Rigorous Analytical Analysis of Resonant Euler-Bernoulli Beams with Constant Thickness and Polynomial Width

被引：3

作者：

Beigelbeck, R. ^{[1
]}

Stiffer, M. ^{[1
]}

Schneider, M. ^{[2
]}

Keplinger, F. ^{[2
]}

Schmid, U. ^{[2
]}

Voglhuber-Brunnmaier, T. ^{[3
]}

Jakoby, B. ^{[3
]}

机构：

[1] Danube Univ Krems, Ctr Integrated Sensor Syst, A-2700 Wiener Neustadt, Austria

[2] Vienna Univ Technol, Inst Sensor & Actuator Syst, A-1040 Vienna, Austria

[3] Johannes Kepler Univ Linz, Inst Microelect & Microsensors, A-4040 Linz, Austria

来源：

2014 IEEE INTERNATIONAL ULTRASONICS SYMPOSIUM (IUS) | 2014年

关键词：

TRANSVERSE VIBRATIONS;

D O I：

10.1109/ULTSYM.2014.0522

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

We report a novel exact closed-form solution of the Euler-Bernoulli beam equation expressible in terms of Meijer Gfunctions. This solution allows for analytically studying the natural frequencies and mode shapes of a very general class of beams characterized by both a polynomially varying flexural beam bending stiffness EI. x/and beam cross section A(x), but a constant E1(x/A(x))-ratio. Its application is exemplarily demonstrated on cantilevers characterized by a uniform thickness and a spatially narrowing width of either linear form (i.e., trapezoid cantilevers) or describable by a power function of higher order. The analytically deduced results are validated by computer numerical simulations and compared to test measurements carried out on micromachined thin-film cantilevers.

引用

页码：2095 / 2099

页数：5

共 14 条

[1]

Abramowitz M., 1964, Handbook of mathematical functions with formulas, graphs, and mathematical tables, DOI DOI 10.1119/1.15378

[2]

[Anonymous], 1955, HIGHER TRANSCENDENTA

[3]

[Anonymous], 1953, Higher transcendental functions

[4] Vibration tailoring of inhomogeneous rod that possesses a trigonometric fundamental mode shape [J].

Calio, Ivo ;

Elishakoff, Isaac .

JOURNAL OF SOUND AND VIBRATION, 2008, 309 (3-5) :838-842

[5] Classical Jacobi polynomials, closed-form solutions for transverse vibrations [J].

Caruntu, Dumitru I. .

JOURNAL OF SOUND AND VIBRATION, 2007, 306 (3-5) :467-494

[6] Dynamic modal characteristics of transverse vibrations of cantilevers of parabolic thickness [J].

Caruntu, Dumitru I. .

MECHANICS RESEARCH COMMUNICATIONS, 2009, 36 (03) :391-404

[7]

Clough R., 1975, Dynamics of Structures

[8] Vibration tailoring of heterogeneous beams and annular plates [J].

Elishakoff, I ;

Chandra, D .

JOURNAL OF SOUND AND VIBRATION, 2006, 291 (3-5) :1255-1260

[9] A selective review of direct, semi-inverse and inverse eigenvalue problems for structures described by differential equations with variable coefficients [J].

Elishakoff, I .

ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING, 2000, 7 (04) :451-526

[10]

Erdelyi A., 1953, Higher transcendental functions, V2

← 1 2 →