Задача Д.24, вариант 20 из Задачника Яблонского
Материал из Department of Theoretical and Applied Mechanics
Условие задачи
Определить частоты малых свободных колебаний и формы главных колебаний системы с двумя степенями свободы, пренебрегая силами сопротивления, массами пружин и моментами инерции скручиваемых валов.
= 8 кг; = 10 кг; = 40 Н⁄см; = 60 Н⁄см; = 0,5 м.
Программа
Код программы
Текст программы:
1 const scene = new THREE.Scene();
2 const camera = new THREE.PerspectiveCamera(60, 1, 1, 100);
3 const renderer = new THREE.WebGLRenderer();
4
5 //Постановка задачи(условия)
6 const R = 2;
7 const solution = new function () {
8 this.c1 = 20000;
9 this.c2 = 30000;
10 this.c3 = 10000;
11 this.R = .2;
12 this.t = 0;
13 this.dt = .7;
14
15 this.m1 = 50;
16 this.m2 = 60;
17 this.m3 = 40;
18 this.m4 = 50;
19
20
21 this.a11 = .5*(this.m1+this.m2)*Math.pow(this.R,2);
22 this.a22 = .5*(this.m3+this.m4)*Math.pow(this.R,2);
23 this.c11 = this.c1+this.c2/1.44;
24 this.c22 = this.c2/.81 + this.c3;
25 this.c12 = this.c2/(1.2*.9);
26 this.D = Math.sqrt(Math.pow(this.a11 * this.c22 + this.a22 * this.c11,2) -4 * this.a11 * this.a22 * (this.c11 * this.c22 - Math.pow(this.c12,2)));
27 this.k1 = '' + Math.sqrt((this.a11 * this.c22 + this.a22 * this.c11 + this.D)/(2*this.a11*this.a22));
28 this.k2 = '' + Math.sqrt((this.a11 * this.c22 + this.a22 * this.c11 - this.D)/(2*this.a11*this.a22));
29
30 this.p1 = -(this.c11 - this.a11*Math.pow(this.k1,2))/this.c12;
31 this.p2 = -(this.c11 - this.a11*Math.pow(this.k2,2))/this.c12;
32
33 let self = this;
34
35 this.redraw = function() {
36 self.t = 0;
37 ctx.clearRect(0,-242,500,500);
38 ctx1.clearRect(0,-242,500,500);
39 };
40 };
41 class Construction {
42 constructor(geometry,material,x,y,z) {
43 this.geometry = geometry;
44 this.material = material;
45 this.x = x;
46 this.y = y;
47 this.z = z;
48 this.mesh = new THREE.Mesh(geometry,material);
49 }
50 build(scene,angleX,angleY,angleZ) {
51 this.mesh.position.x = this.x;
52 this.mesh.position.y = this.y;
53 this.mesh.position.z = this.z;
54 this.mesh.rotation.x = angleX;
55 this.mesh.rotation.y = angleY;
56 this.mesh.rotation.z = angleZ;
57 scene.add(this.mesh);
58 }
59 }
60
61 class Moving_parts extends Construction {
62 spin(solution,sign,ratio,r) {
63 let r1 = 1;
64 let r2 = 1;
65 if(r !== 1) {
66 r1 = solution.p1;
67 r2 = solution.p2;
68 }
69 this.mesh.rotation.x = r1 * sign * Math.sin(solution.k1 * solution.t / 1000) * 2 / ratio + r2 * sign * Math.sin(solution.k2 * solution.t / 1000) * 2 / ratio;
70 }
71 static equation(solution,sign,ratio,r,t) {
72 let r1 = 1;
73 let r2 = 1;
74 if(r !== 1) {
75 r1 = solution.p1;
76 r2 = solution.p2;
77 }
78 return r1 * sign * Math.sin(solution.k1 * t / 1000) * 50 / ratio + r2 * sign * Math.sin(solution.k2 * t / 1000) * 50 / ratio;
79 }
80 }
81
82
83 renderer.setClearColor(0xEEEEEE);
84 renderer.setSize(600, 600);
85 let main = document.getElementById("canvas_3d");
86 main.appendChild(renderer.domElement);
87 renderer.domElement.style.border = "1px solid#000";
88
89
90 let gr = new GraphicBulider(450,242);
91 let ctx = gr.dom("canvas_1");
92 let gr1 = new GraphicBulider(450,242);
93 let ctx1 = gr1.dom("canvas_2");
94 let buffer = GraphicBulider.createBuffer();
95 let buffer1 = GraphicBulider.createBuffer();
96
97
98 const spotLight = new THREE.SpotLight( 0xffffff );
99 spotLight.position.set( 50, 80, 20 );
100 scene.add(spotLight);
101
102 const axes = new THREE.AxisHelper( 20 );
103 scene.add(axes);
104
105 //Условия задачи
106 let wall_1 = new Construction(new THREE.CubeGeometry(10,5,1),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: false}),0,0,0);
107 let shaft_1 = new Construction(new THREE.CylinderGeometry(.5,.5,10,20,10),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: false}),5.5,0,0);
108 let wheel_1 = new Moving_parts(new THREE.CylinderGeometry(2*R,2*R,1,20,5),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: true}),11,0,0);
109 let wheel_2 = new Moving_parts(new THREE.CylinderGeometry(2*R*1.2,2*R*1.2,1,20,5),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: true}),11,-(2*R+1.2*R*2),0);
