Single-degree-of-freedom

Fig. 7. Transmissibihty as a function of frequency ratio for single-degree-of-freedom isolators with different degrees of internal damping.

Figure 5-1. System with single degree of freedom.

Natural frequency. This parameter for a single degree of freedom is given by lu = yjk/m. Inereasing the mass reduees lu , and inereasing the spring eonstant k inereases it. From a study of the damped system, the damped natural frequeney loj = ujn J — C is lower than... 

A quick review of system torsional response may help explain why a resilient coupling works. Figure 9-14 is a torsional single degree of freedom system with a disk having a torsional moment of inertia J connected to a massless torsional spring K. 

The definitions and relationships of mass, stiffness, and damping in the preceding section assumed a single-degree of freedom. In other words, movement was limited to a single plane. Therefore, the formulas are applicable for all single degree of freedom mechanical systems. 

The calculation for torque is a primary example of a single degree of freedom in a mechanical system. Figure 43.15 represents a disk with a moment of inertia, /, that is attached to a shaft of torsional stiffness, k. 

A strut is usually viewed as a single degree of freedom constraint. It has a length, and that is its key dehning property. A stmt or column or beam can connect between two nodes, thus dehning the distance between those points. An interesting and important variant of a stmt is a cable. This component can only take tension loads, and cannot carry compressive loads. 

For a quantum system with a single degree of freedom (dimensionality D=l), a procedure parallel to that sketched above leads to the following result... 

If the objective function can be expressed as a function of one variable (single degree of freedom) the function can be differentiated, or plotted, to find the maximum or minimum. 

These force versus deflection relationships are usually nonlinear (due to materials or geometry) and are called resistance functions. They are an essential input parameter for the analysis of equivalent single degree of freedom (SDOF) systems, Resistance functions are not usually needed for analyses of multi-degree of freedom (MDOF) systems. Material models employing nonlinear stress versus strain data, as discussed in Chapter 5, are used in MDOF systems. 

The shear wall is effectively a single degree of freedom system,... 

The basic analytical model used in most blast design applications is the single degree of freedom (SDOF) system. A discussion on the fundamentals of dynamic analysis methods for SDOF systems is given below which is followed by descriptions on how to apply these methods to structural members. 

General solvent extraction practice involves only systems that are unsaturated relative to the solute(s). In such a ternary system, there would be two almost immiscible liquid phases (one that is generally aqueous) and a solute at a relatively low concentration that is distributed between them. The single degree of freedom available in such instances (at a given temperature) can be construed as the free choice of the concentration of the solute in one of the phases, provided it is below the saturation value (i.e., its solubility in that phase). Its concentration in the other phase is fixed by the equilibrium condition. The question arises of whether or not its distribution between the two liquid phases can be predicted. 

We have seen in section 3.1 the application of the concept of the harmonic oscillator in the interpretation of vibrational properties of crystals. For a unidimensional harmonic oscillator, there is a single degree of freedom ... 

On such a two-phase coexistence curve, the system has only a single degree of freedom, so that, for a given T, the pressure P is fixed, and vice versa. For example, if the temperature of a liquid-vapor system is chosen as T = 25°C, the corresponding P (read from the vapor-pressure curve) must be 23.8 Torr, as shown by the dotted line in Fig. 7.1. 

The formulation of the calculation of the optimal control field that guides the evolution of a quantum many-body system relies, basically, on the solution of the time-dependent Schrodinger equation. Messina et al. [25] have proposed an implementation of the calculation of the optimal control field for an n-degree-of-freedom system in which the Hartree approximation is used to solve the time-dependent Schrodinger equation. In this approximation, the n-degree-of-freedom wave function is written as a product of n single-degree-of-freedom wave functions, and the factorization is assumed to be valid for all time. 

Equations 1 and 3 comprise a set of three relationships between four differentials, dT, dP, dy, and d/x. There thus remains a single degree of freedom in the system in agreement with the phase rule. 

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