页

作者： kazunori shinohara Ryoji Takaki Takeshi Akita Faculty of Engineering Chiba Institute of Technology Chiba Japan Institute of Space and Astronautical Science (ISAS) Japan Aerospace Exploration Agency (JAXA) Sagamihara Japan JAXA's Engineering Digital Innovation Center (JEDI) Japan Aerospace Exploration Agency (JAXA) Sagamihara Japan

Contact analysis can be either static or dynamic. In static contact analysis, the position on the contact surface is constant. In dynamic contact analysis, the position on the contact surface changes at every time step. In static contact analysis, the computing results (stress, strain, etc.) of contact states have been verified through the Hertz contact problem in literature. On the other hand, there has been insufficient research into dynamic contact analysis. The contact algorithm is insufficiently constructed in finite element model (FEM) discretization. The gap between two objects cannot be calculated accurately. A contact method is demanded for artificial parameters. Inappropriate setting of artificial parameters causes artificial numerical oscillations on the contact surface between objects. To develop a high-reliability satellite, we started the development of FEM contact-friction modeling techniques in this study. A dynamic contact method was realized by using the appropriate parameters required in the contact analysis. We verified the reproducibility of the physical behavior of the contact friction via numerical simulation techniques by using a computational model of the hinge joints.

关键词： FEM Contact Friction Stress Joints Structural Analysis Advance/FrontSTR Dynamic Contact Analysis Static Contact Analysis

Diamond Rib: A Mechanical Design Method for Improving the Stiffness of a Structure

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Engineering（科研） 2016年第6期8卷 308-319页

作者： kazunori shinohara Masanobu Mizoguchi Shintatsu Suzuki Yasutaka Narusawa Department of Integrated Mechanical Engineering Daido University Nagoya Japan Collaborative Research Center Daido University Nagoya Japan

It is necessary to decrease the weight of space satellites, while maintaining their stiffness. To achieve this weight reduction, many structures, such as honeycomb and isogrid, have been reported in the literature. In this paper, the diamond rib method, a mechanical design method for improving the stiffness of structures, is introduced. By applying this method to a small space satellite, we propose a new structure called the “Diamond Rib Structure”. This structure significantly improves the ability to withstand the vibrational disturbances in a rocket fairing.

关键词： Space Satellite Finite Element Method Optimal Design Natural Frequency Natural Mode Diamond Rib Method Stiffness

A computation design method for architectural artifacts adapted from traditional Kagome bamboo basketry techniques

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Frontiers of Architectural Research 2024年第2期13卷 249-264页

作者： Hiroyuki shinohara Tung Hoi Peter Chan School of Architecture The Chinese University of Hong KongHong KongChina

This study is a digital form-finding and manual fabrication experiment in woven architectural design,with one traditional weaving style,Kagome,used to scale the craft up into an architectural-scale bamboo woven *** is a trihexagonal pattern employed in traditional bamboo basketry as a triaxial weaving system,resulting in an object with a self-bracing capacity without the use of fasteners owing to its interlacing *** existing studies and tools have addressed triaxial weaving design and representation,the current consideration of the advantages of weaving with bamboo is *** address this research gap,this study develops a computational design method based on studies on bamboo *** allows for the representation and exploration of design geometries using combinations of regular triangular meshes for the fabrication of Kagome woven bamboo artifacts.A full-scale mock-up was fabricated to evaluate the effectiveness of the *** mock-up demonstrated the self-bracing properties of Kagome,but there were discrepancies between the mock-up and the *** affecting bamboo weaving on an architectural scale have been identified within this study to inform future research on woven bamboo structures.

关键词： Traditionalbamboo craft Triaxialmaterial interlacing Bamboo Computational design methods Mesh block combinationsystem Architecturalwoven artifact