Mechanics of Microelectromechanical Systems - N.Lobontiu and E.Garcia Part 1 docx

[...]... advanced mechanics of materials textbooks, such as the works of Boresi, Schmidt and Sidebottom [1] , Ugural and Fenster [2] or Cook and Young [3] Many MEMS components and devices are built as thin structures, and therefore the corresponding stresses and strains are defined with respect to a 1 Stiffness basics 11 plane Two particular cases of the general state of deformations described above are the state of. .. and the corresponding deformation Another way of expressing the load-deformation relationship for the spring in Fig 1. 1 is by reversing the causality of the problem, and relating the deformation to the force as: where is the spring’s linear compliance, and is the inverse of the stiffness, as can be seen by comparing Eqs (1. 1) and (1. 2) Figure 1. 1 Load and deformation for a linear spring Similar relationships... particular load Figure 1. 9 Thin microbeams under the action of a tip force: (a) perpendicular to the plane; (b) in-the-plane Example 1. 3 A thin-film microbar, having the configuration and dimensions of Fig 1. 10 is subject to a state of extensional residual stresses (this condition will be detailed in Chapter 6) after microfabrication The state of residual stress will generate an axial deformation of. .. Formally, Eqs (1. 5) and (1. 6) can be written in the form: where the matrix connecting the load vector on the left hand side to the deformation vector in the right hand side is called bending-related stiffness matrix Elastic systems where load and deformation are linearly proportional are called linear, and a feature of linear systems is exemplified in Eq (1. 5), which shows that part of the force is... state of plane stress and the state of plane strain Example 1. 2 A thin microcantilever, for which t . compliance. There is however the case of a beam in bending where a force that is applied at the free end of a fixed-free beam for instance produces both a linear deformation (the deflection) and. three different stiffnesses or compliances, namely: two direct (linear and rotary) and one crossed, define the elastic response at the free end of a cantilever. More details on the spring characterization. defined by: Figure 1. 4 Cantilever with tip force and moment Solution: Equation (1. 10) can be written in the generic form: When left-multiplying Eq. (1. 11) by the following equation is obtained: Equation