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991.
Ivan C. Christov Christo I. Christov 《Mathematical Methods in the Applied Sciences》2017,40(12):4481-4492
We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, Xs(t)=vt is the location of the source with constant velocity v. In the present work, however, we consider a source co‐located with a moving boundary x=Xs(t), where Xs(t) can have an arbitrary functional form. For ‘slowly moving’ boundaries (i.e., ones for which the timescale set by the mechanical motion is large in comparison to the inverse of the frequency of the emitted wave), we present a multiple‐scale asymptotic analysis of the moving boundary problem for the linear wave equation. We obtain a closed‐form leading‐order (with respect to the latter small parameter) solution and show that the variable velocity of the boundary results not only in frequency modulation but also in amplitude modulation of the received signal. Consequently, our results extend the applicability of two basic tenets of the theory of a moving source on a stationary domain, specifically that (i) for non‐uniform boundary motion can be inserted in place of the constant velocity v in the classical Doppler formula and (ii) that the non‐uniform boundary motion introduces variability in the amplitude of the wave. The specific examples of decelerating and oscillatory boundary motion are worked out and illustrated. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
992.
The paper deals with the three-dimensional dynamic problem for an elliptic crack interacting with a normally incident harmonic compression–expansion wave, considering the contact interaction of the crack faces. An asymmetric solution is obtained using an iteration algorithm developed earlier. Numerical results are presented 相似文献
993.
ZhengJunjie PengHong NieChongjun 《Acta Mechanica Solida Sinica》2004,17(4):353-360
Based on the results of conventional triaxial compression tests for a soil, a trilinear elasto-plastic model is proposed to simulate the stress-strain softening curve. According to this curve, the constitutive relation between the bulk strain and two pr… 相似文献
994.
Periodic Solutions of Delay Differential Equations with a Small Parameter: Existence,Stability and Asymptotic Expansion 总被引:1,自引:0,他引:1
Chunhua?Ou Jianhong?WuEmail author 《Journal of Dynamics and Differential Equations》2004,16(3):605-628
We consider a scalar delay differential equation with a small parameter, and employ Walthers method to obtain a result on the existence and stability of a slowly oscillatory periodic solution that represents a refinement of the estimate for the Lipschitz constant of a returning map. We also develop a matching method and obtain asymptotic expansions of the slowly oscillatory periodic solution and its minimal period.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthdayAMS subject classifications: 34K15; 34K20; 34C25. 相似文献
995.
V. B. Larin 《International Applied Mechanics》2006,42(2):221-227
A number of control problems for mechanical systems with feedback are reduced to a matrix algebraic Riccati equation. The
exact solutions of matrix algebraic Riccati equations with singularities are presented. These singularities do not permit
the use of standard solution procedures. Asymptotic solutions of these equations are found in the neighborhood of the singular
points. These results can be used as test examples in developing new solution algorithms for matrix algebraic Riccati equations
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 113–120, February 2006. 相似文献
996.
捷联惯性导航中一种算法的推证 总被引:9,自引:0,他引:9
捷联惯性导航系统中,常常用到解算四元数矩阵微分方程的问题。为此给出了解四元数矩阵微分方程的一个强有力的算式,并给出了详细的数学推导和证明。 相似文献
997.
F. Lanza di Scalea 《Experimental Mechanics》1998,38(4):233-241
The measurement of the coefficients of thermal expansion (CTEs) of composite materials using electrical resistance strain
gages is addressed. Analytical expressions for the CTEs of an orthotropic lamina are derived, accounting for the effects of
transverse sensitivity and possible misalignment of the gages. Experiments are performed for the characterization of the thermal
expansion behavior of a fiber-glass-reinforced epoxy unidirectional lamina using an invar specimen as reference material.
Preliminary training cycles are performed for the determination of an optimal heating rate for the measurements, which ensures
thermal equilibrium conditions. Three measurement cycles yield the principal CTEs of the lamina α1, α2 and α12 with repeatability within ±0.34×10−6, ±0.85×10−6 and ±2.8×10−6/°C, respectively. It is noted that inhomogeneity of the specimen and variation in thermomechanical properties of the gages
can cause a noticeable spead in the measurements. 相似文献
998.
Jean Marie Nianga 《Mechanics Research Communications》2006,33(5):747-752
This paper provides an analysis of the crack propagation criterion for a thin piezoelectric plate with a symmetry of order six. On the basis of Gol’denveizer’s asymptotic integration method or Destuynder’s unidirectional zoom technique, we obtain an extension of the purely mechanical J-integral to piezoelectric materials, with a dependence of the gradient of energy of the plate only on zeroth order terms of asymptotic expansions. 相似文献
999.
We present a deduction of the Kirchhoff–Love and Reissner–Mindlin kinematics of a simply-connected plate by using the formal
asymptotic development method applied to the compatibility conditions of Saint-Venant and the formula of Cesàro–Volterra.
This formal deduction is purely geometrical because we do not use any information coming from the loading or the constitutive behavior.
相似文献
1000.
本文考虑了缓变水深和缓变流对Stokes波包的影响,用WKB展开式推导出一个新的任意水深的四阶波包演化方程,推广了Turpin等人的有限水深三阶Schrdinger方程,在常深度无流条件下,新方程同U Brinch—Nielsen等人的无流任意常水深四阶方程的二维形式完全一致;此外,我们用差分法研究了变地形和流对孤立波包演化的影响。 相似文献