Beam, forced vibrations

Other Transducers. Ultrasound also has been used for the measurement of force, vibration, acceleration, interface location, position changes, differentiation between the composition of differing materials, grain size in metals, and evaluation of stress and strain and elasticity in materials. Sonic devices can used to detect gas leaks, and to count discrete parts by means of an interrupted sound beam. Frequently, an ultrasonic device can be applied where photoelectric derices are used. Particularly tn situations where light-sensitive materials are being processed (hence presence of light must be avoided), ultrasonic devices may be the detectors of choice. 

The expressions for free and forced vibrations are given, respectively, by Eqs. (17.85) and (17.99). If the origin of coordinates is taken at the clamped end of the beam, the assumed boundary conditions are... 

To drive the system out of its stable equilibrium, the whole apparatus is shaken from side to side with an electromagnetic vibration generator. The goal is to understand the forced vibrations of the beam as measured by x(t). the displacement of the tip from the midline of the magnets. 

Hz (shown in Figure 4.16). This is the frequency at which our beam will vibrate when the 500-N force is applied at the indicated position. 

In fact, of course, the electric vector in a light beam is not steady but varies sinusoidally with time, so that the intensity E must be amended to E0 cos 277-vt (where v is the frequency of the light and t the time) the electron imagined above will therefore be executing forced vibrations. By arguments set out by Lorentz (1909) and explained in detail by Partington (1953), the general equation (19) is reached... 

Fig. 7. Schematic diagram for the single cantilever beam apparatus for measurement of the complex Young s modulus. (A forced vibration nonresonance method.)...

Figure 1.3 The resonant gate field effect transistor, one of the first MEMS devices. A released metal cantilever beam forms the gate electrode over the diffused source-drain channel. The input signal is applied to the input force plate, which causes the cantilever beam to vibrate, modulating the current through the transistor. Maximum vibration occurs at the resonant frequency of the cantilever beam, enabling the device to act as a high-Q electromechanical filter. (Reprinted with permission from IEEE Trans. Electron Devices, The resonant gate transistor, H.C. Nathanson, W.E. Newell, R.A. Wickstrom and J.R. Davis Jr., 1967 IEEE.)...

Forced Vibrations or Beam of Hollow Rectangular Cross Section Under Biaxial Bending In order to examine the influence of shear deformation on the free vibrations of beams in the geometrically nonlinear range, a clamped beam... 

Forced Vibrations or Beam of Hollow Rectangular Cross Section Subjected to Axial Compressive Load... 

Nonlinear Dynamic Seismic Analysis, Table 6 Periods Ty, TJ s) of the first cycle and maximum central displacements Vmax(iu), H> ,ax(iu) of the beam of application section Forced Vibrations or Beam of Hollow Rectangular Cross Section Subjected to Axial Compressive Load ... 

Forced Vibrations of Beam of Thin-Walled l-Section Without STMDE... 

In order to investigate the influence of geometrical nonlinearity on the forced vibrations of beams xmder nommiform torsion, the beam of application section Free Vibrations of Beam of Thin-Walled I-Section Without STMDE has been... 

Prismatic Beam of Asymmetric Cross Section Under Harmonic Excitation In this application, the forced vibrations of a hinged steel L-shaped beam of unequal legs (asynunetric cross section) (Fig. 26a) (E = 2.1... 

Nonlinear Dynamic Seismic Analysis, Fig. 25 Time his- beam of application section Forced Vibrations or Beam tory of the axial u (a), transverse v (b), w (c), displace- of Monosymmetric Cross Section Under Eccentric Trans-... 

Fig. F.S. Vibration of a beam. One end of the beam is clamped the displacement and the slope are zero. Another end of the beam is free the force and the torque are zero. The lowest resonance frequency, which corresponds to a vibration without a node, is determined by Eq, (F.32).

Forced sinusoidal vibration of thin cantilever beam specimen by electrodynamic shaker... 

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