I am looking at a simple cantilever beam deflection and have two basic questions:

(1) Force Equations

I understand the general expression for deflection/force would be:

$y_s = \frac{Fx_s^3}{3EI}$

$F = \frac{3y_sEI}{x_s^3}$

What $F$ does that most accurately represent though in this diagram? Is that $F_p$ or $F_⊥$?

Also, is $x_s$ most accurately defined as the true $x$ distance to the bending point, or is it the length of the beam along its true surface to the bending point (ie. slightly longer than $x$)?

If the expression above is for $F_p$ I believe, then what is the equation for $F_⊥$? ($F_{||}$ is mean to be the force of static friction, ie. $F_{||} = μ F_⊥$.)

(2) Viscous Damping

If you were going to add viscous damping to the bending of the beam, would it be as simple as:

$F = \frac{3y_sEI}{x_s^3} - cEIθ_t$

Where the equation for the angle of deflection is $θ = \frac{FL^2}{2EI}$?

I have seen some suggestions that simple damping of cantelever beams is done by applying viscosity to the rate of angle change with respect to time. Is that generally correct?

Thanks for any help or answers/ideas for either question. It is appreciated.

I am looking at a simple cantilever beam deflection:

I understand the general expression for deflection/force would be:

$y_s = \frac{Fx_s^3}{3EI}$

$F_p = \frac{3y_sEI}{x_s^3}$

If you were going to add viscous damping to the bending of the beam, would it be as simple as:

$F = \frac{3y_sEI}{x_s^3} - cEIθ_t$

Where the equation for the angle of deflection is $θ = \frac{FL^2}{2EI}$?

I have seen some suggestions that simple damping of cantelever beams is done by applying viscosity to the rate of angle change with respect to time. Is that generally correct?

I have had some strange behaviors trying this so I'm not sure what the ideal simple solution is.

Thanks for any help or answers/ideas for either question. It is appreciated.

I am looking at a simple cantilever beam deflection and have two basic questions:

(1) Force Equations

I understand the general expression for deflection/force would be:

$y_s = \frac{Fx_s^3}{3EI}$

$F = \frac{3y_sEI}{x_s^3}$

What $F$ does that most accurately represent though in this diagram? Is that $F_p$ or $F_⊥$?

Also, is $x_s$ most accurately defined as the true $x$ distance to the bending point, or is it the length of the beam along its true surface to the bending point (ie. slightly longer than $x$)?

If the expression above is for $F_p$ I believe, then what is the equation for $F_⊥$? ($F_{||}$ is mean to be the force of static friction, ie. $F_{||} = μ F_⊥$.)

(2) Viscous Damping

If you were going to add viscous damping to the bending of the beam, would it be as simple as:

$F = \frac{y_sx^3}{3EI} - cθ_t$

Where the equation for the angle of deflection is $θ = \frac{FL^2}{2EI}$?

I have seen some suggestions that simple damping of cantelever beams is done by applying viscosity to the rate of angle change with respect to time. Is that generally correct?

Thanks for any help or answers/ideas for either question. It is appreciated.

I am looking at a simple cantilever beam deflection and have two basic questions:

(1) Force Equations

I understand the general expression for deflection/force would be:

$y_s = \frac{Fx_s^3}{3EI}$

$F = \frac{3y_sEI}{x_s^3}$

What $F$ does that most accurately represent though in this diagram? Is that $F_p$ or $F_⊥$?

Also, is $x_s$ most accurately defined as the true $x$ distance to the bending point, or is it the length of the beam along its true surface to the bending point (ie. slightly longer than $x$)?

If the expression above is for $F_p$ I believe, then what is the equation for $F_⊥$? ($F_{||}$ is mean to be the force of static friction, ie. $F_{||} = μ F_⊥$.)

(2) Viscous Damping

If you were going to add viscous damping to the bending of the beam, would it be as simple as:

$F = \frac{3y_sEI}{x_s^3} - cEIθ_t$

Where the equation for the angle of deflection is $θ = \frac{FL^2}{2EI}$?

I have seen some suggestions that simple damping of cantelever beams is done by applying viscosity to the rate of angle change with respect to time. Is that generally correct?

Thanks for any help or answers/ideas for either question. It is appreciated.

I am looking at a simple cantilever beam deflection and have two basic questions:

(1) Force Equations

I understand the general expression for deflection/force would be:

$y_s = \frac{Fx^3}{3EI}$

$F = \frac{y_sx^3}{3EI}$

What $F$ does that most accurately represent though in this diagram? Is that $F_p$ or $F_⊥$?

Also, is $x_s$ most accurately defined as the true $x$ distance to the bending point, or is it the length of the beam along its true surface to the bending point (ie. slightly longer than $x$)?

If the expression above is for $F_p$ I believe, then what is the equation for $F_⊥$? ($F_{||}$ is mean to be the force of static friction, ie. $F_{||} = μ F_⊥$.)

(2) Viscous Damping

If you were going to add viscous damping to the bending of the beam, would it be as simple as:

$F = \frac{y_sx^3}{3EI} - cθ_t$

Where the equation for the angle of deflection is $θ = \frac{FL^2}{2EI}$?

I have seen some suggestions that simple damping of cantelever beams is done by applying viscosity to the rate of angle change with respect to time. Is that generally correct?

Thanks for any help or answers/ideas for either question. It is appreciated.

I am looking at a simple cantilever beam deflection and have two basic questions:

(1) Force Equations

I understand the general expression for deflection/force would be:

$y_s = \frac{Fx_s^3}{3EI}$

$F = \frac{3y_sEI}{x_s^3}$

What $F$ does that most accurately represent though in this diagram? Is that $F_p$ or $F_⊥$?

Also, is $x_s$ most accurately defined as the true $x$ distance to the bending point, or is it the length of the beam along its true surface to the bending point (ie. slightly longer than $x$)?

If the expression above is for $F_p$ I believe, then what is the equation for $F_⊥$? ($F_{||}$ is mean to be the force of static friction, ie. $F_{||} = μ F_⊥$.)

(2) Viscous Damping

If you were going to add viscous damping to the bending of the beam, would it be as simple as:

$F = \frac{y_sx^3}{3EI} - cθ_t$

Where the equation for the angle of deflection is $θ = \frac{FL^2}{2EI}$?

I have seen some suggestions that simple damping of cantelever beams is done by applying viscosity to the rate of angle change with respect to time. Is that generally correct?

Thanks for any help or answers/ideas for either question. It is appreciated.