We conducted impact fatigue tests, wherein the magnitude and duration times of impact stresses were varied for JIS SS400 notched specimens to evaluate the effect of strain amplitudes on the impact fatigue strength. The transition of fracture mode from ductile to crack propagation both in impact fatigue and in standard fatigue was experimentally investigated in a range of cyclic loadings up to about 50,000 times using two types of fatigue testing machines. One machine was used for electro-hydraulic servo loading, and the other was for drop-weight cyclic impact loading. To obtain the variation in true strain of the specimen during the impact fatigue tests, the minimum diameter of the specimen was measured using a two-dimensional displacement measurement system. The main results were summarized as follows. A comparison of the nominal stress and the number of cycles to failure between the smooth specimen and the notched specimen showed that the impact fatigue strength of the notched specimens was lower than that of the smooth specimens when the number of cycles to failure was around 8,000 times or more. A comparison of the strain growth and the number of cycles to failure showed that the U-notched R=2.0 specimens fractured with a smaller amount of strain growth in the impact fatigue tests than in standard fatigue tests. Impact fatigue test results indicated the following equation could represent the relationship between the strain growth Δεp and the number of cycles to failure Nf. ΔεpNkf = C, where the exponent k and C are material constants.
When train passes through the rail joint at the heel of tongue rail of railroad switch, impact vibration is caused due to the step difference of the joint. This impact vibration is transmitted to the front rod, which is the attachment device located on the toe of tongue rail and connected with position checker device, induces the wear of bearing and leading to switching failure. Also, the wear of bearing of the special layout switch is more serious than that of the normal railroad switch because the special layout switch is more complex than the normal railroad switch. In order to clarify the mechanism of the wear, we measured the acceleration and axial force of the front rod of the special layout railroad switch in track open for traffic. Then, we have developed the finite element model of the special switch and validated the model by comparing with measured results. On the other hand, we calculated the coefficient of wear amount of bearing from wear test. Combining with the results of finite element analysis and the coefficient of wear amount, we predicted the wear amount of the front rod in the track. The wear amount of bearing of the special railroad switch is 10 to 20 times more than that of the normal railroad switch (Kondo et al., 2015). This is because the material of bearing of special switch is easier to wear than that of normal switch. Furthermore, the result is attributed to the structure of bearing of special switch. The axial constraint of bearing of special switch is weaker than that of normal switch, and so the bearing of special switch is easy to slide.
In this paper, a ferritic CrMo steel SCM440 which satisfies the prerequisites of ASTM E1921 master curve (MC), but which this MC failed to characterize its fracture toughness KJc temperature dependence is introduced. The material was tested at four temperatures -55, 20, 60 and 100°C in the ductile-to-brittle transition temperature region. The obtained reference temperatures T0 (i.e., a temperature that 25 mm thickness specimen is expected to show KJc of 100 MPam1/2) from these tests differed in the range of -9 to 89°C. T0 obtained from all the valid test data was 17°C. Thus, MC using any of these T0’s failed to characterize the material’s KJc temperature dependence. One finding was that this material showed fracture toughness of 100 MPam1/2 at higher temperature than room temperature, which is a rare case reported for the materials that MC is successfully applicable. Remembering Kirk’s opinion that “ASTM E1921 MC exists because MC of the yield temperature dependence (Zerilli equation) exists,” it was noted that the Zerilli equation showed poor fitting performance of yield stress over room temperature for this material. If this yield stress temperature dependence is corrected (i.e., shift in temperature), ASTM E1921 MC will better fit the material’s fracture toughness test data. However, some discrepancy still remained. Because the Zerilli equation shows small yield stress change and might differ from the experimental results in the temperature range over room temperature, a possibility that ASTM E1921 MC might fail to characterize the fracture toughness temperature dependence over room temperature was suggested.
