The frequency of the AC supply current is chosen to be equal to the resonant frequency of the suspended beam, leading to the increase of its deflection magnitude and the overall sensitivity. Throughout this paper, the first-order resonance frequency and the capacity expressions are developed, ...
The microbeam deflection can be approximated as follows: Xn wðx; tÞ ¼ ϕiðxÞuiðtÞ i¼1 ð8Þ where ϕi(x) is selected to be the ith undamped, unforced and linear orthonormal clamped–clamped beam mode shape; ui(t) is the ith modal coordinate; and n is ...
Tensile stresses are desirable because they reduce the possibility of bucking and because they raise the natural frequencies of the beam, which is often a desirable property. The second distinction is large deflection. Unlike large beams and bridges, clamped–clamped microbeams undergo large ...
The modal mass for a simply-supported beam is derived by evaluating the square of the mode shape function given in Eq. (1) and is∫0Lψmψndx=L/2form=n,=0form≠n.This integral involving sine functions can be found in most mathematical handbook of integrals. The modal-mass is then ...
aMeasurement system setup. The inset shows a CCD image of pushing against the SMF of the clamped-beam probe sensor.bSchematic diagram of cantilever-beam deflection under point load Full size image The vertical downward displacement of the probe, i.e., the deflection ΔL, can be accurately con...
Simultaneous determination of transverse deflection and the force function is achieved by expressing these quantities as double series involving appropriate beam eigenfunctions satisfying all the boundary conditions. Results corresponding to increasing transverse (aerodynamic) forces and thermal fields are ...
of inertia; c is the damping coefficient; A is the cross sectional area; ρ is the density; ε is the air permittivity; d is the air-gap thickness; t is time; x is the position along the beam; N is the axial force; b is the beam width; and w is the microbeam deflection. The...
This paper deals with the determination of the thermal deflection in a thin clamped hollow circular disk defined as a ≤ r ≤ b; 0 ≤ z ≤ h under an unsteady temperature field due to internal heat generation within it. A thin hollow circular disk is considered having an arbitrary initial...
In such cases, an efficient design should simultaneously provide low deflection with high capacity of power generation. Clamped-clamped structures restrict the tip beam deflections however, lose part of the power, compared to the cantilever energy harvesters. In this study, we are going to enhance ...
In this approach, the panel displacements and deflection have been approximated by the clamped-clamped beam functions. As a result, an analytical formula for Acknowledgement One of the authors (A.V. Lopatin) acknowledges the support provided by the Ministry of Education and Science of the Russian...