Washing Machine Floor Vibration and Isolation Pads Calculator

The equations are derived here from Newton's laws and Euler–Bernoulli beam energy, with the classical isolation interpretation described by Den Hartog, Mechanical Vibrations, 4th edition (1956; Dover reprint 1985), and the open Purdue isolation notes.

Let $x$ be machine displacement and $y$ floor displacement at its feet, both measured from static equilibrium. For support stiffness $k$ and damping $c$:

The unbalance is $U=m_u e_u$. During the ramp, $\omega=\omega_{max}t/t_r$ and $\theta=\omega_{max}t^2/(2t_r)$; during the hold, $\theta=\omega_{max}(t-t_r/2)$. The vertical excitation is $F=U(\omega^2\cos\theta+\dot\omega\sin\theta)$, including the tangential ramp term.

For $N=W/s$ participating joists, $I=bh^3/12$, $EI_f=NEI$, and line mass $\mu=qW+N\rho bh$, use $\psi=\sin(\pi r_m)$:

Observer acceleration is scaled by $\sin(\pi r_o)/\psi$. The separate static comparison uses the exact beam midpoint stiffness $48EI_f/L^3$, rather than the first-mode approximation. CWC's Canadian Guide to Mid-Rise Wood Construction, attached p. 130, explains the importance of whole-floor construction and concentrated-load deflection; this tool does not implement the complete CSA/NBC vibration-span procedure.

The five configurations are integrated with implicit Newmark average acceleration ($\beta=1/4$, $\gamma=1/2$). Input work uses average endpoint force times displacement increment; damping work uses midpoint velocity, giving an independent discrete energy balance. The solver uses explicitly normalized SI coordinates and restores physical units at its boundaries.

The exact complex two-mass dynamic stiffness gives the steady speed sweeps and transmitted support force. The coupled undamped eigenfrequencies come from $\det(K-\omega^2M)=0$. The rigid-floor comparison is $T=\sqrt{1+(2\zeta r)^2}/\sqrt{(1-r^2)^2+(2\zeta r)^2}$; isolation starts above $r=\sqrt2$.

The forcing history is computed once on the common integration time grid and reused by all five configurations. Exactly zero unbalance gives the analytical zero-motion history. The support-force envelope uses the equivalent machine equilibrium $F_{support}=F-M\ddot x$, avoiding repeated arithmetic without changing the time step or equations.

• One vertical cabinet coordinate and one floor bending mode; rigid bearings, simply supported identical joists, linear small motion and initially stationary static equilibrium.
• The loaded machine mass includes the effective rotating mass. Unbalance, stiffness, damping, floor mass and effective width are editable scenario assumptions, not specifications for a named appliance or timber grade.
• One identical, fully effective, full-span sister is added to every participating joist. Joist bending stiffness and joist mass double; deck mass stays fixed. Partial sisters and connection slip need a separate model.
• Blocking changes the assumed participating width and adds the entered equivalent modal mass. It supplies no invented joist bending-stiffness multiplier. The optional block is rigidly attached to its selected side of the pads.
• Each configuration uses its entered damping ratio, with $c=2\zeta\sqrt{km}$ for the support and floor. Thus changing supported mass while holding the damping ratio also changes the equivalent viscous coefficient. Real pad properties should be measured at that load.
• No CWC/Onysko walking-acceptance verdict is inferred from the 1 kN deflection. The point-load result is a diagnostic of floor flexibility.

A comfort screening for a specified effective unbalance, not an appliance prediction or structural capacity assessment. AISC Design Guide 11, 2nd edition (2016, with subsequent errata), concerns human activity on steel systems. The default 0.005 g peak target is drawn from AISC's public Facts for Steel Buildings 5: Vibration (2018), Table 2-1; applying it to washing-machine vibration is an explicit engineering comparison. Repeated machinery vibration may need a different limit. No ISO frequency weighting, vibration dose or exposure assessment is performed; check against the standard in force.

The floor model omits plate action, composite deck stiffness, higher bending/torsional modes, flexible bearings and neighboring bays. The machine model omits internal tub dynamics, rocking, horizontal motion, slipping and lift-off. Pads remain linear and in contact; revise the model if the motion or contact conditions flag. Effective width, damping and cabinet-referred unbalance often dominate uncertainty. Confirm them by site testing before relying on a retrofit comparison.

The maximum time step is reduced to at least 32 samples per fastest coupled mode or final spin cycle. The default is checked against a halved user step. Newmark time discretization can shift sharp resonances; reduce the advanced time step for low damping or nearly resonant holds. Profiles requiring over 30,000 intervals are outside this tool's numerical range and are blocked. The sweep has 1,501 solved speeds; very narrow resonance peaks can lie between them. The trailing RMS curve uses trapezoidal integration and interpolation of the stored time history; it is unweighted and is not compared with the peak comfort limit.

The animation magnifies dynamic displacement with a common automatic scale and omits static sag. It illustrates the solved mode, not the actual visible movement. Static compression assumes the entered dynamic stiffness also represents static stiffness; verify against the pad load–deflection curve.

Every comparison checks available travel for the four pad configurations and conservatively compares peak absolute dynamic support force with static supported weight for contact. The original feet are exempt from the entered pad travel. Flagged rows remain visible as linear extrapolations but are excluded from the lowest valid peak result; the displayed configuration also receives no comfort verdict outside these limits. If no row remains eligible, no preferred option is reported. At zero excitation all configurations tie and normalized peak ratios are undefined, shown as unavailable.