Yuji Sogabe

Shape optimization of transient response problems

Publisher Summary The computation cost of the shape optimization problem in transient response is fairly higher than that of the stationary problem. This chapter develops a simple and low cost numerical method of shape optimization for transient dynamic problems of solids with proportional viscous damping. A well-known approach for shape optimization problems, which is called the discrete approach, describes a domain shape with parameters of finite numbers and finds out an optimum solution of the parameters by utilizing mathematical programing methods. This approach, however, becomes quite costly in calculating the sensitivity and searching the optimum when the number of design variables increases. An alternative approach, which is called the continuous approach, describes the domain variation with a mapping function and applies the concept of material derivatives to derive the sensitivity, which is known as a shape gradient function. The continuous approach is proved to be cheaper in calculating the sensitivity than utilizing the discrete approach.

Identification of Mechanical Models for Golf Ball Materials Using a Viscoelastic Split Hopkinson Pressure Bar

A viscoelastic (polymeric) split Hopkinson pressure bar (SHPB) was used as a means of determining the dynamic characteristics of low-impedance or soft materials. The present viscoelastic SHPB consists of polymethyl methacrylate (PMMA) bars to account for the impedance mismatch between test specimens and metallic bars. Wave propagation analysis of strain pulses in a PMMA bar was executed in the frequency domain to identify its mechanical model using elementary one-dimensional wave theory. The SHPB made of PMMA bars was applied to evaluate the high strain rate compressive properties of core and cover materials for a two-piece golf ball within nearly 0.10 strain. Complex compliances of polybutadiene rubber (core) and ionomer resin (cover) specimens, which are the ratios of the strain to stress in the frequency domain, were determined to identify the respective mechanical models. To validate the accuracy of the mechanical models for golf ball materials, finite element investigations on axial collisions between the golf ball and a long elastic bar were conducted for comparison with measured contact force histories. It is demonstrated that three-element solid models can describe the dynamic behavior of both the core and cover materials within a given frequency range. The limitations of the models are also discussed.

An Optimal Design Procedure for Golf Clubhead Considering Impedance Matching

This study aims to develop a system for golf clubhead to maximize the flying distance of a golf ball after impact. The procedure consists of a step of pre-design with a CAD software, a process of optimization performed by the combination of a general purpose FEM code and an optimization program developed by the authors, and a step of redesign. For the optimization process, the relation between eigen frequencies and the coefficient of restitution (COR) is verified numerically at first. Based on the results of numerical examination, an approach is proposed for the optimal design in impact problem with basis vector method. And the basis vectors are created by using the sensitivity functions of eigen frequencies obtained by modal analysis. A numerical example is given to demonstrate the validity of the developed system.

Vibration Property of a Rubber Crawler System when Traveling Over Bumps

Abstract This study analyzed the vibration of a transporter with rubber crawlers caused by road surfaces, and compared of the performance of rubber crawlers with and without iron cores to assess the human response to vibration (vibration perceptible to human body) and the reduction of vibration. The human response to vibration was measured using an ISO standard device. Using a walking transporter traveling on an uneven road surface model, three different laden weights, four different road surface bumps dimensions, and four levels of vehicle speed were examined. The frequency-weighted r.m.s acceleration was measured at three locations — the center of gravity of the chassis, the handlebar and the carrying platform. The results revealed that the acceleration properties at each measurement point could be explained using a basic movement model.

Transient Vibration Analysis of Elastically Connected Timoshenko Double-Beam Systems.

Transient vibrations of elastically connected double-beam systems are analyzed taking into account the effects of shear deformation and rotary inertia in accordance with the Timoshenko beam theory. The Finite Integral Transform technique is successfully applied to the elastically coupled two Timoshenko beams having different cross sections and being made of different materials, which are intractable by most other analytical methods. The analytical solution by the present technique results in a series expansion form in terms of generalized orthogonal eigenfunctions defined by the boundary value problem associated with the equations of motion for the system. By solving the boundary value problem, it is shown that there exist four series of eigenvalues and eigenfunctions. Transient responses due to impulsive loading as well as step loading are analyzed and compared with the case of the Bernoulli-Euler double-beam system. It is found that the Timoshenko double-beam system behaves in a slightly different manner from that of the Bernoulli-Euler double-beam system.

