✦ LIBER ✦

EXACT, SINGLE EQUATION, CLOSED-FORM SOLUTION OF VIBRATING SYSTEMS WITH PIECEWISE LINEAR SPRINGS

✍ Scribed by E. CHICUREL-UZIEL

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 343 KB
Volume: 245
Category: Article
ISSN: 0022-460X
DOI: 10.1006/jsvi.2001.3568

No coin nor oath required. For personal study only.

✦ Synopsis

A method is proposed to obtain in a single equation the exact, closed-form displacement response of both free undamped vibrations and the steady state of forced damped vibrations of systems with piecewise linear springs, with continuous or discontinuous force}de#ection relations. Since the displacement equations are exact the velocity and acceleration responses are obtained by di!erentiation. The solutions are complete, they apply for any value of time from zero to in"nity. The method is designed to be handled in a computer either in conjunction with a Symbolic Mathematics package, like Mathematica or Maple, or without it. However, for certain relatively simple problems the phase-plane solution may be obtained even in a hand-held calculator. Two examples are presented.

📜 SIMILAR VOLUMES

EXACT SOLUTIONS OF CYCLICALLY SYMMETRIC

EXACT SOLUTIONS OF CYCLICALLY SYMMETRIC OSCILLATOR EQUATIONS WITH NON-LINEAR COUPLING. PART III: GLOBALLY STABLE SINGLE-FREQUENCY LIMIT CYCLES

✍ FOX, DAVID 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 311 KB

Several authors have found very simple exact limit cycle solutions in certain sets of N cyclically symmetric coupled non-linear oscillator equations. In part I of this paper it was shown that the search for sets of equations with similar solutions is made much simpler if the equations are expressed

EXACT STATIONARY SOLUTIONS OF AVERAGED E

EXACT STATIONARY SOLUTIONS OF AVERAGED EQUATIONS OF STOCHASTICALLY AND HARMONICALLY EXCITED MDOF QUASI-LINEAR SYSTEMS WITH INTERNAL AND/OR EXTERNAL RESONANCES

✍ Z.L. Huang; W.Q. Zhu 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 237 KB

The exact stationary solutions of the averaged equations of stochastically and harmonically excited n-degree-of-freedom quasi-linear systems with m internal and/or external resonances are obtained as functions of both n independent amplitudes and m combinations of phase angles. To make the solutions