More recently, by using a unified approach, Webb et al. [45] considered the widely studied boundary conditions corresponding to clamped and hinged ends and many nonlocal boundary conditions and established excellent existence results for multiple positive solutions of fourth-order nonlinear equations which model deflections of an elastic beam (1.3).
This was particularly true in females (θ1_f and θ2_f < 20°), while in the male and both-sex models, deflection was of intermediate magnitude (θ1_m, θ1_bs, θ2_m, and θ2_bs >30° but <53°).
The three sub-models are: the Static Deflection Model, the Track Model and the Propagation Model.
Based on the model, the deflection can be predicted by integrating the curvatures along the span of the flexural member.
Using the proposed model, the deflection of every individual finger can be calculated and a more reliable design of comb-drive actuator can be achieved.
For the case of I k = 0, k = 1, 2, …, m, and p = 1, problem (1.1) reduces to the differential equation y ( 4 ) ( t ) = f ( t, y ( t ) ) subject to boundary value conditions y ( 0 ) = y ( 1 ) = y ″ ( 0 ) = y ″ ( 1 ) = 0, which can be used to model the deflection of elastic beams simply supported at the endpoints [9 11].
In order to obtain these behaviors of piezoelectric actuator, electromechanical characterization of piezoelectric actuator has been carried out in this paper where a mathematical model for deflection and force response of piezoelectric actuator with voltage is derived with the help of a simple first-order model under a step input voltage.
For example, mathematical models of deflection of beams.
In this model, the bending deflection of blade and the casing deformation during rubbing are taken into account.
Using the equivalent line-spring model, the deflections of the system with a crack are constructed by adding a deflection to the deflections of the uncracked system.
