| Real | t | | Time |
| Real | force | | force |
| Real | m | | linear mass of the material |
| Real | length | | length of the beam |
| Real | EE | | young's modulus of the material |
| Real | JJ | | area moment of inertia |
| Real | beta1L | 1.875 | first root of the function cos(betaL)cosh(betaL)+1=0 |
| Real | beta2L | 4.694 | second root of the function cos(betaL)cosh(betaL)+1=0 |
| Real | beta3L | 7.855 | third root of the function cos(betaL)cosh(betaL)+1=0 |
| Real | beta4L | 10.955 | fourth root of the function cos(betaL)cosh(betaL)+1=0 |
| Real | beta5L | 14.1371 | fifth root of the function cos(betaL)cosh(betaL)+1=0 |
| Real | beta6L | 17.2787 | sixth root of the function cos(betaL)cosh(betaL)+1=0 |
| Real | beta1 | beta1L/length | first beta |
| Real | beta2 | beta2L/length | second beta |
| Real | beta3 | beta3L/length | third beta |
| Real | beta4 | beta4L/length | fourth beta |
| Real | beta5 | beta5L/length | fifth beta |
| Real | beta6 | beta6L/length | sixth beta |
| SIunits.PerUnit | A1 | 4*force*length/(EE*JJ*(m/length)*beta1^4*(sin(beta1L)*exp(beta1L) + exp(2*beta1L) - 1))*(3*sin(beta1L)*(exp(2*beta1L) + 1) - 2*beta1L^3*exp(beta1L) + cos(beta1L)*(3 - beta1L^3*(exp(2*beta1L) + 1) - 3*exp(2*beta1L))) | amplitude of first cos function |
| SIunits.PerUnit | A2 | 4*force*length/(EE*JJ*(m/length)*beta2^4*(sin(beta2L)*exp(beta2L) + exp(2*beta2L) - 1))*(3*sin(beta2L)*(exp(2*beta2L) + 1) - 2*beta2L^3*exp(beta2L) + cos(beta2L)*(3 - beta2L^3*(exp(2*beta2L) + 1) - 3*exp(2*beta2L))) | amplitude of second cos function |
| SIunits.PerUnit | A3 | 4*force*length/(EE*JJ*(m/length)*beta3^4*(sin(beta3L)*exp(beta3L) + exp(2*beta3L) - 1))*(3*sin(beta3L)*(exp(2*beta3L) + 1) - 2*beta3L^3*exp(beta3L) + cos(beta3L)*(3 - beta3L^3*(exp(2*beta3L) + 1) - 3*exp(2*beta3L))) | amplitude of third function |
| SIunits.PerUnit | A4 | 4*force*length/(EE*JJ*(m/length)*beta4^4*(sin(beta4L)*exp(beta4L) + exp(2*beta4L) - 1))*(3*sin(beta4L)*(exp(2*beta4L) + 1) - 2*beta4L^3*exp(beta4L) + cos(beta4L)*(3 - beta4L^3*(exp(2*beta4L) + 1) - 3*exp(2*beta4L))) | amplitude of fourth function |
| SIunits.PerUnit | A5 | 4*force*length/(EE*JJ*(m/length)*beta5^4*(sin(beta5L)*exp(beta5L) + exp(2*beta5L) - 1))*(3*sin(beta5L)*(exp(2*beta5L) + 1) - 2*beta5L^3*exp(beta5L) + cos(beta5L)*(3 - beta5L^3*(exp(2*beta5L) + 1) - 3*exp(2*beta5L))) | amplitude of fifth cos function |
| SIunits.PerUnit | A6 | 4*force*length/(EE*JJ*(m/length)*beta6^4*(sin(beta6L)*exp(beta6L) + exp(2*beta6L) - 1))*(3*sin(beta6L)*(exp(2*beta6L) + 1) - 2*beta6L^3*exp(beta6L) + cos(beta6L)*(3 - beta6L^3*(exp(2*beta6L) + 1) - 3*exp(2*beta6L))) | amplitude of sixth cos function |
| SIunits.Length | x | length | a distance between 0 and length L of the beam |
| SIunits.AngularFrequency | wk1 | (EE*JJ/m)^(1/2)*beta1^2 | 1st natural frequency |
| SIunits.AngularFrequency | wk2 | (EE*JJ/m)^(1/2)*beta2^2 | 2nd natural frequency |
| SIunits.AngularFrequency | wk3 | (EE*JJ/m)^(1/2)*beta3^2 | 3rd natural frequency |
| SIunits.AngularFrequency | wk4 | (EE*JJ/m)^(1/2)*beta4^2 | 4th natural frequency |
| SIunits.AngularFrequency | wk5 | (EE*JJ/m)^(1/2)*beta5^2 | 5th natural frequency |
| SIunits.AngularFrequency | wk6 | (EE*JJ/m)^(1/2)*beta6^2 | 6th natural frequency |
| Real | shape1 | A1/2*((-cosh(beta1*x)) + cos(beta1*x) + ((-cos(beta1L)) - cosh(beta1L))*(sin(beta1*x) - sinh(beta1*x))/(sin(beta1L) - sinh(beta1L))) | |
| Real | shape2 | A2/2*((-cosh(beta2*x)) + cos(beta2*x) + ((-cos(beta2L)) - cosh(beta2L))*(sin(beta2*x) - sinh(beta2*x))/(sin(beta2L) - sinh(beta2L))) | |
| Real | shape3 | A3/2*((-cosh(beta3*x)) + cos(beta3*x) + ((-cos(beta3L)) - cosh(beta3L))*(sin(beta3*x) - sinh(beta3*x))/(sin(beta3L) - sinh(beta3L))) | |
| Real | shape4 | A4/2*((-cosh(beta4*x)) + cos(beta4*x) + ((-cos(beta4L)) - cosh(beta4L))*(sin(beta4*x) - sinh(beta4*x))/(sin(beta4L) - sinh(beta4L))) | |
| Real | shape5 | A5/2*((-cosh(beta5*x)) + cos(beta5*x) + ((-cos(beta5L)) - cosh(beta5L))*(sin(beta5*x) - sinh(beta5*x))/(sin(beta5L) - sinh(beta5L))) | |
| Real | shape6 | A6/2*((-cosh(beta6*x)) + cos(beta6*x) + ((-cos(beta6L)) - cosh(beta6L))*(sin(beta6*x) - sinh(beta6*x))/(sin(beta6L) - sinh(beta6L))) | |