This paper presents theoretical research on an optimum transition curve with a smoothly changing curvature using a multiple clothoid curve for improving the occupant ride comfort of automobiles when vehicle changes a lane from a traveling lane to a passing lane. In the first report, a three dimensional vehicle occupant model was developed, and the multiple clothoid curve was proposed as a new transition curve. In the second paper, application of a newly-developed multiple clothoid curve for the vehicle turning at an intersection was reported. In this paper, application of the multiple clothoid curve for the vehicle lane change is presented. The traveling path from a slow lane to a fast lane consists of the combination of a straight line and an arc of circle. At the connecting points between an inlet straight line and a circular arc, or between a circular arc and an outlet straight line, vehicles cannot run smoothly owing to the discontinuity of curvature. The discontinuity of curvature at connecting points makes highly precise control of apparatus difficult. Then, the smoothly changed curvature of multiple clothoid curve is applied as a transition curve at connecting points. Four sorts of lane change which consists of various combination of a straight line and a circular arc are investigated, and the validity of the application of a multiple clothoid curve as a transition curve at connecting points is explained. According to the prescribed analysis method, a three-dimensional vehicle passenger model is applied and the validity of applying to a multiple clothoid curve is quantitatively demonstrated as compared with the case where a connecting point is not interpolated. It was found that the influence of multiple clothoid curve on the vehicle movement and a ride comfort is superior to those of the non-interpolation. Some results are presented in the form of parametric plots.
In this paper, a flexible morphing wing with piezoelectric materials for morphing actuation is studied. The objectives of this paper are 1) to develop an integrated geometrically nonlinear electro-aeroelastic framework, which allows evaluating performances of flexible morphing wings with piezoelectric actuators, 2) to validate the developed analysis framework, and 3) to demonstrate the capability of the framework and explore the performance. This paper provides a description of the electro-aeroelastic equations of morphing wings taking into account piezoelectric effects, which can be used to actuate morphing wings. The electro-mechanical model is validated by comparing with experimental results. The validation with a single macro fiber composite showed a very good agreement between the experimental result and the simulation. The result of an actuation test with an integrated corrugated structure and macro fiber composite also reasonably agreed with the solution from the present code. Aeroelastic behaviors of a corrugated wing with the piezoelectric actuator are then explored. The camber morphing wing with the corrugated structure actuated by the piezoelectric actuator could provide a larger lift in the vicinity of the trailing edge. Such a camber morphing has a good potential to control aeroelastic response by wing morphing with piezoelectric actuation.
Stress distribution of brake disks during braking is complicated due to sliding contact and frictional heat. To investigate the effect of sliding contact on the fatigue properties of low alloy steel, a new fatigue test method that enables the application of cyclic loading with sliding contact has been developed. Two main results have been obtained by this method. Firstly, the specimens with sliding contact had longer life than those without sliding contact (normal test) under a finite life regime. Secondly, the fatigue limit with sliding contact was 26% lower than that without sliding contact. Moreover, the results of normal test result showed no fatigue failure at more than 106 cycles, whereas the tests with sliding contact had fatigue failure even over 106 cycles. To clarify the fatigue limit reduction caused by sliding contact, fatigue tests applying sliding contact prior to cyclic loading (pre-wear) has been conducted. The results of pre-wear showed no fatigue failure at more than 106 cycles, which is similar to the normal test, but the fatigue limit is lower compared to that in the normal test. The effect of sliding contact on the fatigue properties is discussed from point of wear and surface roughness. Thickness of the test specimens was reduced by wear with an increase of sliding contact duration. This suggests that the sliding contact was possibly contributed to have longer life in the fatigue tests than the normal tests because of elimination of fatigue damaged surface layers. Surface roughness also increased due to sliding contact. This leads decreasing of fatigue limits. √area parameter calculated from surface roughness was used to predict the fatigue limits with sliding contact. The predicted fatigue limits corresponded well to experiment fatigue limits if surface roughness was considered as a single notch. Therefore, it is concluded that surface roughness variation due to sliding contact affects the fatigue strength of the tested low alloy steel.
To design economical frame structures, it is necessary to determine the optimum frame layout and optimum cross-sectional area of each frame member. Although previous studies have proposed a variety of optimization methods, they can be applicable to small-scale frame structures and have been verified only for simple frame structures with a small number of design parameters. Therefore, it is desirable to develop an optimization method applicable to large-scale frame structures with a large number of design parameters. However, no studies have been conducted on an optimization method for large-scale frame structures. This study applies the layout optimization technique to determine both the layout and the cross-sectional area of each member for large-scale structures. In this method, to reduce the number of design parameters, first, only the existence of each member is determined in the layout optimization, and then, the cross-sectional area of each member is determined by the axial stress in the member, calculated through stress analyses. With the reduction of the number of parameters, the present method enables to determine the large-scale frame structures. To confirm the effectiveness, the method is applied to the optimization of a brace layout for a large-scale steel frame structure of a thermal power plant with about 250 design parameters. As a result of applying the method, the total weight of the obtained layout could be reduced by up to 17% from that of the existing layout. The results demonstrate that the method can be applicable to large-scale frame structures with hundreds of design parameters, such as steel frame structures in thermal power plants.
