lysate Probler 弦的横振动方程 u(a t 因为弦是完全柔软的,故 只受到切向应力—张力T 的作用,而没有法向应 力,同时,略去了重力的 作用,因此有
Equations of Mathematical Physics Boundary & Initial Conditions PDE’s Well-posed Problem Transverse Vibration of Strings Longitudinal Vibration of Flexible Rods Heat Conduction Equation Time-independent and Steady-state Problems uîħ Ïu´ R^§ ÉAå ÜåT ^§ vk{A å©Ó§Ñ å ^©Ïdk (T sin θ)x+dx − (T sin θ)x = dm ∂ 2u ∂t2 (T cos θ)x+dx − (T cos θ)x = 0 C. S. Wu 18ù êÆÔn§
lysate Probler 弦的横振动方程 u(a t 因为弦是完全柔软的,故 只受到切向应力—张力T 的作用,而没有法向应 力.同时,略去了重力的 作用.因此有 I cos O)ridr-( cos 0)r-0
Equations of Mathematical Physics Boundary & Initial Conditions PDE’s Well-posed Problem Transverse Vibration of Strings Longitudinal Vibration of Flexible Rods Heat Conduction Equation Time-independent and Steady-state Problems uîħ Ïu´ R^§ ÉAå ÜåT ^§ vk{A å©Ó§Ñ å ^©Ïdk (T sin θ)x+dx − (T sin θ)x = dm ∂ 2u ∂t2 (T cos θ)x+dx − (T cos θ)x = 0 C. S. Wu 18ù êÆÔn§
lysate Probler 弦的横振动方程 u(a t 因为弦是完全柔软的,故 只受到切向应力—张力T 的作用,而没有法向应 力.同时,略去了重力的 作用.因此有 (Tsin 0)x+dr-Tsin 0 )r=d (T cos 0)x+dz-(T cos e)x
Equations of Mathematical Physics Boundary & Initial Conditions PDE’s Well-posed Problem Transverse Vibration of Strings Longitudinal Vibration of Flexible Rods Heat Conduction Equation Time-independent and Steady-state Problems uîħ Ïu´ R^§ ÉAå ÜåT ^§ vk{A å©Ó§Ñ å ^©Ïdk (T sin θ)x+dx − (T sin θ)x = dm ∂ 2u ∂t2 (T cos θ)x+dx − (T cos θ)x = 0 C. S. Wu 18ù êÆÔn§
lysate Probler 弦的横振动方程 02 (Tsin 0)+dr-(Tsin 0)=dm at2 (T cos O)x+dx-(T 02=0
Equations of Mathematical Physics Boundary & Initial Conditions PDE’s Well-posed Problem Transverse Vibration of Strings Longitudinal Vibration of Flexible Rods Heat Conduction Equation Time-independent and Steady-state Problems uîħ (T sin θ)x+dx − (T sin θ)x = dm ∂ 2u ∂t2 (T cos θ)x+dx − (T cos θ)x = 0 C. S. Wu 18ù êÆÔn§
lysate Probler 弦的横振动方程 02 (Tsin 0)+dr-(Tsin 0)=dm at2 (T cos O)x+dx-(T 02=0 小振动近似:x+dx与x两点间任一时刻横向位 移之差u(x+dx,t)-u(x,t),与dx相比是一个小 量,即 1
Equations of Mathematical Physics Boundary & Initial Conditions PDE’s Well-posed Problem Transverse Vibration of Strings Longitudinal Vibration of Flexible Rods Heat Conduction Equation Time-independent and Steady-state Problems uîħ (T sin θ)x+dx − (T sin θ)x = dm ∂ 2u ∂t2 (T cos θ)x+dx − (T cos θ)x = 0 ÄCq µx + dxxü:m?î £ u(x + dx, t) − u(x, t)§ dx'´ þ§= ∂u ∂x 1 C. S. Wu 18ù êÆÔn§