Mass-spring dashpot model

Typically, an accelerometer (or g-cell) consists of a proof mass that is suspended with a spring, or compliant beam, in the presence of some damping, and anchored to a fixed reference. Coupling this mass-spring-dashpot model (Fig. 7.1.2)... 

Fig. 5, this type of system is equivalent to a mass-spring-dashpot-hysteretic element system. The Bouc-Wen model is used in order to account for nonlinear hysteretic response, which involves an additional hysteretic degree of freedom, henceforth denoted as z(f). 

Lu et al. [7] extended the mass-spring model of the interface to include a dashpot, modeling the interface as viscoelastic, as shown in Fig. 3. The continuous boundary conditions for displacement and shear stress were replaced by the equations of motion of contacting molecules. The interaction forces between the contacting molecules are modeled as a viscoelastic fluid, which results in a complex shear modulus for the interface, G = G + mG", where G is the storage modulus and G" is the loss modulus. G is a continuum molecular interaction between liquid and surface particles, representing the force between particles for a unit shear displacement. The authors also determined a relationship for the slip parameter Eq. (18) in terms of bulk and molecular parameters [7, 43] ... 

Boundary Element Method and Its Applications to the Modeling of MEMS Devices, Fig. 2 Spring-mass-dashpot model of a resonator... 

Determination of Parameters The effective mass for a spring-mass-dashpot model of the resonator is related to geometry and the density of the polysilicon. In particular, energy considerations and an application of beam theory lead to a resonator effective mass given by... 

The extension of the previous models to a sphere coupled to the plate via a spring and a dashpot is straightforward. The coupling can be achieved either via a Voigt-type circuit (viscoelastic solid, Fig. 2e) or via a Maxwell-type circuit (viscoelastic liquid, Fig. 2f). Below, we assume that the object is so heavy that it does not take part in the motion. When the mass is infinite, the inertial term drops out of the load impedance. An infinite mass is graphically depicted as a wall. For Voigt-type couphng we find ... 

An example for self-excited vibrations is the stick-slip phenomenon. In machining applications, stick-slip typically arises at the glides. The mechanical model can be seen in Fig. 12. The block of mass m is fixed to the moving wall by a spring of stiffness k and a dashpot of damping c. The wall is moving with velocity vq-The friction force acting on the block is... 

Based on its operation principle, the resonator can be modeled as a simple spring-mass-dashpot system, as shown in Fig. 2, with the shuttle being the proof mass, folder beams being the spring, and the surrounding air being the dashpot damper. The displacement of the proof mass can then be obtained by solving the second-order differential equation... 

Figure 1 shows a lumped mass discretization (i.e., lirmped mass model) that of a horizontally layered soil deposit. Soil mass (m) is lumped at the layer interfaces (layers 1 through n). In each layer, soil stiffness is represented by a nonlinear spring. In addition to hysteretic damping inherent to a nmilinear spring, a viscous damping coefficient (c) is also part of a model shown in Fig. 1, as schematically represented by dashpots. 

An analysis is made with a mechanical spring/dash pot model as shown in Figure 2.17, where a mass M is restrained by a spring of stiffness k and a dashpot with viscosity T). The solution as illustrated in Figure 2.17 is an exponentially decaying cosine wave, that is, the displacement of the mass is given by... 

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