The current state-of-the-art of Japan farming systems is changing. The number of farmers is decreasing and the majority of them are old. These problems are typical of developed countries. Due to these situations, bigger tractor and higher working speeds are required to maintain or increase performance. In addition, there has been a problem associated with off road vehicles that must operate on roads for part of their life and must therefore mixed with other vehicles with considerably higher braking and handling performance. Therefore, in order to meet this situation, new speed regulations are being enforced. In Europe, for example, the new speed regulations for tractors traveling on road increased from 30 to 40 km/h. In Japan, it was increased from 15 to 35 km/h.　This gradual transition towards higher working speeds has brought technical problems. Among these problems are, increased shock loading that cause mechanical failure on the linkages, the violent vibration problems encountered by a traveling tractor on certain road conditions and the tractor handling problems at high speeds. These are highly nonlinear problems. Therefore, they are not easily well-understood using conventional methods of analysis. To be able to understand more deeply the dynamics of farm tractors, systematic experimental studies was conducted on the tractor vibrations from the nonlinear dynamics perspective.

　The study is divided into three parts:
　1) Identification of the resonance and mode shapes of the tractor using a low bump artificial test track;
　2) Classification of the types of vibrations and explanation of the subharmonic frequencies that occurred in the experiments over a wide range of forward speed using the low bump artificial test track; and,
　3) Investigation of the repeated bouncing, free fall and impact phenomenon of farm tractors using a high bump artificial test track.

　Chapter II is mainly on the identification of the resonance and mode shape analysis of farm tractor vibrations. To realize the objectives, two kinds of frequency response test were conducted using a low bump artificial test track installed on a farm gravel road and the forward speed was varied over a wide range. A vertical and pitch mode experiment was conducted to identify the vertical and pitch natural frequencies. In this experiment, all wheels of the tractor run on the test track. A roll mode experiment was also conducted to identify the roll mode of vibration. In this experiment, the right side front and rear wheels run on the test track and the left side wheels passed outside the obstacles. The analysis was conducted in the frequency domain by power spectral analysis using the Campbell diagrams in the identification of the resonance and the synthesized Bode diagram in the identification of the mode shapes. In the vertical and pitch mode experiment, the motion of the tractor was a two-degrees-of-freedom motion. In the roll mode experiment, the tractor was four degrees-of-freedom motion. The subharmonic frequencies that occurred could not be clearly explained in the frequency domain analysis, so that, a time domain analysis was conducted to explain its occurrence.

　In chapter III a time domain analysis using chaos time series analysis was conducted. The data of the vertical and pitch mode experiment were used for this purpose. Chaos time series was applied to classify the types of vibrations of the tractor over a wide range of forward speeds. Qualitative and quantitative analysis of the time series data were conducted. In the qualitative analysis, the phase portrait and Poincare section were used in the determination of the types of vibrations. In the quantitative analysis, the correlation dimension and the trend of the largest Lyapunov exponents were used. The results showed quasi-periodic vibration in the middle speed by using the phase portrait and Poincare section. Quantitative analysis using the correlation dimension analysis and trend of the largest Lyapunov exponents classified the random and chaotic vibrations in the low and high speeds respectively. The vertical and pitch mode of vibrations identified in vertical and pitch mode experiment occurred in the quasi-periodic vibrations in the middle speed range. The influence of the gravel farm road where the test track was installed significantly affected the type of vibration. Thus, random vibrations occurred in the low speed range. The occurrence of the subharmonic frequencies signified chaotic vibrations or dynamic instability of tractor dynamics.

　Chapter IV investigates the tractor handling problems when steering control loss occurs due to no contact of the rolling tires with the ground surface. To produce this phenomenon, a steady state response test of continuous input was conducted. A transient response test during standstill was also conducted to observe clearly the phenomenon. The steady state response test of continuous input resulted to a repeated bouncing, free fall and impact phenomenon. Loss of steering control occurred when the wheels lose contact with the ground surface. This was demonstrated from the time series data that showed a flat -1g acceleration level responses that means no contact of the wheels of tractor with the ground surface The test track used was a multiple force vibration because the force frequency contains higher harmonics that produced nonlinear resonance. Chaos time series analysis was able to identify the types of vibrations and the complexity of the tractor dynamics by being able to identify the number of degrees-of-freedom of the tractor motion. This implies that the time series data contains much information that can elucidate the dynamics of farm tractor such as the degrees-of-freedom of motion of the tractor.　Comparative investigations between the low bump and the high bump test track revealed no bouncing phenomenon when using the low bump test track. Both test tracks are multiple input forced vibration experiments. In the low bump test track, the nature of the input was deterministic with random influence. In the high bump test track, the nature of the test track is a deterministic multiple forced vibration due to the fundamental frequency and its higher harmonic components. Noise in the time series data in low bump test track experiments was due to the gravel farm road where the test track was installed, thus, random vibration occurred in the low speed. In the high bump test track experiments the noise was due to the impact phenomenon between the rolling tires and the ground surface where the test track was installed. Strongly nonlinear dynamics was observed in the high bump test track when compared to the low bump. This is due to the height of the high bump test track, which is twice to that of the low bump. Tractor dynamics of the high bump test track was more complex. The higher embedding dimension of the attractor demonstrated the complex dynamics when using the high bump, compared to the embedding dimension of the low bump test track experiments. Thus, strongly and complex nonlinear dynamics of the tractor is a function of the height of the test track and the forward speed.

