This paper presents a refined parabolic approximation model of the mild slope equation to simulate the combination of water wave refraction and diffraction in the large coastal region. The bottom friction and weakly n...This paper presents a refined parabolic approximation model of the mild slope equation to simulate the combination of water wave refraction and diffraction in the large coastal region. The bottom friction and weakly nonlinear term are included in the model. The difference equation is established with the Crank-Nicolson scheme. The numerical test shows that some numerical prediction results will be inaccurate in complicated topography without considering weak nonlinearity; the bottom friction will make wave height damping and it can not be neglected for calculation of wave field in large areas.展开更多
<span style="font-family:Verdana;">This paper represents</span> <span style="font-family:Verdana;">a continuation of</span><span style="color:#C45911;"> <...<span style="font-family:Verdana;">This paper represents</span> <span style="font-family:Verdana;">a continuation of</span><span style="color:#C45911;"> </span><span><span style="white-space:nowrap;"><a href="#ref1" target="_blank">[1]</a></span><span style="font-family:Verdana;"> and</span> <span style="white-space:nowrap;"><a href="#ref2" target="_blank">[2]</a></span></span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.</span>展开更多
金属橡胶是一种新型材料,文中运用Fourier级数展开和谐波平衡法相结合的方法FHB(the technique of Fourier series expansion combining with harmonic balance method)推导出金属橡胶干摩擦系统在简谐激励下的频响方程,通过数值仿真,...金属橡胶是一种新型材料,文中运用Fourier级数展开和谐波平衡法相结合的方法FHB(the technique of Fourier series expansion combining with harmonic balance method)推导出金属橡胶干摩擦系统在简谐激励下的频响方程,通过数值仿真,比较三次非线性因素和五次非线性因素对金属橡胶干摩擦系统幅频特性的影响,发现对金属橡胶干摩擦系统幅频特性起决定作用的是三次非线性因素,只有五次非线性因素超过1011数量级时才需考虑五次非线性因素的影响,对金属橡胶减振器作动态响应实验,发现减振器的固有频率和传递率幅值都表现出非线性特性。展开更多
基金National Natural Science Foundation of China(Grant No.19732004)
文摘This paper presents a refined parabolic approximation model of the mild slope equation to simulate the combination of water wave refraction and diffraction in the large coastal region. The bottom friction and weakly nonlinear term are included in the model. The difference equation is established with the Crank-Nicolson scheme. The numerical test shows that some numerical prediction results will be inaccurate in complicated topography without considering weak nonlinearity; the bottom friction will make wave height damping and it can not be neglected for calculation of wave field in large areas.
文摘<span style="font-family:Verdana;">This paper represents</span> <span style="font-family:Verdana;">a continuation of</span><span style="color:#C45911;"> </span><span><span style="white-space:nowrap;"><a href="#ref1" target="_blank">[1]</a></span><span style="font-family:Verdana;"> and</span> <span style="white-space:nowrap;"><a href="#ref2" target="_blank">[2]</a></span></span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.</span>
文摘金属橡胶是一种新型材料,文中运用Fourier级数展开和谐波平衡法相结合的方法FHB(the technique of Fourier series expansion combining with harmonic balance method)推导出金属橡胶干摩擦系统在简谐激励下的频响方程,通过数值仿真,比较三次非线性因素和五次非线性因素对金属橡胶干摩擦系统幅频特性的影响,发现对金属橡胶干摩擦系统幅频特性起决定作用的是三次非线性因素,只有五次非线性因素超过1011数量级时才需考虑五次非线性因素的影响,对金属橡胶减振器作动态响应实验,发现减振器的固有频率和传递率幅值都表现出非线性特性。