The rigid plastic finite element method (RPFEM) is used in many re-meshing procedures in material processing analysis. Currently, the four-node quadrilateral element, which can avoid volumetric locking, is applied in the RPFEM. However, it is desirable to apply the three-node triangular element instead because of its easy and robust mesh generation procedure. This study applied the three-node triangular element with drilling and strain degrees of freedoms (GNTri3) to the RPFEM, the validity of which was verified by analyzing some numerical examples. First, as verification for the volumetric locking characteristic of the GNTri3, FEM analysis of a nearly incompressible elastic body under plane strain conditions was performed. Volumetric locking was recognized by applying full integration to the element stiffness matrix of the GNTri3. Therefore, it was revealed that the RPFEM using the GNTri3 is necessary for applying selective reduced integration to the element stiffness matrix. Analysis of the RPFEM using the GNTri3 showed that the tool pressure was in good agreement with theoretical solutions and FEM results obtained using a conventional four-node quadrilateral element at a rigid punch indentation. In addition, reasonable material processing deformations were computed in the plane strain compression test.Therefore, validity of the RPFEM using the GNTri3 was verified by numerical results.
This paper proposes a novel topology optimization method for unsteady state incompressible Navier-Stokes flow. Many methods of topology optimization for steady state flow have been proposed, whereas most fluid flow problems should be considered as unsteady state. Therefore, a topology optimization method focusing on unsteady state fluid flow governed by the incompressible Navier-Stokes equation is considered in this paper. In addition, the defined boundary condition on the wall of an optimized structure should be precisely evaluated because it describes the specific fluid flow profile, such as velocity and pressure, on the wall that the fluid contacts. In order to solve flow profile near walls, an immersed boundary method is applied in the proposed method. The finite volume method is adopted to discretize primal and adjoint problems. These problems are solved using the Pressure-Implicit with Splitting of Operators (PISO) method. In this study, sensitivity analysis based on a topological derivative is applied. The update scheme for the design variable uses a reaction-diffusion equation. Some examples are shown and the effectiveness of our method is discussed in this paper.
The experimental modal analysis is widely used to identify the modal parameters: natural frequency, damping characteristics and mode shape, in the structural dynamic analysis. The existing method, however, is not adequate when the damping characteristics is too low. When the resonance frequency is not close to the measured frequencies, it is difficult to identify low damping characteristics due to lack of FRF data around resonance frequency. Thus, the linear fit method which is applicable to systems with very low damping characteristics is proposed in our previous study. In the proposed method, a set of linear functions with respect to the real and imaginary parts of original Frequency Response Function (FRF) is derived by canceling the residue of FRF. Then, the modal parameters are identified by fitting the experimental data to the obtained linear functions using the least-square method. However, there is a technical issue left in the method: the identified parameters are sensitive to the data range applied due to inhomogeneous error distribution. Here, the weighted least-square method is introduced to improve the identification accuracy. That is, smaller weight is assigned to the data with low accuracy, while larger weight is assigned to the data with high accuracy. A series of experiment was conducted to investigate influence of the data range and the difference of the governing equations derived from FRF. The result validates the modified method coupling with the weighted least-square method.
The aerodynamic noise generated from a perforated metal plate varied by air-flow direction. In the case of expansion type perforated metal plate, it generates very large level aerodynamic noise with a prominent peak in the frequency characteristic. In this paper, velocity fluctuation at some measuring points is measured by a hotwire anemometer to examine its cause. In the experiment, coherent output power (COP) of velocity fluctuation is calculated. The coherence function is defined by the relations between the generated noise and velocity fluctuation of air flow behind perforated metal plate. The expansion type perforated metal plate generates orderly vortex shedding and it brings the vibration of perforated metal plate. The distribution of partial overall value of COP indicates strong correlation with the plate vibration mode. That phenomenon is predicted as lock-in phenomenon between vortex and vibration of the plate.
A bifilar suspension pendulum, a uniform density bar suspended at its two points by two strings of same length from an upper horizontal plane, may swing in two vertical planes or make torsional oscillation about a vertical axis. The free oscillation periods measured in the three modes match well the normal modes derived from linear theory due to the pendulum configuration. These modes are linearly independent of each other, but it is possible to make nonlinear coupling between those as various types of internal resonance. For each mode, a common equation of inertia type shows to give nonlinear hardening/softening. Swing mode 1 has softening as in the simple pendulum, but Swinging-bar mode 2 makes softening/hardening mainly depending on the configuration. Rotational oscillation mode 3 also makes softening/hardening with changing the moment of inertia and the configuration. These are shown analytically and numerically by methods of singular perturbation and numerical computations, prior to an analysis of the internal resonances in a forthcoming paper.
