This paper discusses some notes on the vibration design for the piezoelectric cooling fan. After reviewing the fundamental formulas of the cantilever Euler beam, it is not easy to find the optimal design of the piezoelectric fan. The experiments also show the complicated results of the vibration behavior and air flow. Keywords—Piezoelectric cooling fan, vibration, cantilever Euler beam, air flow.

Free vibration analysis of higher-order shear deformation beam resting on one- and two-parameter elasticfoundation is studied using differential transform method (DTM) as a part of a calculation procedure. First,the governing differential equations of beam are derived in a general form considering the shear-freeboundary conditions (zero shear stress conditions at the top and bottom of a beam). ...

the vibration of cable-stayed bridges subjected to the passage of high-speed trains is studied in this article. the moving train includes a number of wagons, each of which is modeled as a four-axle system possessing 48 degrees of freedom. the car model is nonlinear and three-dimensional and includes nonlinear springs and dampers of primary and secondary suspensions, dry friction between differe...

The vibration problems of uniform and nonuniform Euler-Bernoulli beams have been solved analytically or approximately [1-5] for various end conditions. In order to calculate fundamental natural frequencies and related mode shapes, well known variational techniques such as Rayleigh_Ritz and Galerkin methods have been applied in the past. Besides these techniques, some discretized numerical metho...

In the present analysis, an infinite Euler– Bernoulli beam of constant cross-section resting on an elastic foundation is considered. The beam and foundation are assumed to be homogeneous and isotropic. The foundation is modeled using one parameter without damping. The beam is subjected to a constant point load moving with a constant speed along the beam. An effort has been made to find the solu...

the static pull-in instability of beam-type micro-electromechanical systems is theoretically investigated. two engineering cases including cantilever and double cantilever micro-beam are considered. considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent euler-bernoulli beam model is used based on a modified couple stress theory, c...

Non-prismatic beams have received great attention from engineers due to their capability in optimizing the strength and weight of the structure. In recent years, many researchers have worked on engineering problems related to static and dynamic analysis of either Euler–Bernoulli [1–3] or Timoshenko [4,5] beams. For short thick beams and rotating machineries, the Timoshenko beam theory presents ...

We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an Euler-Bernoulli beam makes a Rayleigh beam and a Timoshenko beam unstable.

We consider the Cauchy problem for the Euler-Bernoulli equation of the vibrating beam and solve it in Gevrey classes under appropriate Levi conditions on the lower order terms.