The objective of this lecture is to review the basic building blocks of lumped parameter translational mechanical systems and to build the foundations that will enable you to model more complex
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Mechanical translational system is characterized by driving source, which is Newtonian force and three passive, linear components; mass, spring (stiffness) and damper (dissipation). Mass and spring are
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Energy may be stored in a spring as its dimension changes. This energy may be released at a later date.
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One-port model elements are used to represent energy storage, dissipation, and sources within a single energy domain.
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This section first reviews mechanical system input and output model elements, and then reviews passive dissipative elements and energy-storing elements. The section also discusses coupling elements
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Kinetic energy stored: W = 21mv2. Elemental equation (Hooke''s law): f (t) = k(x1(t)−x2(t)) The spring constant k has units N m−1. Energy Stored: W = 21k(x1 − x2) In reality, springs are not perfectly
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Mechanical energy storage (MESS) refers to a system that allows for the flexible conversion and storage of energy from various sources, enabling the stored energy to be utilized for mechanical work.
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Clearly, if the energy storage element is ideal, the change of the energy stored in the element is solely determined by the energy transferred over the port. However, we will distinguish between two
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An alternative approach is to write the resistive element (R) as conductance (G); the result is shown in the following matrix equation for the electric circuit in Figure 2.11.
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This example illustrates that the effect of gravity forces can be “ignored” when we define the reference positions for displacements to be the static equilibrium positions of the system under gravity fields.
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