We have developed a small size and high strength spiral bevel gear fabricated by five axis controlled machining center. In the present report, we propose a novel spiral bevel gear with the rib at the end of face width to reinforce the tooth bending strength, which is machined with a ball-nose end-mill tool. We investigate the influence of the rib shape on the bending stress at the tooth root based on 1D-CAE model and demonstrate the effect of rib reinforcement at the proposed spiral bevel gear. As a result, a novel guideline is found to design the small size and high strength spiral bevel gear with the rib at the end of face width from a view of rib shape.
Product-Service System (PSS) is a business model that creates high added value through value co-creation process among stakeholders with sophisticated integration of products and services. In service marketing research field, value-in-context is emphasized as a way of thinking in which the value of a product or service is determined by various stakeholders following their own contexts. In order to improve the value-in-context, stakeholders need appropriate sharing of their context and feedback on its result to build consensus in value co-creation. Currently, On the other hand, the manufacturing industry makes decisions without sufficient context sharing and appropriate consensus building. In other words, information asymmetry occurs among stakeholders involved in not only the PSS but also in various sustainable developments. Against this background, this study aims to provide a method to analyze the factors that cause information asymmetry so as to realize the reliable introduction and operation of a PSS. For this purpose, this paper proposes a modelling method of context, or internal mental elements of stakeholder, to realize information asymmetry analysis from perspective of value-in-context. A design scene in business demonstrates that the proposed method visualizes the asymmetry among various PSS stakeholders. Moreover, it is validated that the proposed method is effective for derivation of solution which resolve the factor of information asymmetry.
Faced with a changing about global environmental issues, there are great expectations to optimize energy saving design in home appliance products. For effective energy saving design in Refrigeration System, integrated design method is highly needed to understand detailed physical behavior of a whole product based on careful study of the interactive influence of each device (e.g., Insulator layout design, Heat exchanger, Compressor and FAN flow rate balance, etc.). Although 1D and 3D-CAE tool become a part of engineer's daily routine in recently, effective integrity interface between the Digital tool and real humanistic collaboration process is the most important key to accomplish the innovative synthesis. This paper presents a practical lean development method using set-based design method which combines digital tool with human tacit knowledge for architecture type product having hierarchical interaction between system and subsystems.
Origami Spring is one of the extendable Origamis which changes from a flat to a tower configuration. The important feature of the Origami Spring is that its whole structure simultaneously extends/contracts with a slight bending as a parasitic motion of the extension/contraction when only one of the segments is actuated. Therefore, such an observed macro motion of the Origami Spring can be regarded as a single DOF motion. Based on its folding diagram, the mobility of the Origami Spring was revealed to be three by the kinematic model obtained with regarding its folds as revolute joints. In order to figure out the discrepancy between the observation and mobility analysis, kinematic analysis of the Origami Spring has been carried out taking into consideration the collision and deformation of components. As the result of the analysis, it was clarified that the Origami Spring has actually three DOFs while one of the three DOFs generates a simple extension-contraction motion and the other two DOFs contribute to adjustments of its configuration to avoid collision of components within a small motion range. It was also presented that the observed behavior of the Origami Spring during extension and contraction can be explained by the internal energy based on deformation of components. Finally, the observed single DOF macro motion is reproduced with a model in which the deformation of the components is considered.
In order to make an electric power of renewable energy source increase, development of a new transmission network is effective. However, it is because installation of a new transmission network takes a huge investment, operating technique regarding improvement of the utilization factor of a transmission network is investigated. On the other hand, stabilization of distribution electric power by hydrogen energy careers, such as ammonia or methyl-cyclohexane (MCH) is expected to contribute to the drastic increase in utilization factor of the transmission network. Moreover, because these hydrogen energy careers can store electric power, it is effective in making the reliability of the transmission network increase. The energy flow of the system accompanied by use of each energy career of ammonia or MCH is clarified, the examination method of the utilization factor of the transmission network with the electric power leveling by the hydrogen career was proposed. The proposal analysis method is applied to a transmission network of Wakkanai, the relation between the amount of introduction of renewable energy and the utilization factor of the transmission network, and the utilization factor of the transmission network using a hydrogen career were clarified.