Dynamic Measurement of Elastic Moduli for Composite Materials Using Disk Specimens

We propose a new method to measure orthotropic elastic moduli for composite materials. In this method, the strain histories of a disk specimen subjected to impact loading in various directions are measured in the experiments. These strains are quantitatively compared in the frequency domain with the numerical results of the dynamic finite element analyses and orthotropic elastic moduli are estimated. Using this method, all elastic moduli may be obtained with only one specimen and one test apparatus. We tried to measure elastic moduli for a carbon fiber/epoxy composite material. As a result, it was found that the orthotropic elastic moduli E 1, E 2, G 12 could be measured easily within acceptable accuracy. but this method was suitable for measuring the Poisson’s ratio v 12.

VISCOELASTIC PROPERTIES OF CFRP SUBJECTED TO IMPACT LOADS

ABSTRACT Longitudinal and torsional impact tests are individually performed on two types of CFRP rods, which were made from the same prepreg but in different fiber orientation. The wave histories resulting from longitudinal impact tests on each CFRP rod are resolved into Fourier components in order to determine the complex tensile compliance. In a similar manner, the complex shear compliance is also obtained from the analysis of torsional impact tests. Furthermore, the conformity of viscoelastic properties between two types of CFRP rods is discussed.

Fracture of Wire Rope Core Rope under Practical Load.

The fracture of a wire rope used in a travelling jig crane caused a serious accident. In order to examine the mechanism of breakage, the reduction of diameter at the fracture portion of the wire rope was measured and the number of fractured wires around the wire rope was counted. Furthermore the sectional appearance near fracture portion and the fracture surface of the wires were observed. The main conclusions obtained in this paper were as follows;(1) Friction among the wires of the wire rope core rope caused the wear of wires to reduce the sectional area of the wire rope. The wear extremely took place between outlayer of outer stand and the wire rope core (inner strand). The wear caused the reduction of sectional area and diameter of the wire rope.(2) The increase of the applied stress in the wire due to the reduction of sectional area causes the growth and propagation of fatigue cracks.(3) Usable limit for wire rope enacted by Japanese Labor Ministry for the structure of travelling crane is considered to be insufficient to use a wire rope core rope safely.

Temperature Dependence of Viscoelastic Properties of CFRP Subjected to Impact Loads.

The effect of temperature on viscoelastic properties of CFRP (carbon fiber reinforced plastic) was examined by means of a wave propagation testing. Specimens used in the present study were two types of CFRP rods, which were made from the same prepreg but in different fiber orientation. Longitudinal impact tests were performed in the temperature range -40-80°C, and strain wave histories were resolved into Fourier components in order to determine the complex compliance as well as the viscoelastic model at each temperature. The experimental results revealed that the dynamic compliance (real part of complex compliance) increased with temperature, but change of the loss compliance (imaginary part of complex compliance) was not monotonous as it showed a maximum value at about -20°C and showed a minimum value at about 40°C. Furthermore, shear properties were evaluated from the longitudinal data on the two types of specimens based on the coordinate transformation law of viscoelastic functions (e.g. complex modulus, complex compliance) which were derived in the previous paper.

DETERMINATION OF VISCOELASTIC MODEL FOR CFRP BY WAVE PROPAGATION TESTING

Longitudinal and torsional impact tests were individually performed on two types of CFRP (carbon fibre reinforced plastic) rods with a view to assessing the dynamic properties of the materials. The wave history resulting from the longitudinal impact tests on each CFRP rod was resolved into Fourier components in order to determine the complex tensile compliance. In a similar manner, the complex shear compliance was also obtained from the analysis of torsional impact tests. The viscoelastic models and parameters both for tension and for shear were subsequently determined based on the variations of the complex compliances with frequency. It was found for each material that the 4-element viscoelastic model should be applied to the dynamic behaviour of the materials both in tension and in shear over a wide frequency range.