110 let shaft_2 = new Construction(new THREE.CylinderGeometry(.5,.5,10,20,10),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: false}),16.5,-(2*R+1.2*R*2),0);
111 let wheel_3 = new Moving_parts(new THREE.CylinderGeometry(2*R*.9,2*R*.9,1,20,5),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: true}),22,-(2*R+1.2*R*2),0);
112 let wheel_4 = new Moving_parts(new THREE.CylinderGeometry(2*R,2*R,1,20,5),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: true}),22,-(2*R+1.2*R*2+.9*R*2+2*R),0);
113 let shaft_3 = new Construction(new THREE.CylinderGeometry(.5,.5,5,20,10),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: false}),19,-(2*R+1.2*R*2+.9*R*2+2*R),0);
114 let wall_2 = new Construction(new THREE.CubeGeometry(10,5,1),new THREE.MeshLambertMaterial({color: 0xff0000,wireframe: false}),17,-(2*R+1.2*R*2+.9*R*2+2*R),0);
115 wall_1.build(scene,0,Math.PI/2,0);
116 shaft_1.build(scene,0,0,Math.PI/2);
117 wheel_1.build(scene,0,0,Math.PI/2);
118 wheel_2.build(scene,0,0,Math.PI/2);
119 shaft_2.build(scene,0,0,Math.PI/2);
120 wheel_3.build(scene,0,0,Math.PI/2);
121 wheel_4.build(scene,0,0,Math.PI/2);
122 shaft_3.build(scene,0,0,Math.PI/2);
123 wall_2.build(scene,0,Math.PI/2,0);
124
125 camera.position.x = 20;
126 camera.position.y = 10;
127 camera.position.z = 40;
128 camera.lookAt(scene.position);
129 scene.rotation.y = -.5;
130 scene.position.y = 8.5;
131
132 let T = solution.dt;
133 let z =.001;
134 let animate;
135 animate = function () {
136 requestAnimationFrame(animate);
137
138 T = solution.dt;
139 solution.a11 = .5 * (solution.m1 + solution.m2) * Math.pow(solution.R, 2);
140 solution.a22 = .5 * (solution.m3 + solution.m4) * Math.pow(solution.R, 2);
141 solution.c11 = solution.c1 + solution.c2 / 1.44;
142 solution.c22 = solution.c2 / .81 + solution.c3;
143 solution.c12 = (1 / (1.2 * .9)) * solution.c2;
144 solution.D = Math.sqrt(Math.pow(solution.a11 * solution.c22 + solution.a22 * solution.c11, 2) - 4 * solution.a11 * solution.a22 * (solution.c11 * solution.c22 - Math.pow(solution.c12, 2)));
145 solution.k1 = '' + Math.sqrt((solution.a11 * solution.c22 + solution.a22 * solution.c11 + solution.D) / (2 * solution.a11 * solution.a22));
146 solution.k2 = '' + Math.sqrt((solution.a11 * solution.c22 + solution.a22 * solution.c11 - solution.D) / (2 * solution.a11 * solution.a22));
147 solution.p1 = -(solution.c11 - solution.a11 * Math.pow(solution.k1, 2)) / solution.c12;
148 solution.p2 = -(solution.c11 - solution.a11 * Math.pow(solution.k2, 2)) / solution.c12;
149
150
151 wheel_1.spin(solution, 1, 1, 1);
152 wheel_2.spin(solution, -1, 1.2, 1);
153 wheel_3.spin(solution, -1, .9, 2);
154 wheel_4.spin(solution, 1, 1, 2);
155
156 if (solution.t === 0) {
157 z = 0;
158 }
159 if (solution.t > 450) {
160 z -= T;
161 }
162 ctx.clearRect(0, 0, buffer.width, 400);
163 ctx.drawImage(GraphicBulider.bufferDraw(buffer, solution.t, T, Moving_parts.equation(solution, 1, 1, 1, solution.t - T), Moving_parts.equation(solution, 1, 1, 1, solution.t), 'red'), z, 0);
164 ctx1.clearRect(0, 0, buffer.width, 400);
165 ctx1.drawImage(GraphicBulider.bufferDraw(buffer1, solution.t, T, Moving_parts.equation(solution, 1, 1, 0, solution.t - T), Moving_parts.equation(solution, 1, 1, 0, solution.t), 'green'), z, 0);
166 solution.t += T;
167 renderer.render(scene, camera);
168 };
169 animate();
170 const gui = new dat.GUI();
171 gui.add(solution, 'm1',20,70).onChange(solution.redraw);
172 gui.add(solution, 'm2',20,70).onChange(solution.redraw);
173 gui.add(solution, 'm3',20,70).onChange(solution.redraw);
174 gui.add(solution, 'm4',20,70).onChange(solution.redraw);
175 gui.add(solution, 'c1',0,35000).onChange(solution.redraw);
176 gui.add(solution, 'c2',0,35000).onChange(solution.redraw);
177 gui.add(solution, 'dt',0,10).onChange(solution.redraw);
178
179 gui.add(solution, 'k1').listen();
180 gui.add(solution, 'k2').listen();
181 gui.add(solution, 'redraw');
182 solution.redraw();
Используемые библиотеки
- three.js
- CurveExtras1.js
- stats.min.js
- dat.gui.js
- OrbitControls.js