Weldline, which has an influence on the strength as well as the surface appearance of a plastic product, is one of the crucial defects in plastic injection molding (PIM). Process parameters such as melt temperature, injection time and so on should be adjusted and optimized for the weldline reduction. Rapid heating cycle molding (RHCM) that controls the mold temperature during the PIM is an effective approach for the weldline reduction, but the mold temperature profile is completely determined by an engineering experience or a trial and error method. In addition, some process parameters such as melt temperature, injection time and packing pressure also play an important role for the weldline and cycle time. In this paper, for weldline reduction and short cycle time, the mold temperature profile and several process parameters in the RHCM are determined by using sequential approximate optimization. The mold temperature during heating time is maximized for the weldline reduction, whereas the cycle time is minimized for the high productivity. Through the numerical result, the trade-off between the mold temperature and the cycle time is clarified. Also, it is found that the higher mold temperature is, the shorter weldline is.
In the mechanical design of a turbine blade for an automotive turbo-charger, it is pointed out that the mistuning effect caused by the difference of the casting condition should be considered. Namely, the difference of the casting condition causes the small variation of Young's modulus of each blade on a turbine wheel. These small variations break the cyclic symmetry, and split the eigenvalue pairs. In the forced response of a mistuned system, the responses of all blades become different, and the response of a certain blade may become extremely large due to splitting of the duplicated eigenvalues and distortion of the vibration modes. In this study, the reduced order model FMM (Fundamental Mistuning Model) is applied to evaluate the resonant response of mistuned system. First, the frequency response analysis of mistuned system is carried out, using both of the FMM and the direct FEM, and the calculated results are compared to confirm the validity of the FMM. Second, the frequency response analysis of mistuned system is carried out using the FMM, the Monte Carlo simulation and the optimal method to examine the effect of various parameters on the maximum response of a mistuned system. In addition, the effect of the intentional mistuning on the reduction of the maximum response is researched using the genetic algorithm.
A vibration isolation device with an active dynamic vibration absorber is developed to remove vibration induced by a cryopump. Cryopump is used to make high-vacuum and low-temperature environments for precise measurement. However, it induces vibrations with multiple frequencies, which may deteriorate measurement accuracy. This study focuses on removing the vibration of low frequencies because conventional vibration isolation devices for cryopump can hardly remove them. In the developed vibration isolation device, an active vibration absorber is used to remove the vibration efficiently at low frequencies. The controller is designed based on the internal model principle. The pole assignment is used to tune the controller. The efficacy of the designed and tuned controller is demonstrated in the developed apparatus.
This paper describes how to produce a biodiesel fuel (BDF) from the waste soup of ramen noodles, especially focusing on the recovery process of the oil (triglycerides) from a large amount of waste soup or the oily wastewater disposed of by pouring it down the sink by a ramen restaurant. By combining a semi-transparent bucket (~6 L) with a cock and solvent extraction, it is shown that oil can be recovered easily from 300 or more bowls of ramen noodle waste soup, with an energy profit ratio (EPR) of more than 5.2. The initial cost of the bucket is about 1600 yen, so it has little effect on the price of the BDF produced from the oil in the ramen noodle waste soup, and it is shown that the increase in running cost to produce BDF by this method is about 2.3 yen/L if the rate of recovery of hexane (solvent) is over 99%, which is approximately equivalent to the production cost of waste-cooking-oil BDF production by previously reported methods. Furthermore, in the case of applying the proposed method based on the solvent extraction to the recovery of oil from the oily wastewater disposed of by a ramen noodle restaurant, it is shown that oil can be recovered from the waste soup of ramen noodles just after disposal as well as from the oily wastewater that spent one day in the grease trap. In the former case, EPR is 5.0, and the estimated amount of BDF is greater than 100 L/month for one restaurant. However, in the case of using the oily wastewater from the grease trap, EPR is less than 2.0 because of the reduction of yield of BDF due to a greater oxidation deterioration of the recovered oil, when the alkyl catalyst method is used. Therefore, it is desirable to recover oil from the oily wastewater at the drain pipe just after the sink.
The prevention of excessive deformation by thermal ratcheting is important in the elevated temperature design of fast breeder reactors (FBR). In an experimental study that simulated a fast breeder reactor vessel near the coolant surface, it was reported that the long distance travel of temperature distribution causes a new type of thermal ratcheting, even in the absence of primary stress. Without excessive stress and travel distance, the inclement of the plastic strain derived from the above mechanism reduced each cycle of thermal transient, and finally reaches to approximately 0. In this paper, we investigate path independency on “saturated” distribution of plastic strain. For this purpose, we carried out several cases of finite element analyses with initial strain distribution, which simulated plastic strain distribution in the middle of accumulating. As the result, we confirmed that the shape of saturated distribution has small dependency on the shape of distribution in the middle of accumulating. Additionally, in the case using conservative initial strain distribution, further accumulation of plastic strain was not observed. This result suggests the possibility of the method that evaluate whether the accumulation of the plastic strain go beyond design limits.
