Formulas for Structural Dynamics: Tables, Graphs and Solutions

Appendix A: Eigenfuimctions and their Derivatives for One-Span Beams with Different Boundary Conditions

TABLES A.1 A.3

Table A.1: Clamped free beam.

First and second eigenfunctions

X 1

X ? 1

X ? 1

X ? ? 1

X 2

X ? 2

X ? 2

X ? ? 2

0

0

0

7.0318

?9.6790

0

0

44.074

?210.71

0.025

0.0022

0.1728

6.7899

?9.6790

0.0132

1.0364

38.804

?210.65

0.05

0.0086

0.3395

6.5479

?9.6775

0.0507

1.9403

33.544

?210.30

0.075

0.0191

0.5001

6.3062

?9.6738

0.1092

2.7136

28.295

?209.34

0.1

0.0335

0.6547

6.0643

?9.6658

0.1853

3.3553

23.084

?207.58

0.125

0.0518

0.8034

5.8227

?9.6525

0.2759

3.8681

17.925

?204.79

0.15

0.0738

0.9460

5.5815

?9.6335

0.3776

4.2526

12.855

?200.83

0.175

0.0991

1.0823

5.3415

?9.6063

0.4874

4.5117

7.896

?195.59

0.2

0.1278

1.2129

5.1016

?9.5718

0.6021

4.6486

3.087

?188.98

0.225

0.1596

1.3376

4.8627

?9.5270

0.7188

4.6676

?1.542

?180.95

0.25

0.1946

1.4562

4.6251

?9.4727

0.8346

4.5733

?5.948

?171.53

0.275

0.2324

1.5689

4.3889

?9.4066

0.9466

4.3720

?10.106

?160.71

0.3

0.2729

1.6756

4.1551

?9.3288

1.0524

4.0704

?13.976

?148.56

0.325

0.3161

1.7766

3.9228

?9.2378

1.1494

3.6761

?17.205

?135.20

0.35

0.3617

1.8718

3.6931

?9.1328

1.2355

3.1970

?20.726

?120.71

0.375

0.4097

1.9613

3.4662

?9.0139

1.3086

2.6431

?23.551

?105.25

0.4

0.4598

2.0452

3.2423

?8.8796

1.3671

2.0226

?25.981

?89.00

0.425

0.5118

2.1234

3.0225

?8.7298

1.4093

1.3475

?27.996

?72.13

0.45

0.5659

2.1963

2.8063

?8.5632

1.4340

0.6266

?

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