The present paper discloses the influence of sampling period on the occurrence of the spillover by approximate theoretical analysis and numerical simulation. The fundamental equation of the system is formulated about a beam-structure. The control law, so called “Direct Output Feedback” is used. Taking the first mode of an uniform cantilever beam as a control mode and the second and third modes as residual modes, numerical simulation has been carried out about many values of the sampling period. Sensor and actuator are collocated at the tip of the cantilever beam. The equation of the present approximate analysis is derived through dropping the terms of coupling and of the feedback of displacement. The formula of stability criterion for each mode is derived through the calculation of the work done by the control force and the structural damping force during the sampling period. The approximate analysis and the numerical simulation disclose the occurrence of a resonant type of spillover in the case where the sampling period is very close to (2m-1)/2 of the natural period of a normal mode. The result of numerical simulation is in good agreement with that of approximate analysis about the ranges of the sampling period which produces the spillover.
The effect on the spillover of the values of the coefficient multiplied to the terms of the square of the control force in the performance index for optimization of feedback gain is studied for several values of the sampling period by numerical simulation. It is disclosed that each value of the sampling period makes a difference on instability behavior due to the variation of the coefficient. Fixing the position of actuator at the tip of the cantilever, numerical simulation is carried out for several values of the sensor position and the sampling period. The results for the ranges of the values of the coefficient and of the sensor position which produces the spillover are well explained by the approximate theory derived in Part 1. Experimental studies have been carried out by a steel cantilever beam of which first natural frequency is 4.38Hz, for many sampling period from 1.28ms to 25.6ms in a regular interval. The experimental results for the spillover are satisfactorily explained by the approximate theory in Part 1.
As a fundamental research problem relating to the amplitude of Pogo oscillation of liquid propellant launch vehicles, an experimental study was conducted in which a cylindrical shell vertically hung and partially filled with liquid was longitudinally excited at the bottom in the authors' previous paper. The vibration of the shell wall was induced at the several specific ranges of exciting frequency by the mechanism of parametric excitation. To analyze this problem, a set of nonlinear equations of vibration is derived with the aid of the finite element method. Axial mode shapes of the axisymmetrical and circumferentially n-wave modes are calculated from the linear part of the set of nonlinear equations. Using these two modes, the set of nonlinear equations is reduced to the coupled equations of two degrees of freedom. The equations to calculate a stationary vibration, and its stability are derived. The range of the parametric excitation is obtained in the plane of exciting force amplitude and frequency.
This paper presents an experimental investigation of the linear (small amplitude) and nonlinear (large amplitude) fundamental vibrations of orthotropic stiffened square plates with a small initial curvature. The stiffened plates are made of toughpitch copper plates by photo-etching. The plates are excited by a speaker and the modes of linear vibration are measured by laser holography. The effects of the initial curvatures on the vibration modes and the variations of eigen-frequencies with the amplitude are clarified. The experimental results are found to verify the previously theoretical investigations.
This paper presents a new guidance law for a missile with constant acceleration. When target velocity and missile acceleration are constant, there exists the straight collision course which depends on the initial positions of a missile and a target. The presented guidance law guides a missile so as to fly along the collision course. The implementation of the guidance law needs the values of missile velocity vector, target velocity vector and the relative position vector between a missile and a target. If the measurement of these variables is difficult, this paper also presents the simplified method of constructing the guidance law by use of only the initial values of time-to-go and missile velocity, which are given from a launcher or a parent aircraft before launch. The performance of the presented laws is compared with that of the conventional proportional navigation using simulation studies of a planar model. The simulation results show that the magnitude of missile acceleration produced with the presented guidance laws are far smaller than that with a proportional navigation.
Investigators of DTNSRDC in USA advocate that PAR-WIG has nearly twice range capability, in comparison with conventional airplanes, due to higher L/D and lower empty weight fraction. Especially PAR-WIG with a wing of low aspect ratio may have the empty weight which is about two-thirds of the conventional airplane's. In this paper empty weight is analysed, based on the data available to the present author, and compared between various kinds. Synthetic effect of the wing aspect ratio on the operational efficiency is also examined. The opinions of DTNSRDC seem to be somewhat too optimistic, and so valid only with some reduction.