　The following conclusions can be drawn from this study:
　1) The resonance and mode shapes of tractor vibrations were identified by performing a vertical and pitch mode experiment and roll mode experiment by using a low bump test track.
　2) Chaos time series analysis classified the types of vibrations of the tractor such as random vibration in the low speed, quasi-periodic in the middle speed, and chaotic vibrations in the high speeds in the low bump test track experiments. The subharmonic frequencies that occurred in when using the low bump artificial test track signified the chaotic vibrations of the tractor.
　3) Loss of steering control that occurs when the wheels of the tractor lose contact with the ground surface occurred when using the high bump artificial test track. The nature of the high bump test track is a multiple forced vibration due to the fundamental force frequency and higher harmonics that produced nonlinear resonance of the tractor vibrations.
　4) Chaos time series analysis classified the types of vibrations such as quasi-periodic, weakly chaotic, period doubling and strongly chaotic vibrations.
　5) Comparative investigations between the low bump and the high bump test track revealed a strongly and more complex nonlinear dynamics when using the high bump test track experiments.

　経営の大規模化は先進国でよく見られる農家数の減少という農業構造の変化に対処する 一つの方策である。その流れの中でトラクタの大型化と高速化が進むものと予測される。特に高速作業化に移行 する過程において，スピードの制御は技術的な問題を発生させものと思われる。すなわち，高速化によって， 機械部品間の機械的破損の原因になる衝撃荷重，ある道路条件で走行するトラクタに発生する異常な振動や 高速時における走行不安定性が増大する。これらは，すべて非線形問題である。したがって，これまで使われて きた慣行的・古典的手法ではあまり理解されない。この非線形的なトラクタのダイナミックスをより深く理解 するために，非線形ダイナミックスの視点から基本的かつ系統立った実験的研究を実施した。

　本研究は次の3つの解析・考察から構成される。
　1）低い突起物で構成した人工悪路を加振源とし場合のトラクタ共振現象と振動モードの同定
　2）同突起物乗り越し実験で走行速度をパラメータとした場合に発生する振動の分類と分数調・波高調波成分の解析
　3）高い突起物で構成した人工悪路を加振源とし場合のトラクタ共振現象と反復する衝撃・落下・バウンシング現象の解析

　第2章では，主に線形振動の観点からトラクタ車体の剛体振動の共振と振動モードの同定について述べる。 この目的を実現するため，2種類の周波数応答実験を実施した。一つは，非舗装農道に三角アングルを 等間隔に配置し，その上を速度を変えて走行実験を行った。このテストの於いて，バウンスとピッチモードを 測定するためトラクタ左右両側車輪が乗り越す実験と，ロールモードを測定するため，左側の前・後輪だけが 突起物を乗り越す実験を実施した。共振振動数を見いだすためCampbell線図(丸解析図)作成し，トラクタ車体の 剛体の振動モードを見いだすため，ボード線図(Bode diagram)を作成した。

　第3章では，第2章の線形振動アプローチを非線形振動に拡張し，トラクタの振動に関して， 複雑系を理解する手法として近年注目されているカオス時系列解析（ Chaos time series analysis） を適用した。即ち，相図(Phase portrait)とポアンカレ断面(Poincare section)を用いて振動のタイプを 分類した。走行速度が中速領域では準周期振動であることが明確に分離されたが，低速域と高速域では 相図と断面図の2つで同様な傾向を示し判別できなかった。このため，さらに相関次元解析 (correlation dimension analysis）とリヤプノフ指数(Lyapunov exponent)を算出し，低速域がランダム振動と カオス振動，高速域がカオス振動であることを同定した。

　第4章は高さの異なる障害物を乗り越えるそれぞれの場合のトラクタの高速安定性問題を考察する。 連続凹凸入力に対する定常応答試験を実施し，上下方向振動の時系列データ結果から，タイヤが地面から 離れる状態を発生させ，そのときの繰り返しバウンス，自由落下，衝撃現象を観察した。すなわち，走行中常に タイヤが地面に接地している場合と，タイヤが宙に浮き，落下している状態（この時マイナスＧが現れる場合が あること）を確認した。自由落下を明確に把握するために，定置の過渡落下試験も実施した。

　この高突起物乗越試験では，入力条件の性質から，基本振動数の高調波が同時に入力され， 非線形共振現象が認められた。すなわち，倍長波共振と分数長波共振が認められた。

　本研究の結論は以下のようにまとめられる。
　1）上下振動とピッチング・モードとロール・モードのそれぞれに関して，トラクタの共振現象と 振動モード解析を行った。これらの解析は，低突起物乗り越し実験で行われた。キャンベル線図が 共振振動数の同定に，フーリエ解析を用いたボード線図解析から振動モードを解析した。
　2）カオス時系列解析の手法を加速度波形の時系列信号に適用し，周波数領域の解析のみでは 説明が困難な分数調波の出現機構を解析した。走行速度をパラメータとして整理すると，最終的には 低速・中速・高速の3つの速度領域に分類された。低速時に於いて，非舗装路面からの影響と考えられる ランダム振動が発生していた。中速域では，準周期振動(quasi-periodic vibration）となり，高速域では， カオス振動が発生していた。特に，このカオス振動の出現は，トラクタの高速時の不安定性をもたらす ものである。
　3）トラクタ・タイヤが地面との接触を失う状態が発生するトラクタの操縦安定性（高速安定性） 問題を検討した。ある速度以上で突起物を乗り越す場合に発生する反復バウンス・自由落下・衝撃現象を 実験的に発生させた。速度を変えることによって，この現象が発生する臨界速度があり，動的不安定性 （dynamic instability）を証明し，非線形共振を発生させた。カオス時系列解析によって，トラクタ振動を 分類し，その複雑性が，走行速度と突起物の高さに依存することを確かめた。