Nonlinear vibration of micromechanical resonators

... Chapter Nonlinear vibration of micromechanical resonators 10 2.1 Linear model of micromechanical resonators 10 2.2 Nonlinear model of micromechanical resonators 13 2.2.1 Nonlinear ... resonator nonlinearities (i.e k3) 2.4 Summary In this chapter, we have introduced both linear and nonlinear equations of motion of micromechanical resonators Three key paramet...

Ngày tải lên: 14/09/2015, 14:13

... various va lu es of param eters and the stab ility of vib ration is in v estig a ted , '"he rotating m otion of the p e n d u lu m an d its sta b ility ,a r e also considered S I E Q U A TIO N OF M ... '•rank ON o f length R rotates around o w ith a c o n sta n t a n g u la r v e lo c ity n and translates slo tted bar BA of len gth L along slides 1.1 We shall ta k e the o...

Ngày tải lên: 08/04/2015, 15:30

... Performance Parameters of Micromechanical Resonators Copyright  2010 by Lynn Khine Abstract Performance Parameters of Micromechanical Resonators by Lynn Khine Doctor of Philosophy ... bulk-mode square resonators 2.2 Different types of micromechanical resonators Early research on micromechanical resonators has been on comb finger type of resonators with l...

Ngày tải lên: 11/09/2015, 10:16

... the world of root finding 350 Chapter Root Finding and Nonlinear Sets of Equations for (i =1; i

Ngày tải lên: 07/11/2013, 19:15

... 1-800-8 72- 7 423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) a x2 x3 b x1 d c f e 351 9.1 Bracketing and Bisection 3 52 Chapter Root Finding and Nonlinear Sets of Equations ... known to be within an interval of size n , then after the next iteration it will be bracketed within an interval of size 354 Chapter Root Finding and N...

Ngày tải lên: 15/12/2013, 04:15

... nrerror("Maximum number of iterations exceeded in rtflsp"); return 0.0; Never get here 35 8 Chapter Root Finding and Nonlinear Sets of Equations Ridders’ Method f(x1 ) − 2f(x3 )eQ + f(x2 )e2Q = (9.2.2) ... 1-800-872-74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) f(x) 35 5 9.2 Secant Method, False Position Method, and Ridders’ Metho...

Ngày tải lên: 15/12/2013, 04:15

... 360 Chapter Root Finding and Nonlinear Sets of Equations x= [y − f(a)][y − f(b)]c [y − f(b)][y − f(c)]a + [f(c) − f(a)][f(c) ... contain a root Brent’s method combines root bracketing, bisection, and inverse quadratic interpolation to converge from the neighborhood of a zero crossing While the false position and secant ... taken as the next estimate of the root x...

Ngày tải lên: 15/12/2013, 04:15

... Chapter Root Finding and Nonlinear Sets of Equations of the desired root But that means that in the neighborhood of an extremum there must be a tiny, perhaps distorted, copy of the basin of convergence ... Derivative f(x) 364 Chapter Root Finding and Nonlinear Sets of Equations f(x) Figure 9.4.3 Unfortunate case where Newton’s method enters a nonconvergen...

Ngày tải lên: 15/12/2013, 04:15

... roots of arbitrary polynomials You can easily verify (see, e.g., [6] ) that the characteristic polynomial of the special m × m companion matrix 3 76 Chapter Root Finding and Nonlinear Sets of Equations ... 370 Chapter Root Finding and Nonlinear Sets of Equations f (x) f (x) (a) x (b) Figure 9.5.1 (a) Linear, quadratic, and cubic behavior at the roots of po...

Ngày tải lên: 15/12/2013, 04:15

... Chapter Root Finding and Nonlinear Sets of Equations no root here! two roots here f pos g pos M f=0 g pos g= g neg f pos f neg g neg = g g= g pos x Figure 9.6.1 Solution of two nonlinear equations ... REFERENCES AND FURTHER READING: Ortega, J., and Rheinboldt, W 1 970 , Iterative Solution of Nonlinear Equations in Several Variables (New York: Academic Press) 9...

Ngày tải lên: 15/12/2013, 04:15

... 384 Chapter Root Finding and Nonlinear Sets of Equations Line Searches and Backtracking When we are not close enough to the minimum of f , taking the full Newton ... http://www.nr.com or call 1 -80 0 -87 2-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) λ=− 386 Chapter Root Finding and Nonlinear Sets of Equations temp=fabs...

Ngày tải lên: 15/12/2013, 04:15

... wing is shown in the Figure below Save the model Go to Pro/MECHANICA, assign aluminum as the wing material, and fix the largest end of cross section Run the modal analysis, and obtain modes of ... material, and fix the largest end of cross section Run the modal analysis, and obtain modes of vibration

Ngày tải lên: 19/01/2014, 05:20

... Correlation effects in atomic thermal vibration of fcc crystals 27 The purpose of this work is to study the correlation effects in atomic vibrations of fcc crystals in XAFS, i.e., to develop ... vibrate under influence of the neighboring environment Taking into account the influences of the nearest atomic neighbors the Einstein effective interaction poten...

Ngày tải lên: 05/03/2014, 14:20

... procedure for calculation and analysis of the dispersion relation and real atomic vibration of fcc crystals containing dopant atom has been developed using the anharmonic effective potential Analytical ... acoustic and optic branches, forbidden zone between them, effective force constant, Debye frequency and temperature, amplitude and phase changes...

Ngày tải lên: 14/03/2014, 13:20

... materials concerning the subject of this book, the nonlinear stability of nite volume methods for hyperbolic systems of conservation laws, have never been put together and detailed systematically ... (2.23) (2.24) Lemma 2.8 The left-hand side of (2.23) and the right-hand side of (2.24) are nonincreasing functions of r and l respectively In particular, for (2....

Ngày tải lên: 23/03/2014, 01:20