This study has developed a model for stability analysis in a balance piston mechanism. The balance piston mechanism is employed to suppress an axial vibration in the turbopump. For its high rotational speed and discharged pressure, many turbopumps use balance piston mechanism to balance axial direction thrust, however sometimes axial vibration occurs because of decreased axial damping. It means that the balance piston mechanism has possibility of occurrence of self-excited vibration due to its dynamics. The occurrence of self-excited vibration depends on the structure of the balance piston mechanism. Therefore, the relationship between the stability and the structure should be predicted in advance. The proposed model using an active control can analyze the relationship concerned with the occurrence of self-excited vibration, namely stability and the structure of the balance piston mechanism. Moreover, the optimal structure for the balance piston mechanism can be decided based on a support vector machine.
When one rides a car on a gravel road, a noise due to collision of gravels rolled up by tires makes him uncomfortable. The collisions are assumed as random impacts with respect to mass, collision time, position, velocity, angle and so on. In order to probabilistically estimate the noise, the time history of impact force in the case where a force sensor on a rigid pendulum hits a peripherally clamped thin rectangular plate is precisely measured for various impact speeds, angles and positions. The vibration response and sound pressure radiating from the plate are then estimated with the measured impact forces based on Rayleigh-Ritz method and impulse response method. It was then revealed that the time history of impact force could be represented with a certain time function for any impact speeds, angles and positions and that the component of the impact force perpendicular to the plate determined the maximum of the impact force. The time history of impact force can also be approximated as a superposition of the extreme function and Gaussian function. The estimated vibration acceleration of the plate and sound pressure agree very well the measured values. The noise generated by random impacts was estimated probabilistically. It was found that the noise strongly depends on the natural vibration modes of the plate.
The absolute nodal coordinate formulation (ANCF) is one of effective ways for describing the large rotation and deformation in multibody system analysis. A distinctive feature of the ANCF is to use absolute nodal coordinates and global slopes as the element nodal coordinates. Accordingly, it gives a constant and symmetric mass matrix. On the other hand, elastic forces, which are generally expressed by highly nonlinear terms, affects computational performance. Therefore, one of significant topics in the implementation of the ANCF is to derive mathematical descriptions of the elastic forces which can be calculated efficiently. The authors proposed an efficient calculation procedure for the ANCF beam element under the assumption of the Euler-Bernoulli beam theory. Thus, this study is aimed at extending the method to the two dimensional shear deformable ANCF beam element. In particular, we introduce the method called the elastic line approach, which can avoid the shear locking problem. In the present formulation, the strain and the kinetic energies are expressed as functions of the element and the global coordinates, respectively. Then, algebraic constraints regarding the relations between the global and the element coordinate systems are introduced by means of the Lagrange's method of undetermined multipliers. Therefore, this method can be categorized into augmented formulation techniques. The equations of motions of this constrained system are derived by the Lagrange's equation. As the result, equations of motion are given by the differential algebraic equation with index-1. After that, in order to evaluate the proposed method, it is applied to the large deformation problem in the plane case.
A vibration-isolating bed for ambulances using an inerter is proposed. The structure of the vibration-isolating bed is assumed to consist of a bottom frame fixed to the ambulance floor and an upper frame on which the stretcher is placed. Both are connected only by the suspension, including the inerter, in the vertical and horizontal directions. Because the inerter can reduce the gain of the high frequency band and delay the response, the time when maximum acceleration is applied to vibration-isolating bed can be shortened in a limited space in ambulance. We consider the vibration-isolating bed as a plant and the designed suspension as a controller, and then formulate the state equation. To reduce the acceleration within the movable range of the bed in ambulance, the controller that minimizes the H∞ norm of the transfer function from the external force acting on the vibration-isolating bed to vibration-isolating bed acceleration is calculated by bilinear matrix inequality. The transfer function determinates the structure and coefficient of the suspension by assuming that the transfer function is the sum of mechanical admittance of spring, damper and inerter. The usefulness of the vibration-isolating bed is verified by numerical simulations by using MATLAB assuming braking and turning.